Several fraternities and sororities are suing Harvard University over a 2016 rule that discourages students from joining single-gender clubs.

Two fraternities and two sororities filed a lawsuit against Harvard in Boston's federal court on Monday, while another sorority sued the school in Massachusetts state court.

The lawsuits say Harvard's rule discriminates against students based on their sex and spreads negative stereotypes about students who join all-male or all-female groups. They're the first lawsuits challenging the rule.

Harvard officials did not immediately provide comment.

The rule says students in single-gender social clubs can't lead campus organizations or sports teams, and the school won't endorse them for fellowships.

It was meant to curb secretive all-male groups that the school previously accused of having misogynistic attitudes, but it also prompted some fraternities and sororities to close or go co-ed.