In the 1920s, what type of hat was associated with gangsters?

Fedoras were much associated with gangsters during the Prohibition era in the United States, a connection coinciding with the height of the hat's popularity between the 1920s and the early 1950s. In the second half of the 1950s, the fedora fell out of favor in a shift towards more informal clothing styles. In addition, well-known gangsters such as Al Capone, Charles Luciano, and Benjamin "Bugsy" Siegel used the fedora to create a "tough guy" image.

Source: Wikipedia