Why is every subgroup of order $p^{n-1}$ normal?
7108
Normal subgroup of prime index
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
61373
A normal subgroup that is not a characteristic
75568
Subgroup of index $2$ is Normal
134353
A group of order $108$ has a proper normal subgroup of order $\geq 6$.
118337
Let $S$ be a normal p-subgroup of a finite group $G$. Prove that $S \subseteq P$ for every Sylow p-subgroup $P$ of $G$
44165
the image of normal subgroups
113357
Groups of order $pqr$ and their normal subgroups
151029
The number of non normal subgroups of a group cannot be $1$?
47731
Intersection of all $p$-Sylow subgroups is normal
104505
Is every normal subgroup the kernel of some endomorphism?
51359
Prove that every subgroup of an abelian group is a normal subgroup.
122266
equivalent definition of normal subgroup
12667
How many subgroups of order $n$ does $D_n$ have?
99999
A question on identifying normal subgroups of $S_4$