Prove that there is a subgroup of index 2
53409
Show group of order $4n + 2$ has a subgroup of index 2.
127996
$M_1$ and $M_2$ are subgroups and $M_1/N=M_2/N$. Is $M_1\cong M_2$?
52105
Prove that $HK$ is a subgroup iff $HK=KH$.
144582
Index of a subgroup in $SL_2(\mathbb{Z})$
49666
Generalization of index 2 subgroups are normal
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
74970
Subsubgroups are subgroups of subgroups / Multiplicative Property of the Index
57309
Show that the free group on $n$ generators is a finite index subgroup of $F_2$
17510
Proving a set is an abelian group.
75068
subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
156154
Sylow 2 subgroups of S4
58135
Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$
94999
A subgroup with an index of 2 is normal to the group.
99346
Prove a result on transitive group actions.
103002
Group equals union of two subgroups
151130
When is the product of $n$ subgroups a subgroup?