Any maximal subgroups of a finite group are conjugate then G is cyclic.
12912
Finite groups with exactly one maximal subgroup
34552
Proper subgroups of non-cyclic p-group cannot be all cyclic?
133954
Does every infinite group have a maximal subgroup?
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
11043
A normal subgroup is the union of conjugacy classes.
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
48273
If a maximal subgroup is normal, it has prime index
61513
Prove that all cyclic groups of the same order are isomorphic
118894
Cyclic subgroup of dihedral group
127306
Is the group of units of a finite ring cyclic?
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
98145
If $G$ is cyclic then $G/H$ is cyclic?
96878
A finite group with the property that all of its proper subgroups are abelian
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
28576
Galois Groups are isomorphic to subgroups of symmetric groups.
142421
Conjugacy Classes in Finite Groups