Nontrivial subgroup

Symbol-free definition
A subgroup of a group is termed nontrivial, if the subgroup is not the Defining ingredient::trivial group, i.e. it has more than one element.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed nontrivial if $$H$$ is not the Defining ingredient::trivial group: the one-element group comprising the identity element.

Note that if the group itself is trivial, it cannot have any nontrivial subgroup.

Opposite
The opposite of the property of being nontrivial is the property of being trivial, i.e. being the subgroup comprising only the identity element.

Stronger properties

 * Weaker than::Nontrivial normal subgroup