Is G/H a group even if H is a subgroup of G but not a normal subgroup?
5024
Why do we define quotient groups for normal subgroups only?
39165
Suppose $G$ is a group and $H,K \trianglelefteq G$. If $H \cap K =1$ the $hk=kh$ for all $k \in K, h \in H$?
129830
A group with no proper non-trivial subgroups
141265
Finding a normal and not normal subgroup of $S_3$
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
103423
Normal subgroup where G has order prime
57883
Example of a Subgroup That Is Not Normal
91021
Torsion elements of a group aren't necessarily a subgroup
35124
Can every non-simple group $G$ be written as a semidirect product?
55976
Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
1220
Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
6134
Some Subgroup of Dihedral Group is Normal