For a subgroups $H_1$ and $H_2$ of $G$ and a normal subgroup $N$ of $G$: $H_1/N \cong H_2/N \Rightarrow H_1 \cong H_2$. Is it true?
127996
$M_1$ and $M_2$ are subgroups and $M_1/N=M_2/N$. Is $M_1\cong M_2$?
111886
Let $(G,•)$ be a group in which $(a•b)^3 = a^3•b^3$. Prove that $H=\{x^3 : x \in G\}$ is a normal subgroup of $G$.
137949
If the quotient group $G/N$ be isomorphic to $G_2$, is $G$ isomorphic to $G_1\times G_2$ where $N$ is isomorphic to $G_1$?
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
93666
Does the closedness of a subgroup $H$ of $G$ imply that for $h\in H, g\in G \setminus H : hg \not \in H$?
133915
In which case $M_1 \times N \cong M_2 \times N \Rightarrow M_1 \cong M_2$ is true?
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
116786
normal subgroups of Alternating group
151029
The number of non normal subgroups of a group cannot be $1$?
12667
How many subgroups of order $n$ does $D_n$ have?
145511
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
100974
Showing H is a normal subgroup by calculating left and right coset
123677
Normal subgroups of infinite symmetric group
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$
123610
How to show that the commutator subgroup is a normal subgroup
98542
Prove that $H$ is a subgroup of an abelian group $G$