When a group G has a normal subgroup N other than { 1 } and G itself, questions about G can sometimes be reduced to questions about N and ⁠ G / N ⁠. A nontrivial group is called simple if it has no such normal subgroup. Finite simple groups are to finite groups as prime numbers are to positive integers: they serve as building blocks, in a sense made precise by the Jordan–Hölder theorem.