If G solvable and S a subgroup, then S is solvable
43750
Subgroups of finite solvable groups. Solvable?
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
152904
Groups with Same Number Of Elements and Subgroups
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
11957
G is the product of its Sylow subgroups
72150
Union of the conjugates of a proper subgroup
65744
How can I Prove that H=G or K=G
99999
A question on identifying normal subgroups of $S_4$
139218
Is this group solvable?
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
11825
Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \in H \iff a \in H\}$. Prove that $K$ is a subgroup of $G$.
92064
A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$
145254
$G$ be a non-nilpotent and supersoluble finite group.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$