We enumerate three classes of non-medial quasigroups of order 243 = 3 up to isomorphism. There are 17004 non-medial trimedial quasigroups of order 243 (extending the work of Kepka, Bénéteau and Lacaze), 92 non-medial distributive quasigroups of order 243 (extending the work of Kepka and Němec), and 6 non-medial distributive Mendelsohn quasigroups of order 243 (extending the work of Donovan, Gri...

We study conjugacy closed loops (CC-loops) and power-associative CC-loops (PACC-loops). If Q is a PACC-loop with nucleus N , then Q/N is an abelian group of exponent 12; if in addition Q is finite, then |Q| is divisible by 16 or by 27. There are eight nonassociative PACC-loops of order 16, three of which are not extra loops. There are eight nonassociative PACC-loops of order 27, four of which h...