Any group of index 2 is normal
75568
Subgroup of index $2$ is Normal
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
1996
$A_n$ is the only subgroup of $S_n$ of index $2$.
67150
Index with exercise numbers
53409
Show group of order $4n + 2$ has a subgroup of index 2.
124179
Proof that every metric space is normal
106660
Every subgroup of the integers has finite index
116786
normal subgroups of Alternating group
86872
normalized subgroup by another subgroup
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
103423
Normal subgroup where G has order prime
74970
Subsubgroups are subgroups of subgroups / Multiplicative Property of the Index
37971
Prove that the center of a group is a normal subgroup
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
115204
Show that SO(n) is a normal subgroup of O(n)
92837
Solvable and nilpotent groups, normal series and intuition
1360
Every group of order $150$ has a normal subgroup of order $25$