(1) If G is a finite group and H ≤ G, then |G:H| =|G|/|H|.

(2) For each element a of G, |a| divides |G|.

(3) Groups of prime order are cyclic.

(4) If G is a finite group, then for any element a of G, a^|G| = e.

(5) Fermat’s Little Theorem