Finding a nontrivial normal subgroup of a group of rank 36
89508
Existence of normal subgroups for a group of order $36$
137691
What are the self-normalizing subgroups of $S_n$?
80381
Groups with "few" subgroups
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
109060
Group containing no subgroup of index 2
27780
Subgroup which is generated by odd elements
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
94999
A subgroup with an index of 2 is normal to the group.
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime
22444
Normal subgroups of dihedral groups
87766
Using Cayley's Theorem to find an isomorphic subgroup.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
7973
Groups of order $pq$ have a proper normal subgroup
8066
Sort-of-simple non-Hopfian groups