How do i show any subgroup of index $p$ is normal?
7108
Normal subgroup of prime index
142413
Normal Subgroups of $SU(n)$
61373
A normal subgroup that is not a characteristic
122266
equivalent definition of normal subgroup
57227
Maximal normal $\pi$-subgroups and torsion subgroups
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
137691
What are the self-normalizing subgroups of $S_n$?
154398
Show that H is a subgroup of G
19720
A normal subgroup intersects the center of the $p$-group nontrivially
99999
A question on identifying normal subgroups of $S_4$
54082
Group with exactly two subgroups of index 2
54911
The preimage of a normal subgroup under a group homomorphism is normal
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
2174
Proving that HK is a subgroup when K is normal
58937
Finite Index of Subgroup of Subgroup
97928
Normal subgroup of a normal subgroup