Show the intersection of six subgroups of order $24$ is normal in $G$?
51747
Showing that the intersection of all subgroups of order $n$ is normal
134353
A group of order $108$ has a proper normal subgroup of order $\geq 6$.
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
49257
How to show that Klein four-group is a normal subgroup of the alternating group $A_4$
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
129157
An exercise on isomorphic groups of order 24
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
115204
Show that SO(n) is a normal subgroup of O(n)
7973
Groups of order $pq$ have a proper normal subgroup
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
145511
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
63780
to show characteristic subgroup is normal in G
15630
Normal subgroup of prime order is characteristic