6 problems

Completeness conjecture. There are no other nonassociative Moufang loops of order $64$.

Lower-bound conjecture. The order of $C$ satisfies

Let $p>3$ be a prime, and consider right Bol loops of order $3p$, with two such loops identified when they are isotopic. Enumeration claim. The number of right Bol loops of order…

Exhaustiveness conjecture. No additional nonassociative Moufang loops of order $64$ exist; equivalently, the construction gives all nonassociative Moufang loops of order $64$.

Conjecture on the isomorphism classes. There are precisely three isomorphism classes of such automorphic loops.

Classification conjecture. The loops $Q(A)$ and $Q(B)$ are isomorphic if and only if $A$ and $B$ are of the same type.