Only $1$ Nontrivial Subgroup $\Longrightarrow |G| = p^2$
7640
Exactly one nontrivial proper subgroup
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
3213
There exists only two groups of order $p^2$ up to isomorphism.
156549
Prove that there is no group $G$ s.t. $\operatorname{Aut}(G)=\mathbb{Q}$
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
63798
How can you show there are only 2 nonabelian groups of order 8?
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
91287
Is $G/pG$ is a $p$-group?
141125
Group with order $p^2$ must be abelian . How to prove that?
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
9612
Frattini subgroup $Φ ( G )$ is not trivial
42582
Infinite group with only two conjugacy classes
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
87766
Using Cayley's Theorem to find an isomorphic subgroup.
154398
Show that H is a subgroup of G
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order