Show a group to be a subgroup
11825
Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \in H \iff a \in H\}$. Prove that $K$ is a subgroup of $G$.
44165
the image of normal subgroups
79452
How to prove that it is a group?
53409
Show group of order $4n + 2$ has a subgroup of index 2.
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
80381
Groups with "few" subgroups
151130
When is the product of $n$ subgroups a subgroup?
43750
Subgroups of finite solvable groups. Solvable?
91997
Product of two subgroups the whole group?
129830
A group with no proper non-trivial subgroups
156319
Show that a group with $|G| = 33$ contains an element of order $3$
118022
Show that a group of order $180$ is not simple.
74970
Subsubgroups are subgroups of subgroups / Multiplicative Property of the Index
98542
Prove that $H$ is a subgroup of an abelian group $G$
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
156463
The complement of a proper subgroup generates the whole group