We extend a result of J. Andres and K. Pastor, concerning scalar time-periodic first order ordinary differential equations without uniqueness, by proving that the existence of just one subharmonic implies the existence of large sets of subharmonics of all given orders. Since these periodic solutions must coexist with complicated dynamics, we might paraphrase \cite{LiYo} by loosely saying that in this setting even period two implies chaos. Similar results are obtained for a class of differential inclusions.
