Assume that there is such that divides order of . Then by Cauchy's theorem there exists and element of order which is not a power of - a contradiction. Thus, all prime divisors of must be equal to and so .

I am not sure exactly what you are looking for.2. Tell as much as possible about the subgroups of a group of order 30 and of a group of order 40.

But for order it can be shown (I looked up a classification table) that these groups are: .