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