Find all pairs of lattices (L,K)(up to isomorphism) such that

a) L x K contains 20 elements

b) L is non-distributive

c) K has at least 3 elements

d) the greatest element of L x K covers precisely 4 elements.

From what I understand from this question K can have 4, 5, 10, 20

elements, but since L is non-distributive it has to be at least 5 elements since it has to be isomorphic to M3 and N5.

So K has to be 4 elements.

How do you find these lattices???