Index of the subgroup $\operatorname{Im}(f)$
48397
Index of a sublattice in a lattice and a homomorphism between them
122110
Character of the subobject classifier in the topos of $\mathbf{M}$-sets.
54082
Group with exactly two subgroups of index 2
146028
$GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$
39938
Subgroups of a cyclic group and their order.
53409
Show group of order $4n + 2$ has a subgroup of index 2.
50130
$\operatorname{Aut}(V)$ is isomorphic to $S_3$
98474
Show the existence of a certain subgroup of F2
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
74970
Subsubgroups are subgroups of subgroups / Multiplicative Property of the Index
94215
Fundamental group of the connected sum of manifolds
105610
Normalizer of upper triangular group in ${\rm GL}(n,F)$
44165
the image of normal subgroups
114811
Characteristic subgroups and automorphisms
7418
The Center of $\operatorname{GL}(n,k)$
110217
$GL(n,K)$ is open in $M(n,K)$
149578
Subgroups of $(\mathbb Z_n,+)$