COLLOTON, Circuit Judge.

Counsel who presented argument on behalf of the petitioner was Chelsea R. McLean, of Minneapolis, MN. Also appearing on petitioner’s brief were Jaime Stilson and Virgil Owen Wiebe, both of Minneapolis, MN.

Counsel who presented argument on behalf of the respondent was Julia Tyler, USDOJ, OIL, Washington, DC.

Before SMITH, Chief Judge, MURPHY and COLLOTON, Circuit Judges.

COLLOTON, Circuit Judge.

Sandra Maritza Pena de Rivas ("Rivas") and her two minor children, Brittany Pamela Mejia-Pena and Maria Santana Mejia-Pena, petition for review of an order of the Board of Immigration Appeals. The Board denied their applications for asylum, withholding of removal, and relief under the Convention Against Torture. With respect to Rivas’s petition, we conclude that there was no legal error and that substantial evidence supports the Board’s decision, so we deny the petition. As to the children, however, the record shows that they presented independent applications, but the Board failed to decide the applications separately from their mother’s. We therefore grant the petitions filed by the children and remand their cases for further consideration.

I.

There is no challenge to the factual findings of the immigration judge, so we report the facts accordingly. Rivas and her daughters are citizens of El Salvador. In September 2013, Rivas witnessed a member of the El Salvadoran gang called the M-18 shoot her brother Carlos outside of her parents’ home after Carlos refused to join the gang. The gang member pointed his gun at Rivas and told her to be careful about what she said.

Rivas helped her brother inside the home, where Brittany and Maria witnessed his injuries. Rivas’s partner Juan then drove Carlos, Rivas, and Rivas’s mother to the hospital. To obtain medical care for Carlos, a police officer at the hospital required Rivas to answer questions about the shooting, and Rivas complied. After Carlos received medical treatment, Rivas and Juan took Carlos to see a relative who could offer additional medical care. Thereafter, Carlos went into hiding.

When members of the M-18 could not find Carlos, they began to question and threaten Juan and Rivas. Gang members stopped Juan on his way home to ask where to find Carlos, but Juan denied knowing Carlos’s whereabouts. Juan fled to Mexico in October 2013.

Three days after Juan left the country, two men from the M-18 approached Rivas in a store to ask where Carlos was hiding; Rivas told them she did not know. About a week later, female gang members visited Rivas at Juan’s grandparents’ home to inform her that Saul Pineda, the leader of the M-18 and Rivas’s relative, wanted to speak with her. The women escorted Rivas to a nearby field where the M-18 frequently beats or kills people, and handed Rivas a cellular phone so that she could talk to Pineda. Pineda asked for Carlos’s location, but Rivas refused to tell him. When Rivas did not disclose Carlos’s whereabouts, the women beat her and left her in the field.

Rivas and her children then fled to her sister’s house, located in a different city of El Salvador. Pineda called the house in March 2014 to speak to Rivas, this time offering her protection from the gang in exchange for her visiting him in jail and having sex with him. Rivas refused, left El Salvador with her children, and joined Juan in Mexico.

Rivas and her children entered the United States in December 2014. They were arrested at the border and detained pending deportation. In January 2015, the Department of Homeland Security commenced removal proceedings.

Rivas, Brittany, and Maria applied for asylum, withholding of removal, and relief under the Convention Against Torture ("CAT"). Although Rivas’s counsel initially represented that the children would file as derivative beneficiaries of Rivas’s application, all three aliens ultimately filed independent applications. Rivas also named her daughters as derivative beneficiaries on her application for asylum. An immigration judge conducted a two-day removal hearing. Rivas was present and testified; counsel waived appearances for the children.

The immigration judge found Rivas credible, but denied her application. The judge also denied the children’s applications. The judge reasoned that the children had not submitted independent applications and that they were merely derivative beneficiaries of Rivas’s application. On administrative appeal, the Board of Immigration Appeals found no error in the immigration judge’s denial of Rivas’s application. Although the Board noted that the two children had submitted independent applications, the Board declined to remand the children’s claims to the immigration judge for independent adjudication because the children’s applications were "each derivative of their mother’s claim." The Board therefore dismissed petitioners’ appeal.

Rivas and her children petition for review of the Board’s decision. We review the Board’s legal conclusions de novo , according deference where appropriate. See INS v. Aguirre-Aguirre , 526 U.S. 415, 424, 119 S.Ct. 1439, 143 L.Ed.2d 590 (1999). Administrative findings of fact are conclusive unless any reasonable adjudicator would be compelled to conclude to the contrary. 8 U.S.C. § 1252(b)(4)(B).

II.

Rivas first argues that the Board erred by denying her application for asylum. An applicant is eligible for asylum if she is unable or unwilling to return to her country "because of persecution or a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion." 8 U.S.C. § 1101(a)(42)(A) ; 8 C.F.R. § 1208.13(a). Rivas claims that she suffered persecution on account of her membership in three particular social groups: (1) women who are targeted to become "gang girlfriends," (2) witnesses to a crime who report the crime to the police, and (3) her family.

Under the Board’s analysis, whether an asserted group qualifies as a "particular social group" turns on whether the group is "(1) composed of members who share a common immutable characteristic, (2) defined with particularity, and (3) socially distinct within the society in question." Matter of M-E-V-G- , 26 I. & N. Dec. 227, 237 (BIA 2014). Rivas does not meaningfully challenge the validity of this standard, so we take it as a given in this appeal.

The Board concluded that the first two proposed social groups—targeted gang girlfriends and witnesses to a crime who report it to the police—lack particularity and are not socially distinct. We see no error in this conclusion. Particularity requires that the social group be "defined by characteristics that provide a clear benchmark for determining who falls within the group." Id. at 239. But Rivas’s proposed group of targeted gang girlfriends lacks such a benchmark. Membership in the group also depends entirely on whom the persecutor targets, and the size and composition of the group will therefore change based on the perspective of the persecutor. The proposed group is not "discrete with definable boundaries," but rather "amorphous, overbroad, diffuse, or subjective." Id.

Rivas also failed to prove that El Salvadoran society recognizes "targeted gang girlfriends" as a socially distinct group. Rivas relies on evidence suggesting that women, once targeted, are subjected to violence if they refuse to become a gang girlfriend. But "persecutory conduct alone cannot define the group." Id. at 242. "Whether a given particular social group is perceived as distinct by the society of which it is part depends on evidence that the society makes meaningful distinctions based on the common immutable characteristics defining the group." Gonzalez Cano v. Lynch , 809 F.3d 1056, 1059 (8th Cir. 2016) (internal quotation marks omitted); see M-E-V-G- , 26 I. & N. Dec. at 238. Rivas presented evidence about women who had already become gang girlfriends, but she did not establish that El Salvadoran society meaningfully distinguishes between women who are targeted to become gang girlfriends and women who are not.

Rivas argues that the Board’s rejection of "targeted gang girlfriends" as a social group is arbitrary or capricious because the government (through the United States Citizenship and Immigration Services) allegedly granted asylum to Juan’s sister based on her membership in the same group. But the record contains no explanation for why asylum was granted, so the Board had no basis to compare the claims made by Rivas and Juan’s sister. The Board considered only Rivas’s case and did not apply the statute arbitrarily.

The Board also did not err by concluding that Rivas’s second group—witnesses who report crimes to the authorities—is not cognizable. Rivas presented no evidence that this group is socially distinct or identifiable within El Salvadoran society. See Lopez-Morales v. Lynch , 674 F. App'x 594, 595 (8th Cir. 2017) (per curiam); cf. Ngugi v. Lynch , 826 F.3d 1132, 1138 (8th Cir. 2016).

As for Rivas’s third proposed group, although the Board has acknowledged that "members of an immediate family may constitute a particular social group," Matter of L-E-A- , 27 I. & N. Dec. 40, 42 (BIA 2017), there must be a nexus between the persecution suffered and the applicant’s membership in that social group. See Martinez-Galarza v. Holder , 782 F.3d 990, 994 (8th Cir. 2015). An applicant therefore will not be eligible for asylum unless she can demonstrate that her membership in the particular social group is "at least one central reason" for the persecution. 8 U.S.C. § 1158(b)(1)(B)(i).

The record does not compel the conclusion that Rivas was persecuted on account of her membership in a family consisting of Carlos, Juan, and Juan’s relatives. Rivas testified that gang members sought her out because she had been with Carlos when he was shot and witnessed what had happened to him. She contends that her relationship with her brother was the only reason she witnessed the shooting in the first place, so the gang’s persecution of her was directly tied to her membership in her family. But "the fact that a persecutor targets a family member simply as a means to an end is not, by itself, sufficient to establish a claim." Matter of L-E-A- , 27 I. & N. Dec. at 45 ; see Ramirez-Mejia v. Lynch , 794 F.3d 485, 493 (5th Cir. 2015). The evidence established only that gang members persecuted Rivas because she was a witness to her brother’s shooting, was one of the last people to see him before he went into hiding, and had information concerning his whereabouts. The record does not compel a conclusion that family relationship—independent of these other factors—was a central reason for persecution.

Rivas also admitted that several members of her immediate family—her parents, oldest daughter, siblings, and uncles—remain in El Salvador unharmed, despite their familial relationship with Carlos. That Rivas’s other family members have not suffered persecution at the hands of the M-18 further supports the Board’s conclusion that Rivas was persecuted on account of her membership in the family. See Aguinada-Lopez v. Lynch , 825 F.3d 407, 409 (8th Cir. 2016).

For these reasons, we conclude that the Board permissibly denied Rivas’s claim for asylum. It follows that Rivas cannot meet the higher standard of proof for withholding of removal. Ngengwe v. Mukasey , 543 F.3d 1029, 1033 (8th Cir. 2008). Finally, Rivas argues that the Board erred in denying her relief under the Convention Against Torture. To qualify for CAT relief, an alien must prove that "it is more likely than not that he or she would be tortured if removed to the proposed country of removal." 8 C.F.R. § 1208.16(c)(2). She must show that torture would be inflicted "by or at the instigation of or with the consent or acquiescence of a public official or other person acting in an official capacity." 8 C.F.R. § 1208.18(a)(1). " ‘Acquiescence’ requires that the public official be aware of the activity and ‘thereafter breach his or her legal responsibility to prevent such activity.’ " Aguinada-Lopez , 825 F.3d at 409-10 (8th Cir. 2016) (quoting § 1208.18(a)(7) ).

The Board did not err by rejecting Rivas’s CAT claim. Rivas cites examples of police corruption in El Salvador as evidence of acquiescence, but the record also shows that El Salvador has taken steps to abate gang violence. "Certainly, El Salvador has struggled to protect against gang violence, but it has not acquiesced to gang violence." Id. at 410. Accordingly, we deny Rivas’s petition for review.

III.

Brittany and Maria petition for review of the Board’s dismissal of their appeals. They argue that the Board failed to conduct an individualized assessment of their applications. The government contends, however, that the children never distinguished their claims from their mother’s, because the children relied largely on the same facts as Rivas, and because petitioners’ counsel focused on Rivas’s claims during closing argument at the removal hearing.

According to its own regulations, the Board must "resolve the questions before it." 8 C.F.R. § 1003.1(d)(1). If the Board overlooks a claim that an alien properly presented for review, then it fails to discharge its obligations under its own regulations, and a remand for further proceedings is appropriate. See Alemu v. Mukasey , 509 F.3d 907, 909 (8th Cir. 2007) ; Kone v. Holder , 620 F.3d 760, 764 (7th Cir. 2010). The agency should provide an adequate explanation in the first instance; the court will not resolve unaddressed claims before the Board has an opportunity to decide them. See Gonzales v. Thomas , 547 U.S. 183, 186, 126 S.Ct. 1613, 164 L.Ed.2d 358 (2006) (per curiam); INS v. Orlando Ventura , 537 U.S. 12, 16, 123 S.Ct. 353, 154 L.Ed.2d 272 (2002) (per curiam).

The record here shows that while the children did pursue Rivas’s claims derivatively, they also raised at least one unique basis for granting relief and requested independent evaluation of their claims. The children’s applications alleged a fear of future persecution based on their membership in a unique family group composed of their parents and their uncle. They addressed this family group in their pre-hearing brief. When the immigration judge mistakenly concluded that the children had not filed separate applications, the children argued to the Board that the judge failed to adjudicate their independent claims and requested that the Board remand the case to the immigration judge for proper consideration. These arguments before the immigration judge and the Board were sufficient to present a separate claim for relief on behalf of the children.

Although the children were granted a full hearing before the immigration judge and an opportunity to appeal to the Board, the immigration judge mistakenly concluded that the children had not submitted independent applications, so the judge did not analyze or reach a decision on their independent claims. The Board acknowledged the children’s independent applications, but merely rejected their claims as "derivative of their mother’s claim." The Board, too, overlooked that the children pursued an independent ground for relief and failed to conduct an individualized assessment of the children’s independent claims.

The government urges that the Board properly concluded that an individualized assessment of the children’s claims was not necessary because their claims failed for the same reasons that Rivas’s claims failed. But the Board did not provide that explanation in its decision, and it is not for us to supply the Board’s reasoning in the first instance. See SEC v. Chenery Corp. , 318 U.S. 80, 87, 63 S.Ct. 454, 87 L.Ed. 626 (1943).

The record, moreover, was not developed on the children’s independent claims. The immigration judge made no findings on whether the children had suffered persecution by the M-18 or whether they had a well-founded fear of future persecution based on their membership in a family consisting of Rivas, Juan, and Carlos. The Board could not have relied on the immigration judge’s finding that Rivas’s fear of persecution lacked a nexus with her membership in her family, because that finding was specific to Rivas and the circumstances under which gang members pursued her for information about Carlos. The children raised a different theory—namely, that they feared persecution by the gang, on account of their membership in the family, as a means of retaliating against their mother. We therefore conclude that the Board failed to resolve all of the questions before it, and the case must be remanded for further proceedings on the applications of the children. We express no view on the merits of those applications.

* * *

Rivas’s petition for review is denied, but the petitions of her children, Brittany Pamela Mejia-Pena and Maria Santana Mejia-Pena, are granted. The case is remanded for further proceedings on the applications of the children.