Many groups are contained within other [groups](Groups.md). Such groups are _subgroups_ of those groups. ^22a57b Consider a [subset](Subsets.md) $H$ of a group $G.$ $H$ is a _subgroup_ of $G$ if $H$ is also [closed](Closure%20under%20an%20operation.md) under the binary operation in $G$ and if $H$ if equipped with the [[Induced operation]] from $G$ is also a group (i.e. if $H$ is still a group if we equip it with the same group operation that $G$ has). ^4ad44e As an example of a group we consider the [the integer group.](Groups.md#The%20integer%20group) This group is also a [subgroup](Groups.md#The%20integer%20group%20as%20a%20subgroup) of the [the rational number group.](Rational%20numbers.md#The%20rational%20number%20group) ^c39ac6 #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory