If a subgroup has smallest prime index, then it is normal
7108
Normal subgroup of prime index
58205
$ N $ normal in a finite group $ G $, $ |N| = 5 $ and $ |G| $ odd. Why is $ N \subseteq Z(G) $?
70373
Intersection of normal subgroups proof
58914
Any group of index 2 is normal
19720
A normal subgroup intersects the center of the $p$-group nontrivially
23941
Normal Subgroups that Intersect Trivially
94999
A subgroup with an index of 2 is normal to the group.
7973
Groups of order $pq$ have a proper normal subgroup
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
19458
Finite groups and Normal subgroups - $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$.
138108
If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.
64408
Subgroup of $\mathbb{Q}$ with finite index
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime
48273
If a maximal subgroup is normal, it has prime index
33309
Subgroup of $\mathbb{R}$ either dense or has a least positive element?
80186
How to show that $K\leq S_4$ is a normal subgroup?