$p$ smallest prime dividing $G$ subgroup with index $p$ normal in $G$
7108
Normal subgroup of prime index
75568
Subgroup of index $2$ is Normal
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
118337
Let $S$ be a normal p-subgroup of a finite group $G$. Prove that $S \subseteq P$ for every Sylow p-subgroup $P$ of $G$
6134
Some Subgroup of Dihedral Group is Normal
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
91287
Is $G/pG$ is a $p$-group?
4402
Group of order $pqr$, $p < q < r$ primes
29802
Part of simple proof of nontrivial center in p-group
38853
Cyclic group of prime order
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
99999
A question on identifying normal subgroups of $S_4$
94999
A subgroup with an index of 2 is normal to the group.
89508
Existence of normal subgroups for a group of order $36$
37971
Prove that the center of a group is a normal subgroup
64408
Subgroup of $\mathbb{Q}$ with finite index