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## Homework Statement

Given a class equation of a group H of 20=1+4+5+5+5, does H have a subgroup of order 5? Of order 4?

## The Attempt at a Solution

Order 5 I can't get, but for order 4 I think I am correct in saying that H does have a subgroup of order 4 because each summand in the class equation is either |Z(H)| or is the index of the normalizer subgroup. So H has 3 subgroups of order 4.

Is this enough of an answer for the subgroup of order 4 part?

And any help on the order of 5 part?

Thanks