We classify all triples (G, V, H) such that SLn(q) ≤ G ≤ GLn(q), V is a representation of G of dimension greater than one over an algebraically closed field 픽 of characteristic prime to q, and H is a proper subgroup of G such that the restriction V↓H is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups in finite classical groups.