Same thing as for the PG group (https://milotorda.net/index.php/pg-packings/) can be done for the CM group. At least for regular convex polygons. That is, given a CM packing one construct a P2MG packing with exactly same density, fairly easily. For most of regular polygons CM a P2MG packings have the same densities. The exceptions are regular convex polygons with 12k-1 and 12k+1 rotational symmetries. See: https://milotorda.net/index.php/packings/
Below are some examples of densest CM packings converted to P2MG packings. The P2MG packings are not the densest P2MG packings in these instances. From left to right: CM and P2MG
11-gon with density 0.8279530
13-gon with density 0.8321287
23-gon with density 0.8386501
