Rigid Rectangles in Squares

The following pictures show the fewest possible rigid rectangles (no rectangle can slide in any direction) packed inside squares of side n.

2 x 1 Rectangles

3 x 1 Rectangles

4 x 1 Rectangles

3 x 2 Rectangles

5 x 2 Rectangles

4 x 3 Rectangles

Torsten Sillke has some more information.