  We give a complete classification of left invariant generalized complex
structures of type 1 on four dimensional simply connected Lie groups and we
compute for each class its invariant generalized Dolbeault cohomology, its
invariant generalized Bott-Chern cohomology and its invariant generalized
Aeppli cohomology. We classify also left invariant generalized K\"ahler
structures on four dimensional simply connected Lie groups.
