It is clear that for a given connected reductive $\mathbb{Q}$-group $G$, there are at most finitely many Shimura data of the form $(G,X)$ up to isomorphism. But in what case is it unique?

Moreover, in a given Shimura datum $(G,X)$, say we have a subdatum $(H,X_H)$, is it possible to find other subdatum of the form $(H,X'_H)$ with $X'_H\neq X_H$ as subsets of $X$? Of course there are a priori only finitely many choices for such $X_H'$, but I doubt if one is essentially reduced to the trivial case.

thanks a lot!