Pariah

Implicit definition
A pariah is a sporadic simple group that does not occur as a subquotient of the Monster group.

Explicit definition
The following are the pariahs:


 * Three of the Janko groups viz $$J_1$$, $$J_3$$ and $$J_4$$
 * The O'Nan group
 * The Rudvalis group
 * The Lyons group