  We introduce a sub-symmetry of a differential system as an infinitesimal
transformation of a subset of the system that leaves the subset invariant on
the solution set of the entire system. We discuss the geometrical meaning and
properties of sub-symmetries, as well as an algorithm for finding
sub-symmetries of a system. We show some of the benefits of using
sub-symmetries in the search for solutions of a system; in particular , we show
how sub-symmetries can be used in decoupling a differential system. We also
discuss the role of sub-symmetries in the deformation of known conservation
laws of a system into other (often, new) conservation laws and show that, in
this regard, a sub-symmetry is a considerably more powerful tool than a regular
symmetry. We demonstrate that all lower conservation laws of the nonlinear
telegraph system can be generated by sub-symmetries.
