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The number of groups of order $n$ (upto isomorphism)is

a)finite for all values of $n$

b)finite only for finitely many values of $n$

c)finite for infinitely many values of $n$

d)infinite for some values of $n$

I think option (b) is correct.please help me

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    See whether this helps you: http://math.stackexchange.com/questions/466395/number-of-distinct-groups-of-order-n-upto-isomorphism-for-a-fixed-integer-n – 2017-01-06
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    And hopefully you can choose more than one option because (a) implies (c) [and, less importantly, (b) implies (d)] :-) – 2017-01-06

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Note that on a set $G$ with $n$ elements, there are $n^{n^2}$ maps $G \times G \to G$, hence there are at most $n^{n^2}$ non-isomorphic groups of order $n$.