Monster group
The finite simple groups  have been completely classified (the classification of finite simple groups). There are two kinds of finite simple groups in the list of finite simple groups. The first kind has 18 countably infinite families. The second kind has 26 sporadic groups. They are not as systematic. The Monster group is the largest of these sporadic groups. It contains all but six of the other sporadic groups inside of it. Robert Griess has called these six exceptions pariahs. The rest make up the happy family.