If G is a p-group, the number of nonnormal subgroup is a multiple of p?
75670
Questions around the number of subgroups of a $p$-group
76962
Sylow $p$-subgroups of $GL_n(\mathbb{F}_p)$
99999
A question on identifying normal subgroups of $S_4$
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
113357
Groups of order $pqr$ and their normal subgroups
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
63798
How can you show there are only 2 nonabelian groups of order 8?
157841
Existence of a non-abelian group of order $p^n$.
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
137691
What are the self-normalizing subgroups of $S_n$?
151130
When is the product of $n$ subgroups a subgroup?
96614
Finite number of subgroups $\Rightarrow$  finite group
29802
Part of simple proof of nontrivial center in p-group
55178
When there is a unique Sylow p-subgroup it is normal, does this mean that non-unique p-subgroups are not normal?