If a school is Div 1, it is division 1 for all sports; it could opt to host a club team in a sport, and many schools do that but a Div 1 school cannot play any sport in D3… To be a Div 1 school, the school has to host a certain number of sports for men/women (I think it is 10 each). If a school is Div 3, the school can have one men’s/one women’s team ‘play up’. Hopkins is Div 3 but plays up in lacrosse, and is the B1G 10 for both teams. Colorado College plays D1 hockey for men, D1 soccer for women. A tiny school like Presbyterian (~1200 students) can be Div 1 while a fairly big school like UCSC 916,000+) can be D3. The size of the school doesn’t determine which division they play in.