Classifying Groups of Small Order

For groups of finite order there are only a finite number of groups, up to isomorphism. For example, ifprime, thenthe cyclic group of orderIfis not prime then more possibilities exist, but  there is still a finite number of possible groups up to isomorphism.

For groups up to order 8 these are:

Various methods exist for finding these groups – using Sylow's theorems, analysis of the conjugacy class equation, Lagrange's equation.