Showing that the conjugates of a proper subgroup do not cover the group.
72150
Union of the conjugates of a proper subgroup
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
61373
A normal subgroup that is not a characteristic
67383
Prove that $G'$ is not planar.
145254
$G$ be a non-nilpotent and supersoluble finite group.
156941
Subgroups of $\mathbb{Z}$
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
70373
Intersection of normal subgroups proof
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
9612
Frattini subgroup $Φ ( G )$ is not trivial
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
107091
Taking the automorphism group of a group is not functorial.
92493
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
142228
Proof that a subset closed under group operation of a finite group is a subgroup
71035
Non abelian subgroup of a abelian group.