The largest mathematical proof in history is generally considered to be the classification of finite simple groups. The proof consists of tens of thousands of pages, published in several hundred journal articles, by about 100 authors, mostly between 1955 and 2004. It states that every finite simple group is isomorphic to one of the following groups:
The diagram above gives an overview of the 26 sporadic finite simple groups and the relations between them. The largest group is called the Monster and has order 808017424794512875886459904961710757005754368000000000. Nineteen other sporadic groups are involved in the Monster as subgroups or quotients of subgroups; together with the Monster group itself they form the “happy family”. The other six groups have no connection with the Monster and are called the “pariahs”. An arrow in this diagram means that one group is a homomorphic image of a subgroup of the other.