Found this link through a women's writing group that I'm part of. The UN is running an ad campaign to highlight misogyny throughout the world. It's pretty shocking!
Basically if you google 'women should / cannot / shouldn't...' etc the autocomplete results are appalling. Google suggests whatever the most popular searches are to match the terms you type in and for phrases like 'women should' it has 'women should shut up' 'women should stay at home' and so on. This shows that these phrases are popular search terms.
I was skeptical at first but I've checked myself for 'men should' and 'men cannot' and the results are much more innocuous, things like 'men should always pray' or ironically 'men cannot be feminists'. Pretty awful to see such a dire contrast between what people search for related to men and what they search for related to women.