**Jordan's theorem** is a statement in finite group theory. It states that if a primitive permutation group *G* is a subgroup of the symmetric group *S*_{n} and contains a *p*-cycle for some prime number *p* < *n* − 2, then *G* is either the whole symmetric group *S*_{n} or the alternating group *A*_{n}.

The statement can be generalized to the case that *p* is a prime power.