BOSTON (CN) – Crying foul over steps Harvard University has taken to discourage participation in single-gender social clubs, a collection of fraternities and sororities filed suit Monday in both state and federal court.

“A Harvard undergraduate could join the American Nazi Party, or could create an off-campus undergraduate chapter of the Ku Klux Klan, without running afoul of the Sanctions Policy or any other Harvard student-conduct policy,” says the federal complaint, led by the sorority Kappa Alpha Theta. “Those groups may be heinous, but they are co-ed, so under Harvard’s rules, its students may belong without any threat of sanction.”

While Theta filed its suit in U.S. District Court for the District of Massachusetts, the sorority Alpha Phi is lead plaintiff in the suit filed in Suffolk County Superior Court.

Theta is represented by the Washington firm Arnold & Porter, while Alpha Phi is represented by Boston-based attorneys at Zalkind, Duncan & Bernstein.

Representatives for Harvard did not respond to an email seeking comment, but the complaints say that sororities are bearing the brunt of an attempt by the the administration to solve three of its biggest headaches — alcohol use, campus sexual assault and classism — in one misguided swoop.

“Through a new student-conduct policy that punishes undergraduates who join single-sex social organizations, Harvard succeeded, perversely, in eliminating nearly every women’s social organization previously available to female students at Harvard. In response to Harvard’s Sanctions Policy, nearly all of Harvard undergraduates’ all-female social clubs — their once vibrant sororities, their women’s final clubs, and The Seneca, whose mission is to create opportunities, resources, and sustainable networks for women in social, educational, and professional environments— closed their doors or renounced their proud status as women’s social organizations and became co-ed social organizations.”

Under the new rules, any student that joins a single-gender organization is barred from leadership positions in on-campus student organizations and athletic teams. They are also ineligible for post-graduate fellowships, such as Rhodes, Marshall and Mitchell scholarships.

“Single-sex all-female social organizations were virtually eliminated in 2018 after the university, in an initiative led by Rakesh Khurana as dean of Harvard College, conducted a multiyear campaign to eliminate single-sex groups from campus life,” Alpha Phi’s complaint states.

In the federal complaint, the fraternal organizations Kappa Kappa Gamma, Sigma Chi and Sigma Alpha Epsilon joined as co-plaintiffs. Mass Gamma, an endangered chapter of SAE, is also a co-plaintiff.

Alpha Phi Iota Tau and the Delta Gamma Fraternity Management Corp. are co-plaintiffs in the state court suit.