I know about some (many?) of them. Let me try to summarize:
1. whitecels (mayocels) vs ethnicels: because ethnicels often accuse whitecels (mayocels) of having it easy due to that JBW (Just be whte) theory (which is not a very right theory).
2. oldcels vs. youngcels: because oldcels sometimes claim youngcels are not fully confirmed as incels, since they may outgrow inceldom or ascend later. (until you're young the chances are more, isn't it?)
3. femcels vs. mancels: because mancels claim female inceldom is a myth due to juggernaut law (and mostly they're right, aren't they?)
4. truecels vs. nearcels: because truecels accuse nearcels of being fakecels (and they got some point, right?)
5. mentalcels vs. uglycels: because uglycels accuse mentalcels of being fakecels or nearcels because it's easier to do with the psychology than with the looks. (or another reason).
6. shortcels vs. tallcels: because shortcels call tallcels "fakecels"; tallcels in turn get mad at shortcels because they realize that JBT (just be tall) isn't working everytime.
7. fatalist determinism ("just LDAR bro!") vs. non-fatalist determinism (remains optimistic for sanity and to ascend) vs. positive optimism (every incel may ascend) etc.
8. Religious incels vs. nonreligious incels.
9. Pacifists vs. upriser, rioting people.
10. social engineering vs. biological essentialism within the context of female sexual preference toward betas
11. sadistic, suicidal incels vs. normal incels who want to help people like them or at least not to harm anybody.
12. patriarchalcels vs. non-patriarchal/ feminists vs. anti-feminists.
13. some believe men should not be attracted to teenage women; those who disagree with them call them "agecucks".
14. blackpillers vs. the rest (metapillers, redpillers, whitepillers, purplepillers, etc.)