Abstract
We show that if G ≤ S A is a permutation group on a finite set A satisfying |A| ≥ 3, then the set of G-closed clones on A that contain all constant operations is finite iff G = S A, A A, AGL(1,5) (|A| = 5), PSL(2,5) (|A| = 6), PGL(2,5) (|A| = 6), PGL(2,7) (|A| = 8), PGL(2,8) (|A| = 9), or PΓL(2,8) (|A| = 9).
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