normal subgroups of group of order $399$
19016
Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple
76962
Sylow $p$-subgroups of $GL_n(\mathbb{F}_p)$
61373
A normal subgroup that is not a characteristic
43651
Normal subgroups and factor groups
156154
Sylow 2 subgroups of S4
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
133298
Assume $|G|=40$. Show that the subgroup of order $8$ is normal and unique.
2767
Subgroups of the Klein-4 Group
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
133770
Subgroups of finite abelian groups.
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
99114
Subgroups of index 3 are normal
70373
Intersection of normal subgroups proof