Answer
$5,209,344$
Work Step by Step
Suppose there are two groups with $n$ and $m$ objects. If we form a group choosing $r(r\leq n)$ and $s (s \leq m)$ objects from these two groups respectively and order doesn't matter, then there are $C(n, r) \times C(m, s)$ ways of forming such a group.
$C(4,2) \times C(8,3) \times C(20,5) = 6 \times 56 \times 15,504= 5,209,344$