In "Group Theory and Its Application to Physical Problems" by Morton Hamermesh, Morton states Cayley's theorem: Every group *G* of order *n* is isomorphic with a subgroup of the symmetric group *S _{n}*, which makes sense to me.

Later the book discusses regular permutations and regular subgroups, and makes this statement: "...suppose that *n* is a prime number. Then the group of order *n* is isomorphic to a regular subgroup of *S _{n}*." (page 19 in the Dover edition)

Why is the last sentence true? Is every group of *any* order *n* isomorphic to a regular subgroup of *S _{n}*?