Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Does someone have an idea about a possible way to count the number of normal subgroup that a group of order $p ^n $ has ($n \in \mathbb{N}$ )? Is there anyway we can count the maximal subgroups it has (i.e.- the groups of order $p^{n-1} $ ? ) ?

Thanks in advance!

share|cite|improve this question
Counting maximal subgroups is equivalent to counting p-cycles in the elementary abelian group $P/\phi(P)$. – peoplepower Oct 1 '12 at 23:38
It's going to depend a lot on the group, isn't it? Just among groups of order 8, the answer varies from 4 to 16. – Gerry Myerson Oct 1 '12 at 23:56
In case you aren't the same person, there is a thread about this on MO. – Alexander Gruber Oct 2 '12 at 4:09

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.