Normal subgroup implies quotient group?
5024
Why do we define quotient groups for normal subgroups only?
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
12589
Show that every subgroup of the quaternion group Q is a normal subgroup of Q
40846
When can a (finite) group be written as the quotient of some other group by its center?
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
37971
Prove that the center of a group is a normal subgroup
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other
97928
Normal subgroup of a normal subgroup
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
75568
Subgroup of index $2$ is Normal
58694
Which non-abelian finite groups have the property that every subgroup is normal?
23941
Normal Subgroups that Intersect Trivially
2174
Proving that HK is a subgroup when K is normal