How to find restriction matrix for branching?

Question

Yesterday I asked this question. Let $G = Sp_{2g}(\mathbb{C})$ and $H$ be the subgroup of $G$ generated by matrices of the form

$$\begin{pmatrix} M&0\\ 0&(M^{t})^{-1} \end{pmatrix}$$

with $M \in SL_n(\mathbb{C})$, so $H \cong SL_n(\mathbb{C})$. I have a decomposition of a $G$-rep into irreducibles, and I want to use the branch function in LiE to decompose the restriction to $H$ into $H$-irreducibles.

I'm struggling to find the restriction matrix $m$ to input into the branch function.

Things I've tried:

1. res_mat(A5, C6) returns "Group C6 has no maximal subgroup of type A5(in res_mat)"

2. In the LiE manual, Example 5.10.2 outlines how to branch from $F_4$ to $B_4$. I'm not sure if this example is helpful for me or not. I don't know exactly how $F_4$ sits inside $B_4$, and I don't know what a root system is (is it necessary for me to learn this to proceed?).

I believe $M \in SL_n(\mathbb{C})$ acts as $V \oplus V^*$, where $V$ is the standard representation of $SL_n(\mathbb{C})$ and $V^*$ is its dual, if this helps.