Lenny Conundrum 354

Twenty Darblats each laid twelve eggs.

Each of those eggs hatched, and each of those Darblats laid three eggs.

When those eggs hatched, each of those Darblats laid five eggs.

When those eggs hatched, each of those Darblats laid seven eggs. (except for one Darblat, who was a boy, and didn't lay any eggs)

When those eggs hatched, each of those Darblats laid eleven eggs.

When those eggs hatched, each of those Darblats laid fifteen eggs.

When those eggs are hatched, how many total Darblats are there?