How do I find the order of a subgroup of $G$ under the canonical epimorphism?
24966
Converse of Lagrange's theorem for abelian groups
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
39938
Subgroups of a cyclic group and their order.
9612
Frattini subgroup $Φ ( G )$ is not trivial
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
132856
Find the derived subgroup of $A_4$
98474
Show the existence of a certain subgroup of F2
56607
gcd and order of elements of group
54911
The preimage of a normal subgroup under a group homomorphism is normal
131946
Order of an Element Under a Homomorphism
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
41731
Question about the order of the product of two elements in an abelian group
115746
Find the order of a subgroup of $S_5$ generated by two elements
113357
Groups of order $pqr$ and their normal subgroups
123796
Order of automorphism group of a $p$-group is divisible by $p$.
152589
How to show that if $G$ is union of three proper subgroups, then there is an epimorphism from $G$ to the Klein 4-group?
90192
Kernel and Image of a group homomorphism