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Hello all, I am making a program to scan subgroups and coset groups of Rubik's cube. For testing purposes, I scanned the square subgroup. It appeared that the corner coordinate of the square subgoup always satisfies a multiple of four antisymmetries (half of which are symmetries). Below follow the results. I computed modulo counts for all 420 antisymmetry subgroups, of which I choose six to display.

Square group table for FTM:
Level   |        | SO     | GO     | inv    | SO+inv | GO+inv |
--------+--------+--------+--------+--------+--------+--------+
    0   |      1 |      1 |      1 |      1 |      1 |      1 |