Normalizer is subgroup of G
41085
Conjugate subgroup strictly contained in the initial subgroup?
48273
If a maximal subgroup is normal, it has prime index
20386
Any subgroup of index $p$ in a $p$-group is normal.
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
92493
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
105610
Normalizer of upper triangular group in ${\rm GL}(n,F)$
115204
Show that SO(n) is a normal subgroup of O(n)
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
54911
The preimage of a normal subgroup under a group homomorphism is normal
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
137691
What are the self-normalizing subgroups of $S_n$?
11957
G is the product of its Sylow subgroups
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
116936
Commutator subgroup and subgroup generated by square.
151699
Group of inner automorphisms of a group $G$
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple