Gasdynamics equations submodels hierarchy in case of state equation with separated density

We consider the gasdynamics equations with the state equation of the separated density. The optimal system of subalgebras for 12 dimentional Lie algebra admitted by the gasdynamics equations is constructed. For each subalgebra from the optimal system of subalgebras a submodel (invariant, partially invariant, differential invariant) can be constructed. The solutions of the submodel can be particular solutions of another submodels. In this case the submodel subalgebra include the subalgebra of another submodel, that is overalgebra. We consider submodels hierarchy for 5 dimentional self-normalized subalgebra. The graph of inserted subalgebras is constructed. The invariants for subalgebras from graph are calculated. All invariant submodels are constructed.