Showing the image of a subgroup is a subgroup.
6466
Image of subgroup and Kernel of homomorphism form subgroups
92064
A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$
80381
Groups with "few" subgroups
91997
Product of two subgroups the whole group?
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
40069
The image of a homomorphism is a group?
130706
Group presentations and the Dihedral Group
121257
Image of Homomorphism of Lie groups
39938
Subgroups of a cyclic group and their order.
103002
Group equals union of two subgroups
149578
Subgroups of $(\mathbb Z_n,+)$
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
17510
Proving a set is an abelian group.
24181
Showing that $G$ is a group under an alternative operation.
151210
How can we find and categorize the subgroups of $\mathbb{R}$?
114811
Characteristic subgroups and automorphisms