# Math Help - Prove that any nontrivial subgroup of G is cyclic.

1. ## Prove that any nontrivial subgroup of G is cyclic.

Let G be a group of order pq, where p and q are primes. Prove that any nontrivial subgroup of G is cyclic.

2. Originally Posted by rainyice
Let G be a group of order pq, where p and q are primes. Prove that any nontrivial subgroup of G is cyclic.

What are the possible orders for such a subgroup according to Lagrange's Theorem? Then what can you deduce?

Tonio