If you really want to see all of them, then look at the list on this site. It's pretty large !
Music Genre List - A complete list of music styles, types and ...
www.musicgenreslist.com/
What are the different genres of music?
Country, pop, classic rock, metal, rap... Country, rock, rap, and classical/orchestral for sure. Any others might be considered sub genres... Like rock there's classic, glam, metal, pop, punk, acid the list could go forever.
Zydeco. Bubblegum latin. Latino jazz. Hillbilly. Classic rock. Metal. Head bangers the list goes on