Jorge Rodriguez Galvan is a native and citizen of Mexico who conceded that he was removable pursuant to 8 U.S.C. § 1182(a)(6)(A)(i) as an illegal alien who had entered the United States without being admitted or paroled. He unsuccessfully sought various forms of relief from removal. Pertinent here are the denials of his applications for cancellation of removal, withholding of removal based on his membership in a particular social group (“PSG”), and relief under the Convention Against Torture (“CAT”). Rodriguez Gal-van appealed the denial of his requests for relief, but the Board of Immigration Appeals (“BIA”) dismissed the appeal. Rodriguez Galvan now petitions for review of that order.
Rodriguez Galvan contends that the immigration judge (“IJ”) and the BIA erred in determining that cancellation of removal was not warranted under 8 U.S.C. § 1229b(b) because he had not demonstrated that his removal “would result in exceptional and extremely unusual hardship to” his United States citizen wife. Rodriguez Galvan does not assert any legal or constitutional error in this regard but disagrees with the decisions of the IJ and the BIA that he did not show that his wife would suffer the requisite level of hardship to warrant relief. We lack jurisdiction to review the hardship determination on which the denial of relief was based, and that portion of the petition *206challenging the denial of cancellation of removal is dismissed. See Rueda v. Ashcroft, 380 F.3d 831, 831 (5th Cir.2004).
Regarding his application for withholding of removal, Rodriguez Galvan asserted a fear that, upon being returned to Mexico, he would be persecuted by the Mexican drug cartel Los Zetas based on his membership in a PSG made up of family members who are opposed to members of the cartel. Rodriguez Galvan and his wife testified that two of her cousins were tortured and killed by the cartel in Mexico because they refused to do its bidding. Rodriguez Galvan thus claims that the BIA erred in determining that there was no indication that any of his direct family had been targeted for any reason. He also maintains that, in light of the murders of his wife’s cousins, he had clearly shown that his life would be in grave danger in Mexico. He testified, however, that his parents and two of his siblings had been living peacefully and undisturbed by the cartel in Mexico since 2003. Moreover, he makes no argument at all with respect to the determination that his purported PSG was too broad and amorphous to qualify as a PSG for purposes of withholding of removal. Because the BIA’s decision is supported by substantial evidence, see Zhang v. Gonzales, 432 F.3d 339, 344 (5th Cir.2005), we deny that portion of the petition for review challenging the denial of withholding of removal.
Rodriguez Galvan has failed to brief any challenge to the determination by the IJ and the BIA that he was not entitled to relief under the CAT. Thus, he has abandoned any challenge to that determination. See Soadjede v. Ashcroft, 324 F.3d 830, 833 (5th Cir.2003).
The petition for review is DISMISSED in part and DENIED in part.