1.21: Complex
A complex is a subset obtained from a group by choosing part of its elements in such a way that the closure property of groups is not respected. Therefore, a complex is not a group itself.
A typical example of complexes is that of cosets. In fact, a coset does not contain the identity and therefore it is not a group.
A subgroup is a particular case of complex that obeys the closure property and is a group itself.