These three discontinuous tiles remove $48$ then $12$ then $3$ squares. The first layer pattern leaves a $4\times4$ replica of the original board, the second layer leaves a $2\times2$.
XXXXXXXX -------- -------- XOXOXOXO -X-X-X-X -------- XXXXXXXX -------- -------- XOXOXOXO -X-O-X-O ---X---X XXXXXXXX -------- -------- XOXOXOXO -X-X-X-X -------- XXXXXXXX -------- -------- XOXOXOXO -X-O-X-O ---X---OXXXXXXXX -------- -------- XXXXXXXX -------- -------- XXOOXXOO --XX--XX -------- XXOOXXOO --XO--XO ---X---X XXXXXXXX -------- -------- XXXXXXXX -------- -------- XXOOXXOO --XX--XX -------- XXOOXXOO --XO--XO ---X---OThese two come from making a block from coordinates $(1,1),(1,2),(2,1),(5,5)$ and $(1,1),(1,3),(3,1),(5,5)$ (from the L-solution) respectively, and using this mapping as a tiling. The second one uses a neat rotation trick with the second layer.
Also,
XXXXXXXX -------- -------- XXXXXXXX -------- -------- XXOOXXOO --XX--XX -------- XXOOXXOO --XX--XX -------- XXXXXXXX -------- -------- XXXXXXXX -------- -------- XXOOXXOO --XX--OO ------XX XXOOXXOO --XX--OO ------XO
If we label the two mappings given as $[2,2]$ and $[3,3]$, the remaining mappings are $[2,3], [2,5]$ and $[3,5]$.
