Example of A, B, G such that A is a normal subgroup of B, B is a normal subgroup of G, but A is not a normal subgroup of G
13523
Are normal subgroups transitive?
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
132704
If G is not commutative, then is there always a subgroup that is not a normal subgroup?
91021
Torsion elements of a group aren't necessarily a subgroup
113925
Normal Subgroup Counterexample
124732
Finding a nonempty subset that is not a subgroup
89190
Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
124709
Suppose G be a non-abelian group and H,K be two abelian subgroups of G. Then must HK be an abelian subgroup of G?
13453
Bijection map from a set of subgroup to another set of subgroup under some condition.
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
129120
Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
61373
A normal subgroup that is not a characteristic
97928
Normal subgroup of a normal subgroup
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal