        Optimal Sequences for < U, R > group elements (positions)
        ---------------------------------------------------------

Edge 3-cycle
UR1 = U3 R1 U2 (R1 U1)^2 R2 U3 R3 U3 R2 U1                      (16 q, 13 h)
UR1a= F1 U2 (F1 U1)^2 F2 U3 F3 U3 F2                            (14 q, 11 h)
UR1b= F3 U1 F3 (U3 F3)^2 U1 F1 U1 F2                            (12 q, 11 h)

Double adjacent edge swap
UR2 = U2 R3 U3 R2 U1 R1 U1 R3 U3 R1 U1 (R1 U3)^2 R3             (18 q, 16 h)

Diagonal Corner twist
UR3 = U1 R1 U3 R1 U3 R2 U1 R1 U1 R3 (U3 R1)^2 U2 R3 U3 R3       (20 q, 18 h)

Double opposite edge swap, also in sq group 24 q, 12 h
UR4 = R2 U2 R3 (U2 R2)^2 U2 R3 U2 R2                            (20 q, 11 h)

Edge 7-cycle, equivalent to (U1 R1)^15
UR5 = U3 R1 U3 R3 U3 R1 U2 R3 U1 R3 U2 R1 U3 R3 (U3 R1)^2       (20 q, 18 h)

Corner Tri-Twist
UR6 = (U3 R3)^2 U1 R1 U3 R3 U3 R2 U1 R2 U3 R3 U3 R1 U1 R3       (20 q, 18 h)

Corner Quad-Twist, Flat style
UR7 = R1 U3 (R1 U1)^2 (R3 U3)^2 R2 U3 R1 U1 R3 U3 R1 U3 R3      (20 q, 19 h)

Corner Quad-Twist, Arms & Legs style
UR8 = R1 U1 R3 U1 R3 U3 R1 U1 R1 (U3 R3)^2 (U1 R1)^2 U3 R3 U3   (20 q, 20 h)

ML Max Position                                                 
UR9 = (U2 R2)^2 U2 R3 U1 R2 (U3 R2)^2 U1 R1                     (22 q, 14 h)
Same position found by hand: (a non-optimal 24 q, 15 h)
      (U2 R2)^3 U1 R1 (U2 R3)^2 U2 R1 U1

4 Opp Corner Swap, also in sq group at 26 q, 13 h
UR10 = U3 R3 (U1 R1)^2 U2 R3 U1 R1 (U2 R2)^2 U1 R3 U1           (22 q, 17 h)

6 Twist, Equivalent to (U1 R1)^35= (R1 U1)^35 & Shift Invariant (22 q, 20 h)
UR11 = (U2 R1 U1 R1 (U1 R3)^3 )^2

6 Twist + 4 Opp Corner Swap or UR10 + UR11                      (22 q, 19 h)
UR12 = U1 R3 U3 R3 U1 R1 U1 R3 U3 R1 U2 (R2 U1 R3 U3 R2 U3 R1 U1)

First Antipodal Process                                         (25 q, 20 h)
UR13 = U2 R1 (U3 R2)^2 U3 R1 U2 R3 U1 R3 U3 R1 U1 R2 (U1 R3)^2

First Q+H Antipodal Process                                     (24 q, 20 h)
UR14 = (U3 R3)^4 U1 R2 U1 (R3 U2)^2 R3 U1 R2 U1 R3

        Other Subgroups within reach
        ----------------------------

11. |<U, R2, L2>|              = 2^12 3^4 5^2 7        =             58060800
12. |<U2, R, L2>|              = 2^12 3^4 5^2 7        =             58060800
17. |<U, R2, F2>|              = 2^8 3^5 5^2 7         =             10886400
21. |<U, R2, L2, D2>|          = 2^13 3^4 5^2 7        =            116121600
22. |<U, R2, L2, D>|           = 2^15 3^4 5^2 7^2      =           3251404800
