  Let $k$ be an arbitrary field. We classify the maximal reductive subgroups of
maximal rank in any classical simple algebraic $k$-group in terms of
combinatorial data associated to their indices. This result complements [S,
2022], which does the same for the exceptional groups. We determine which of
these subgroups may be realised over a finite field, the real numbers, or over
a $\mathfrak{p}$-adic field. We also look at the asymptotics of the number of
such subgroups as the rank grows large.
