DITKOFF, J.

The case was submitted on briefs.

Ethan C. Stiles, Pembroke, for the defendant.

Timothy J. Cruz, District Attorney, & Audrey Anderson, Assistant District Attorney, for the Commonwealth.

Present: Wolohojian, Maldonado, & Ditkoff, JJ.

DITKOFF, J. The defendant appeals from his convictions, after a Superior Court jury trial, of two counts of rape of a child, G. L. c. 265, § 23, two counts of incest, G. L. c. 272, § 17, one count of indecent assault and battery on a child, G. L. c. 265, § 13B, and two counts of open and gross lewdness, G. L. c. 272, § 16. The Commonwealth concedes that there was insufficient evidence of open and gross lewdness and asks us to enter convictions on the lesser-included offenses of indecent exposure, G. L. c. 272, § 53. Concluding that indecent exposure is a lesser-included offense of open and gross lewdness, but that there was insufficient evidence of that offense as well, we reverse the convictions of open and gross lewdness and remand for the entry of required findings of not guilty. Further concluding that the defendant was not entitled to a lesser-included offense instruction on the counts of rape of a child and that there was no prejudice to the defendant from the admission of prior bad act evidence, we affirm the other convictions.

1. Background. "Because the defendant challenges the sufficiency of the evidence, we recite the facts the jury could have found in the light most favorable to the Commonwealth." Commonwealth v. Salazar, 481 Mass. 105, 107, 112 N.E.3d 781 (2018). The defendant is the father of three girls. The defendant routinely woke up his eldest daughter by coming into her room completely naked. When the oldest daughter was eleven or twelve, she had a bandage on her upper right thigh. When the defendant was changing the bandage, "he had one hand on the bandage and stuck the other hand up [her] vagina." He "wiggled" his fingers around inside her.

While in elementary school, the middle daughter took gymnastics. Usually by the time the middle daughter returned from her gymnastics practices, everybody but the defendant and the middle daughter would be asleep. The defendant and the middle daughter routinely would massage each other's backs. The defendant "would put his hands further down [her] back, until his hands were ... around ... [her] vagina." He placed one hand "between [her] labia." His hand was "[m]ore on the inside." This happened so often that it became "routine," and the middle daughter came to think it was normal. One time during these massage sessions, the defendant flipped over so that the middle daughter's hand was on his penis. Her hand was on his penis for approximately forty-five seconds and then she felt something wet come from his penis.

Most mornings, the defendant masturbated in his bedroom with the door open, and the eldest and middle daughters observed his penis in his hand in a mirror. This happened both before and after the rape of the eldest daughter.

When the eldest daughter was in middle school, her best friend often came over to her house both before and after school. The eldest daughter's best friend saw the defendant in a state of undress three times. Once, he was standing by the washer and dryer and had an open towel. He said, "Oh, sorry." Another time, he was naked in his bedroom getting dressed and made eye contact with the friend. The third time, she walked into the living room while he was masturbating, and he made eye contact with her.

The defendant was charged with nine crimes. He was charged with two counts each of rape of a child and incest, one relating to the eldest daughter, and one relating to the middle daughter. The jury convicted him of all four of these crimes. He was charged with two counts of indecent assault and battery on a child, both relating to the middle daughter. The jury convicted him of the count charging him with touching her vagina but acquitted him of the count charging him with making her touch his penis. He was charged with two counts of open and gross lewdness, one relating to each victim's seeing him masturbating. The jury convicted him of both counts. Finally, he was charged with lewd and lascivious behavior, G. L. c. 272, § 53, relating to his exposing himself to the eldest daughter's best friend while masturbating. The jury acquitted him of that charge. This appeal followed.

2. Lesser-included offense of open and gross lewdness. a. Sufficiency of the evidence of open and gross lewdness. The defendant argues, and the Commonwealth agrees, that there was insufficient evidence of open and gross lewdness. In addition to the four elements described infra, the fifth element of that crime is that the defendant's conduct "did, in fact, produce ‘alarm or shock’ in one or more persons." Commonwealth v. Pereira, 82 Mass. App. Ct. 344, 346, 973 N.E.2d 679 (2012). "This requires evidence of strong negative emotions -- a subjective inquiry -- most commonly corroborated by an immediate physical response." Commonwealth v. Maguire, 476 Mass. 156, 159, 65 N.E.3d 1160 (2017). See Commonwealth v. Militello, 66 Mass. App. Ct. 325, 334, 848 N.E.2d 406 (2006) (nervousness and discomfort not enough).

The eldest daughter described the significant emotional damage that the rape caused her, but she was neither asked for nor described any reaction to observing the defendant's masturbation. Indeed, she merely got up and got ready for school. Similarly, the middle daughter testified that it was "upsetting" that the defendant had to move out, and that she "wish[ed] he hadn't done the things he's done, 'cause then I could have him in my life," but was neither asked for nor described any reaction to observing the defendant's masturbation. Having fulfilled our duty of independently determining whether there was error, we agree with the Commonwealth's concession that there was insufficient evidence of open and gross lewdness. See Commonwealth v. Tiernan, 96 Mass. App. Ct. 588, 589 n.2, 137 N.E.3d 426 (2019).

The Commonwealth asks us to enter convictions on these counts for indecent exposure. When there is insufficient evidence to support a conviction, but there is sufficient evidence of a lesser-included offense of the crime of conviction, we vacate the conviction and "remand for entry of a conviction of the lesser included offense and for resentencing." Commonwealth v. Sudler, 94 Mass. App. Ct. 150, 156, 112 N.E.3d 828 (2018). Accord Commonwealth v. Garrett, 473 Mass. 257, 266-267, 41 N.E.3d 28 (2015). Accordingly, we determine first whether indecent exposure is a lesser-included offense of open and gross lewdness and second whether there is sufficient evidence of indecent exposure.

b. Comparison of open and gross lewdness to indecent exposure. "[A] lesser included offense is one whose elements are a subset of the elements of the charged offense." Commonwealth v. Labadie, 467 Mass. 81, 86, 3 N.E.3d 1093, cert. denied, 574 U.S. 902, 135 S.Ct. 257, 190 L.Ed.2d 191 (2014), quoting Commonwealth v. Porro, 458 Mass. 526, 531, 939 N.E.2d 1157 (2010). "The test is whether, ‘[i]n order to convict [of the greater offense], all the elements of [the lesser offense] must be found, plus an additional aggravating factor.’ " Commonwealth v. Kelly, 470 Mass. 682, 703, 25 N.E.3d 288 (2015), quoting Commonwealth v. Schuchardt, 408 Mass. 347, 351, 557 N.E.2d 1380 (1990).

The elements of open and gross lewdness are "[1] That the defendant exposed his [or her genitals, buttocks, or female breasts] to one or more persons; [2] That the defendant did so intentionally; [3] That the defendant did so ‘openly’^{[ ]} ...; [4] That the defendant's act was done in such a way as would alarm or shock a reasonable person; and [5] That at least one person was alarmed or shocked." Instruction 7.400 of the Criminal Model Jury Instructions for Use in the District Court (May 2017). Accord Commonwealth v. Taranovsky, 93 Mass. App. Ct. 399, 400 n.1, 105 N.E.3d 266 (2018). According to the model instruction, the elements of indecent exposure are "[1] That the defendant exposed his [or her genitals] to one or more persons; [2] That the defendant did so intentionally; and [3] That one or more persons were offended by the defendant's thus exposing himself [or herself]." Instruction 7.340 of the Criminal Model Jury Instructions for Use in the District Court (2009). Accord Commonwealth v. Kennedy, 478 Mass. 804, 811-812, 90 N.E.3d 722 (2018). The Supreme Judicial Court has not yet determined whether there is a fourth element to indecent exposure, that the exposure would offend a reasonable person. Cf. Maguire, 476 Mass. at 159, 65 N.E.3d 1160 (for open and gross lewdness, declaring that, "[i]n future cases, ... it will be incumbent on the Commonwealth to demonstrate not only subjective ‘shock’ or ‘alarm’ on the part of a victim, but also that the victim's reaction was objectively reasonable"). A mechanical comparison of the elements of the two crimes yields the following:

Open and gross lewdness Indecent exposure exposure of genitalia, exposure of genitalia buttocks, or female breasts intentional intentional openly done in a manner that (would offend a reasonable would shock or alarm a person)⁵ reasonable person at least one person was at least one person was shocked or alarmed offended

[Editor's Note: The preceding image contains the reference for footnote ].

See Kennedy, supra ; Taranovsky, supra.

At first blush, this comparison suggests that indecent exposure is not a lesser-included offense of open and gross lewdness, because of the mismatch in the first and fifth elements. Closer examination reveals that this mismatch is illusory.

Concerning the fifth element, it is important to understand that shock or alarm for open and gross lewdness means an offensive shock or alarm. For example, if a patient exposed his genitalia to a doctor to reveal an advanced cancerous growth, the doctor very well may be alarmed. But that sort of nonoffensive alarm is not the kind of shock or alarm that open and gross lewdness involves. See, e.g., Pereira, 82 Mass. App. Ct. at 346-348, 973 N.E.2d 679 (witness angry and disgusted by defendant masturbating in car); Commonwealth v. Melo, 95 Mass. App. Ct. 257, 258-260, 123 N.E.3d 791 (2019) (witnesses shocked and frantic when defendant pulled down pants and danced in donut shop parking lot, exposing his buttocks). Cf. Commonwealth v. Ora, 451 Mass. 125, 128, 883 N.E.2d 1217 (2008) ("the central purpose of G. L. c. 272, § 16 [open and gross lewdness], [is] one of preventing fright and intimidation"). Once this is understood, it is evident that the shock or alarm necessary for open and gross lewdness is simply a more pronounced form of the offense required to show indecent exposure. Thus, shock or alarm for purposes of open and gross lewdness is a subset of offense. See Ora, supra at 127, 883 N.E.2d 1217 (open and gross lewdness "requires a substantially more serious and negative impact" than indecent exposure).

Concerning the first element, the crime of open and gross lewdness historically required the exposure of genitalia, just like the crime of indecent exposure. See Commonwealth v. Quinn, 439 Mass. 492, 497, 789 N.E.2d 138 (2003). Accord Commonwealth v. Arthur, 420 Mass. 535, 541, 650 N.E.2d 787 (1995) ("Cases of conduct ... brought pursuant to the provisions of G. L. c. 272, § 16, invariably have involved exposure of the genitalia"). In 2003, however, the Supreme Judicial Court expanded the crime of open and gross lewdness to include also the exposure of buttocks or female breasts, prospectively only. Quinn, supra at 501, 789 N.E.2d 138.

It is well-settled that, where a crime may be committed under different theories with different elements, another crime may be a lesser-included offense of it under one theory, but not others. See Commonwealth v. Thompson, 89 Mass. App. Ct. 456, 463-464, 50 N.E.3d 845 (2016). Accord Commonwealth v. Roderiques, 462 Mass. 415, 421, 968 N.E.2d 908 (2012). Thus, where (as here) the crime of open and gross lewdness is prosecuted with the element of exposure of genitalia, indecent exposure is a lesser-included offense. See Maguire, 476 Mass. at 162, 65 N.E.3d 1160. In the case in which it is prosecuted instead with the element of exposure of buttocks or female breasts, indecent exposure is not a lesser-included offense.

c. Sufficiency of the evidence of indecent exposure. In this case, the sufficiency issue turns on the element of the defendant's conduct having given offense to at least one person. It is not correct to instruct a jury, as the trial judge did here, that the lesser-included offense of indecent exposure is proven if the Commonwealth proves the first three elements of open and gross lewdness but fails to prove the fourth (done in such a way as to shock or alarm a reasonable person) or fifth (at least one person was shocked or alarmed) elements. Rather, the Commonwealth must still prove that at least one person was offended by the exposure (and, possibly, that the exposure was objectively offensive). See Commonwealth v. St. Louis, 473 Mass. 350, 364, 42 N.E.3d 601 (2015).

Offense for purposes of indecent exposure means "displeasure, anger or resentment." Kennedy, 478 Mass. at 812, 90 N.E.3d 722, quoting St. Louis, 473 Mass. at 364, 42 N.E.3d 601. See Commonwealth v. Swan, 73 Mass. App. Ct. 258, 262, 897 N.E.2d 1015 (2008) (testimony that victim "felt embarrassed and threatened" enough to show offense). It is considerably easier to prove offense than it is to prove the kind of offensive shock or alarm required for open and gross lewdness. See Commonwealth v. Kessler, 442 Mass. 770, 774, 817 N.E.2d 711 (2004) ("That the exposure be ‘offensive to one or more persons’ is an element required for indecent exposure, ... but an open and gross lewdness charge requires more"). It may be proved circumstantially. See St. Louis, supra at 365, 42 N.E.3d 601 (although victim did not testify she was offended, sufficient evidence of offense where victim said no and expressed "her desire to detach herself from the situation"). It must, however, be proved to establish the crime of indecent exposure.

Here, the Commonwealth failed to elicit any reaction whatsoever on the parts of the daughters to the defendant's masturbation. The eldest daughter described the emotional damage she suffered as resulting from "having my dad touch me," but described no reaction to witnessing the masturbation. The middle daughter similarly described no reaction to witnessing the masturbation. The evidence was further devoid of any circumstantial evidence that would allow a jury to find that either daughter was offended by the defendant's masturbation. Accordingly, the Commonwealth failed to establish that either daughter was offended. For this reason, the Commonwealth failed to produce sufficient evidence of the crime of indecent exposure.

3. Lesser-included offense of rape of a child. It is well-settled that indecent assault and battery on a child is a lesser-included offense of rape of a child. See Commonwealth v. Suero, 465 Mass. 215, 219-220, 987 N.E.2d 1199 (2013) ; Commonwealth v. Prado, 94 Mass. App. Ct. 253, 260, 113 N.E.3d 365 (2018). The question, then, is whether the trial judge here properly declined the defendant's request that he instruct the jury on this lesser-included offense.

"A lesser included offense instruction should be given where ‘the evidence at trial presents "a rational basis for acquitting the defendant of the crime charged and convicting him of the lesser included offense." ’ " Commonwealth v. Rios, 96 Mass. App. Ct. 463, 476, 135 N.E.3d 1056 (2019), quoting Commonwealth v. Donlan, 436 Mass. 329, 335, 764 N.E.2d 800 (2002). "In making this determination, we draw all reasonable inferences from the evidence in favor" of the defense. Commonwealth v. Dyous, 436 Mass. 719, 731, 767 N.E.2d 51 (2002). Nonetheless, "even when evidence is introduced that would justify conviction for a lesser included offense, the defendant is not entitled to an instruction thereupon unless the proof on the ‘elements differentiating the two crimes is sufficiently in dispute so that the jury may consistently find the defendant innocent of the greater and guilty of the lesser included offense.’ " Donlan, supra, quoting Commonwealth v. Souza, 428 Mass. 478, 494, 702 N.E.2d 1167 (1998).

The eldest daughter testified that the defendant "had one hand on the bandage and stuck the other hand up [her] vagina," and "wiggled" his fingers around inside her. Thus, the only sexual contact described was penetrative. See Commonwealth v. Olmande, 84 Mass. App. Ct. 231, 239, 995 N.E.2d 797 (2013).

The middle daughter testified that the defendant placed one hand "between [her] labia." Her description that his hand was "[m]ore on the inside" might well create some ambiguity whether he fully entered her vagina. The Commonwealth, however, had no duty to prove that the defendant's fingers entered the victim's vagina. "Intrusion into the vagina itself is not required to make out the wrongful penetration. Touching by the male of the vulva or labia ... is intrusion enough." Donlan, 436 Mass. at 336, 764 N.E.2d 800, quoting Commonwealth v. Baldwin, 24 Mass. App. Ct. 200, 204-205, 509 N.E.2d 4 (1987), overruled on other grounds, Commonwealth v. Pagan, 445 Mass. 161, 170, 834 N.E.2d 240 (2005). There was, therefore, no version of the sexual assault in evidence that did not include touching of the labia. See Olmande, 84 Mass. App. Ct. at 239, 995 N.E.2d 797.

To be sure, the jury had the right to disbelieve any portion of the evidence, and could have selectively disbelieved portions of the victims' testimony of penetration. "[T]he mere possibility that the jury might not credit a portion of the Commonwealth's evidence," however, is not enough to entitle the defendant to an instruction on a lesser-included offense. Donlan, 436 Mass. at 337, 764 N.E.2d 800.

4. Prior bad act evidence. The victims' grandmother described an incident when the eldest daughter was six years old. The grandmother was staying with the entire family in a one-room cottage on a vacation in New Hampshire. In the morning, she observed the defendant's semi-erect penis protruding from the blankets of his bed. She testified that she "wasn't sure if it was an intentional act."

"Evidence of prior bad acts is generally inadmissible to show a defendant's propensity to commit a crime." Commonwealth v. Don, 483 Mass. 697, 713, 136 N.E.3d 680 (2019). Nonetheless, "[s]uch evidence may be admitted ‘to show a common scheme or course of conduct, a pattern of operation, absence of accident or mistake, intent, or motive.’ " Commonwealth v. Beaulieu, 90 Mass. App. Ct. 773, 780, 68 N.E.3d 644 (2016), quoting Commonwealth v. Julien, 59 Mass. App. Ct. 679, 686, 797 N.E.2d 470 (2003). "[E]ven if the evidence is relevant to one of these other purposes, the evidence will not be admitted if its probative value is outweighed by the risk of unfair prejudice to the defendant." Commonwealth v. Bryant, 482 Mass. 731, 734, 128 N.E.3d 40 (2019). "These matters are ‘entrusted to the trial judge's broad discretion and are not disturbed absent palpable error.’ " Commonwealth v. Childs, 94 Mass. App. Ct. 67, 71, 110 N.E.3d 477 (2018), quoting Commonwealth v. Keown, 478 Mass. 232, 242, 84 N.E.3d 820 (2017), cert. denied, ––– U.S. ––––, 138 S. Ct. 1038, 200 L.Ed.2d 292 (2018).

Here, the defense to the lewd and lascivious behavior charge was that the defendant's exposures to the best friend were accidental. For that reason, had the grandmother's testimony truly sketched out a prior bad act, it might have been admissible to show an absence of accident or mistake as to that charge. See Commonwealth v. Mazariego, 474 Mass. 42, 56, 47 N.E.3d 420 (2016) ; Childs, 94 Mass. App. Ct. at 73, 110 N.E.3d 477. As it was, the grandmother described something that even she thought could be an accident, and thus was entirely consistent with the defense. The prosecutor ignored this evidence altogether in her closing argument. Accordingly, even if there was error, it was not prejudicial "due to the ‘scant attention’ given to the evidence at trial" Don, 483 Mass. at 715, 136 N.E.3d 680, quoting Commonwealth v. McGee, 467 Mass. 141, 158, 4 N.E.3d 256 (2014).

5. Conclusion. On the two indictments charging the defendant with open and gross lewdness, the judgments are reversed, the verdicts are set aside, and judgments shall enter for the defendant. On the indictments charging the defendant with rape of a child, incest, and indecent assault and battery on a child, the verdicts are affirmed, the sentences are vacated, and the case is remanded to the Superior Court for resentencing.

So ordered.