gr.group theory - When and how is a group of order n isomorphic to a regular subgroup of equal order?

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?