Importance of Normal subgroups
30793
Intuition behind normal subgroups
99114
Subgroups of index 3 are normal
99999
A question on identifying normal subgroups of $S_4$
63780
to show characteristic subgroup is normal in G
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
103423
Normal subgroup where G has order prime
109236
Subgroups containing kernel of group morphism to an abelian group are normal.
7973
Groups of order $pq$ have a proper normal subgroup
1220
Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
20386
Any subgroup of index $p$ in a $p$-group is normal.
92837
Solvable and nilpotent groups, normal series and intuition
93147
Topological groups, why need them?
89508
Existence of normal subgroups for a group of order $36$
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
123677
Normal subgroups of infinite symmetric group
1360
Every group of order $150$ has a normal subgroup of order $25$