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You sure? There are 22 PLL cases with no parity (included the solved case), yes, but that is because there are a lot of identicals theough symmetry thanks to AUF. I'm not entirely sure it's the same with parity.

For example, see "corners only" PLLs: without parity, there are 4 of them (Aa, Ab, E, H), but with parity, there are 5 at least (UFL-UFR swap, UFL-UBR swap, Oa swap, Ob swap, zig-zag)
 
You sure? There are 22 PLL cases with no parity (included the solved case), yes, but that is because there are a lot of identicals theough symmetry thanks to AUF. I'm not entirely sure it's the same with parity.

For example, see "corners only" PLLs: without parity, there are 4 of them (Aa, Ab, E, X), but with parity, there are 5 at least (UFL-UFR swap, UFL-UBR swap, Oa swap, Ob swap, zig-zag)
But if you include solved as a CPLL, then that's 5 and 5. Same with EPLLs: without parity there's solved, Ua, Ub, H, Z, and with there's adj, opp, Oa, Ob, zig-zag. I was thinking something similar to what you're thinking, but actually after what you've said I think there are probably just 22.
 
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