Does every group have a maximal normal subgroup?
133954
Does every infinite group have a maximal subgroup?
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
1360
Every group of order $150$ has a normal subgroup of order $25$
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
58251
To show every sylow p-subgroup is normal in G
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
58694
Which non-abelian finite groups have the property that every subgroup is normal?
125498
Check whether subgroup is normal in $ S_4$
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
30793
Intuition behind normal subgroups
97928
Normal subgroup of a normal subgroup
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
116786
normal subgroups of Alternating group
153797
Is a quotient group a subgroup?
155502
Index of a maximal subgroup in a finite group
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.