Inserted invariant submodels for motion of monatomic gas

We consider the gas dynamics equations with the state equation of the monatomic polytropic gas. From optimal system of a 14-dimensional Lie algebra admitted by the model we select subalgebras containing projective operator which is specific to this model. The optimal system consists of 73 subalgebras. The graph of all inserted subalgebras was constructed. It submits from 6 fragments. For any 4-dimensional subalgebra a hierarchy of inserted invariant submodels was constructed.