C-loops are loops that satisfy the identity x(y(yz)) = ((xy)y)z. In this note we use the order of nuclei of C-loops to show that (1) nonassociative C-loops of order 2p, where p is prime, are Steiner loops, (2) nonassociative C-loops of order 3n are non-simple and non-Steiner, (3) no nonassociative C-loop of order 2·3t, t > 1 exists, and (4) if every element of the commutant of a C-loop is of odd order the commutant forms a subloop.