An exhaustive description of the non-splitting subalgebras of the LP (1, 4) algebra with respect to P (1, 4) conjugation is presented.

Some general results on the subalgebras of the Lie algebra ASch(n) of the generalized Schrödinger group Sch(n) and on the subalgebras of the Lie algebra ASch(n) of the generalized extended Schrödinger group Sch(n) have been obtained. The subalgebra structure of the algebras ASch(n) and ASch(n) are studied with respect to inner automorphisms of the groups Sch(n) and Sch(n), respectively. The maximal Abelian subalgebras and the one-dimensional subalgebras of the algebras ASch(n) and ASch(n) have been explicitly found. The full classification of the subalgebras of the algebras ASch(3), ASch(3), which are nonconjugate to the subalgebras of ASch(2), ASch(2), respectively, has been carried out.

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Some general results on the subalgebras of the Lie algebra AP (1, n) of the extended Poincaré groupP (1, n) (n ≥ 2) with respect toP (1, n) conjugation have been obtained. All subalgebras of AP (1, 4) that are nonconjugate to the subalgebras of AP (1, 4) are classified with respect toP (1, 4) conjugation. The list of representatives of each conjugacy class is presented.