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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

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Show that a group is finite iff it has a finite number of subgroups.

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    okay so i use the fact above to show that Sn has finite # of subgroups and all non-isomorphic groups in F are isomorphic to atleast one subgroup of Sn and therefore there are finitely many non-isomorphic groups in F, therefore F is a finite set!2012-12-14
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    Indeed so, just as Alex and Quinn already hinted in their comments.2012-12-14
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    thanks a lot for ur help!!2012-12-14