Let $|G| = p^n$ where $p$ is prime. Show that the number of non-normal subgroups of $G$ is $pm$.
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
80186
How to show that $K\leq S_4$ is a normal subgroup?
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
47731
Intersection of all $p$-Sylow subgroups is normal
141265
Finding a normal and not normal subgroup of $S_3$
154076
How to show this property of $\mathbb{RP}^{n}$.
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
142413
Normal Subgroups of $SU(n)$
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
58251
To show every sylow p-subgroup is normal in G
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
102622
K is a subgroup of G. Show that K is not a normal subgroup
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.