No proper subgroup of finite index
64408
Subgroup of $\mathbb{Q}$ with finite index
144582
Index of a subgroup in $SL_2(\mathbb{Z})$
46121
Does the intersection of two finite index subgroups have finite index?
101735
A finite $p$-group cannot be simple unless it has order $p$
156549
Prove that there is no group $G$ s.t. $\operatorname{Aut}(G)=\mathbb{Q}$
137691
What are the self-normalizing subgroups of $S_n$?
51352
Subgroups of a finite abelian group
133770
Subgroups of finite abelian groups.
7973
Groups of order $pq$ have a proper normal subgroup
49666
Generalization of index 2 subgroups are normal
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
10816
Infinitely generated subgroup of a finitely one (weird)
98474
Show the existence of a certain subgroup of F2
72150
Union of the conjugates of a proper subgroup
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
61064
Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists