The subalgebras of the rank two symplectic Lie algebra

The semisimple subalgebras of the rank 2 symplectic Lie algebra sp(4,C) are well-known, and we recently classified its Levi decomposable subalgebras. In this article, we classify the solvable subalgebras of sp(4,C), up to inner automorphism. This completes the classification of the subalgebras of sp(4,C). More broadly speaking, in completing the classification of the subalgebras of sp(4,C) we have completed the classification of the subalgebras of the rank 2 semisimple Lie algebras.