Let the torus T^2n be equipped with the standard symplectic structure and a Hamiltonian H that is periodic in the time variable. A subharmonic solution is a periodic orbit of the Hamiltonian flow with minimal period an integral multiple m of the period of H, with m>1. We prove: If the Hamiltonian flow has only finitely many orbits with the same period as H, then there are subharmonic solutions with arbitrarily high minimal period. Thus there are always infinitely many distinct periodic orbits. This was proved in the nondegenerate case by Conley and Zehnder, and in the case n=2 by Le Calvez.