Suppose we have finite groups $H \le G$, and we know a lot about $G$'s representation theory over $\Bbb C$. Every isomorphism class of $H$-irreps appears in a restriction of some $G$-irrep.
To an outsider it seems like there might be situations in which this could help one determine some information on the irreps/characters of $H$. Has this ever been useful in actual research? Could you please provide examples if it has? Maybe in $p$-groups (just a wild guess)?
