  We classify all triples $(G,V,H)$ such that $SL_n(q)\leq G\leq GL_n(q)$, $V$
is a representation of $G$ of dimension greater than one over an algebraically
closed field $\FF$ of characteristic coprime to $q$, and $H$ is a proper
subgroup of $G$ such that the restriction $V\dar_{H}$ is irreducible. This
problem is a natural part of the Aschbacher-Scott program on maximal subgroups
of finite classical groups.
