According to the classification of finite simple groups, there are 18 countably infinite families and 26 sporadic simple groups. The latter groups do not fit into any systematic classification, but there are a number of links between them. For example, the Monster group$M$, the largest of the sporadic groups, contains all but six (the ‘pariahs’, $J_1, J_3,Ru,ON,Ly,J_4$) of the other sporadic groups as subquotients.