Conversation so far:
What were Hohokam cultural divisions?
Designating culture groups, such as the Hohokam, tends to create an image of group territories separated by clear-cut boundaries, like modern nation states.
What were some of the cultural names for prehistoric peoples?
Cultural labels such as Hohokam, Ancient Pueblo (Anasazi), Mogollon, or Patayan are used by archaeologists to define cultural differences among prehistoric peoples.
What were the different cultural divisions in the southwest?
Hohokam cultural divisions have three specfic limitations; archaeological research, style, and culture group.

Question: What division did they belong to?
Self-contained rewrite: What division did the Hohokam belong to?