In $E(6)$ inspired models of supersymmetry, the inclusion of Lie subgroups $$ SO(10) \times U(1) \hookrightarrow E_6 $$ is important object of interest. See here for my motivating example.

In particular, paper uses the decomposition of some irreducible representations of $E(6)$ into its irreducible sub-representations with respect to the subgroup $SO(10) \times U(1)$.

Such rules as these are called "branching rules". Does there exist a single branching rule of the general $E(6)$ irreducible representation to its irreducible $SO(10) \times U(1)$-irreducible subrepresentations? What is a best reference?