# A set of non-isomorphic finite groups is a finite set

Let F= set of all non-isomorphic groups of order n where n>=2. I want to show that F is a finite set.

I want to use the fact: Every group |G|=n is an isomorphic to a subgroup of Sn. But i don't know how.

Can anyone give me a direction please? Thank you

-
How many subgroups of $S_n$ are there? (Can there be infinitely many?) – Quinn Culver Dec 14 '12 at 16:18
How many distinct multiplication tables can you write down on a set of size $n$? – Alex B. Dec 14 '12 at 16:19