| name | generators | size of the group | size of the class | number of orbits |
| X1 | identity | 1 | 1 | 205035 |
| X2 | (TI,R) | 2 | 36 | |
| X3 | (I,SR) | 2 | 36 | |
| X4 | (IQ,SRF) | 2 | 4 | |
| X5 | (T3IQ,S4RF) | 2 | 4 | |
| X6 | (T2Q,S2F) | 2 | 9 | |
| X7 | (Q,F) | 2 | 9 | |
| X8 | (TI,S6) | 2 | 6 | |
| X9 | (T6,R) | 2 | 6 | |
| X10 | (T2Q,R) | 2 | 18 | |
| X11 | (T3IQ,R) | 2 | 12 | |
| X12 | (TI,S2F) | 2 | 18 | |
| X13 | (T2Q,S6) | 2 | 3 | |
| X14 | (T3IQ,S6) | 2 | 2 | |
| X15 | (TI,S4RF) | 2 | 12 | |
| X16 | (T6,S4RF) | 2 | 2 | |
| X17 | (T6,S2F) | 2 | 3 | |
| X18 | (T3IQ,S2F) | 2 | 6 | |
| X19 | (T2Q,S4RF) | 2 | 6 | |
| X20 | (T6,S6) | 2 | 1 | |
| X21 | (T4,S4) | 3 | 2 | |
| X22 | (I,SR), (T6Q,S6F) | 4 | 36 | |
| X23 | (TI,R), (T4Q,S8F) | 4 | 36 | |
| X24 | (I,SR), (Q,F) | 4 | 36 | |
| X25 | (TI,R), (T10Q,S2F) | 4 | 36 | |
| X26 | (TI,S6), (T6,R) | 4 | 36 | |
| X27 | (TI,R), (T6,S6) | 4 | 18 | |
| X28 | (TI,R), (T3IQ,S6) | 4 | 36 | |
| X29 | (TI,R), (T10Q,S6) | 4 | 36 | |
| X30 | (TQ,SF) | 4 | 18 | |
| X31 | (T3IQ,R), (T2Q,S2F) | 4 | 36 | |
| X32 | (TI,R), (T7I,S2F) | 4 | 36 | |
| X33 | (TI,R), (T6,S2F) | 4 | 36 | |
| X34 | (TI,R), (T3IQ,S2F) | 4 | 36 | |
| X35 | (T2Q,R), (T3IQ,S2F) | 4 | 36 | |
| X36 | (T3IQ,R), (T6,S10RF) | 4 | 12 | |
| X37 | (T6,R), (TI,S2F) | 4 | 36 | |
| X38 | (T6,R), (T3IQ,S2F) | 4 | 12 | |
| X39 | (TI,S6), (T3IQ,R) | 4 | 36 | |
| X40 | (T6,S6), (IQ,SRF) | 4 | 2 | |
| X41 | (T3I,S4RF), (Q,F) | 4 | 36 | |
| X42 | (TI,S6), (T6,S4RF) | 4 | 12 | |
| X43 | (T6,R), (T3IQ,S6) | 4 | 12 | |
| X44 | (TI,S2F), (T3IQ,S6R) | 4 | 36 | |
| X45 | (T6Q,S4R), (Q,F) | 4 | 18 | |
| X46 | (TI,S2F), (T4Q,S8F) | 4 | 18 | |
| X47 | (T3IQ,S6), (TI,S4RF) | 4 | 12 | |
| X48 | (TI,S6), (T3IQ,S10RF) | 4 | 12 | |
| X49 | (T6,S4RF), (T3IQ,S6) | 4 | 4 | |
| X50 | (T3I,S6), (Q,F) | 4 | 18 | |
| X51 | (T6,S2F), (T6Q,S6) | 4 | 9 | |
| X52 | (T6,S2F), (T3IQ,R) | 4 | 12 | |
| X53 | (TI,S2F), (T10Q,R) | 4 | 36 | |
| X54 | (TI,S4RF), (T10Q,S6) | 4 | 12 | |
| X55 | (T6,S4R), (Q,F) | 4 | 18 | |
| X56 | (T6,S6), (TI,S4RF) | 4 | 6 | |
| X57 | (TQ,S3) | 4 | 6 | |
| X58 | (T6,S6), (T3IQ,R) | 4 | 6 | |
| X59 | (T3,SF) | 4 | 6 | |
| X60 | (TI,R), (T4,S4) | 6 | 24 | |
| X61 | (T4,S4), (IQ,SRF) | 6 | 8 | |
| X62 | (T4,S4), (T2Q,R) | 6 | 12 | |
| X63 | (TI,S2F), (T4,S4) | 6 | 12 | |
| X64 | (T6,S6), (I,SR), (Q,F) | 8 | 18 | |
| X65 | (T3IQ,S6), (T6Q,S4R), (Q,F) | 8 | 36 | |
| X66 | (T3I,S4R), (T6,S6F), (Q,F) | 8 | 36 | |
| X67 | (TI,R), (TQ,S5F) | 8 | 36 | |
| X68 | (T6,R), (TI,S6), (T4Q,S8F) | 8 | 36 | |
| X69 | (TI,S6), (T4Q,F), (T6,S4RF) | 8 | 36 | |
| X70 | (TQ,S3), (TI,S4RF) | 8 | 12 | |
| X71 | (T3,SF), (IQ,SRF) | 8 | 12 | |
| X72 | (T6,S4R), (T9I,S6F), (Q,F) | 8 | 36 | |
| X73 | (T6,S6), (T3I,S4R), (Q,F) | 8 | 18 | |
| X74 | (T3,S3), (Q,F) | 8 | 18 | |
| X75 | (T3,S3), (I,SR) | 8 | 36 | |
| X76 | (T3Q,S3F), (I,SR) | 8 | 36 | |
| X77 | (T3,SF), (I,S5R) | 8 | 36 | |
| X78 | (T3Q,S3), (I,SR) | 8 | 36 | |
| X79 | (T6,S6), (T3I,S4RF), (Q,F) | 8 | 18 | |
| X80 | (T3,S3F), (Q,F) | 8 | 18 | |
| X81 | (I,SR), (T2IQ,S3RF) | 12 | 24 | |
| X82 | (T2,RF), (TI,S2F) | 12 | 24 | |
| X83 | (T7IQ,S2RF), (T2Q,S4R) | 12 | 24 | |
| X84 | (T7IQ,S2RF), (TI,R) | 12 | 24 | |
| X85 | (T7IQ,S10), (TI,R) | 12 | 24 | |
| X86 | (T3,SF), (I,S5R), (Q,S4F) | 16 | 36 | |
| X87 | (T3,S3), (I,SR), (Q,F) | 16 | 36 | |
| X88 | (T2,S2), (TI,R), (TQ,S5F) | 24 | 24 | |
| X89 | (T2,RF), (TI,S2F), (Q,S4F) | 24 | 24 | |
| X90 | (T,S), (I,SR), (Q,F) | 48 | 24 |