For any category K we investigate the family of all factorization structures on K. In particular, for each such structure, (E,M), we investigate the complete lattice of all factorization structures on K with left factor a subclass of E; this investigation is based on a Galois connection between all such structures and the lattice of all full isomorphism-closed subcategories of K. The Galois-closed families are precisely all the E-reflective subcategories of K and all the (E,M)-dispersed factorization structures of Herrlich, Salicrup and Vazquez.