If there is only one subgroup of a certain order, it is normal
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
23533
All subgroups normal $\implies$ abelian group
86872
normalized subgroup by another subgroup
43651
Normal subgroups and factor groups
133298
Assume $|G|=40$. Show that the subgroup of order $8$ is normal and unique.
54195
Do groups of prime order have one subgroup?
5089
An element of a group has the same order as its inverse
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
15630
Normal subgroup of prime order is characteristic
37971
Prove that the center of a group is a normal subgroup
103002
Group equals union of two subgroups
66510
A group is abelian if and only if the center of the group is all the group
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
20386
Any subgroup of index $p$ in a $p$-group is normal.
51747
Showing that the intersection of all subgroups of order $n$ is normal
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$
88344
Order of a group and subsequent subgroups