Suppose that a group $G$ has an involution, then it has an odd number of involutions
26398
Group of even order contains an element of order 2
46940
On Groups of Order 315 with a unique sylow 3-subgroup .
102429
There are 2 groups of order 6 (up to isomorphism)
42582
Infinite group with only two conjugacy classes
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
116786
normal subgroups of Alternating group
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
18881
Number of elements of order $7$ in a group
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
72767
Center of the dihedral group with odd and even number of vertices
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
132280
Let $G$ be a group of order 35. Show that $G \cong Z_{35}$
83061
Generating the symmetric group $S_n$
84132
Number of preimages of a group element under a homomorphism.
99999
A question on identifying normal subgroups of $S_4$
151699
Group of inner automorphisms of a group $G$