If $G$ is a group, $H,K \leq G$, $K \subseteq H$, $\left[G:H\right]$ and $\left[H:K\right]$ both finite then...
58937
Finite Index of Subgroup of Subgroup
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
100974
Showing H is a normal subgroup by calculating left and right coset
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
39165
Suppose $G$ is a group and $H,K \trianglelefteq G$. If $H \cap K =1$ the $hk=kh$ for all $k \in K, h \in H$?
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
85129
If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?
133770
Subgroups of finite abelian groups.
139100
A question on the group algebra $k[G]$ of a finite abelian group
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
147253
Prove for any $K \leq G$, either $K \leq N$ or $KN=G$ and $[K:K \cap N]=p$ where N is normal in G and $[G:N]=p$
61550
Existence of elements of order $p^k$ in a finite group