Help with Lagrange's theorem.

Lagrange's Theorem states that: 'If H is a sub-group of a finite number G, then the order of H is a factor of G'.

It follows that 'The period of an element is a factor of the order of the group.'

Use the two theorems above and you knowlegde of groups to justify the proposition that only 2 groups of the order 6 exists, one Abelian and one non-Ablien. (please DON'T use cosets, and do use identities and subgroups or periods)

Provision of the supporting arguments in the form of proof :)

Thanks (Rofl)