Double coset density in classical algebraic groups

We classify all pairs of reductive maximal connected subgroups of a classic al algebraic group G that have a dense double coset in G. Using this, we sh ow that for an arbitrary pair (H, K) of reductive subgroups of a reductive group G satisfying a certain mild technical condition, there is a dense H, K-double coset in G precisely when G = H K is a factorization.