$A_n$ normal subgroup of $S_n$
45277
The alternating group is a normal subgroup of the symmetric group
125244
Equivalent definitions of normal subgroups
11731
Normal subgroups of $S_4$
97865
On Conjugacy Classes of Alternating Group $A_n$
89508
Existence of normal subgroups for a group of order $36$
10998
Embedding $S_n$ in $A_{2n}$
102622
K is a subgroup of G. Show that K is not a normal subgroup
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
76962
Sylow $p$-subgroups of $GL_n(\mathbb{F}_p)$
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
54911
The preimage of a normal subgroup under a group homomorphism is normal
68201
Cyclic group of order $n$
157819
Every group of order $56$ has a proper non - trivial normal subgroup?
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
151130
When is the product of $n$ subgroups a subgroup?
47731
Intersection of all $p$-Sylow subgroups is normal