This The Man in the Iron Mask photo contains
boater, leghorn, panama, panama hat, sailor, skimmer, straw hat, fedora, felt hat, homburg, stetson, trilby, porkpie, and porkpie hat.
There might also be
dress hat, high hat, opera hat, silk hat, stovepipe, top hat, topper, beaver, sombrero, pith hat, pith helmet, sun helmet, topee, and topi.