| name | generators | size of the group | size of the class | number of orbits |
| Y1 | identity | 1 | 1 | 101258 |
| Y2 | P | 2 | 48 | |
| Y3 | (TI,R) | 2 | 36 | |
| Y4 | (I,SR) | 2 | 36 | |
| Y5 | (TI,S6) | 2 | 12 | |
| Y6 | (IQ,SRF) | 2 | 4 | |
| Y7 | (T2Q,S2F) | 2 | 9 | |
| Y8 | (TI,S2F) | 2 | 36 | |
| Y9 | (TI,S4RF) | 2 | 24 | |
| Y10 | (T2Q,S6) | 2 | 6 | |
| Y11 | (T3IQ,S6) | 2 | 4 | |
| Y12 | (T3IQ,S4RF) | 2 | 4 | |
| Y13 | (T2Q,S4RF) | 2 | 12 | |
| Y14 | (Q,F) | 2 | 9 | |
| Y15 | (T6,S6) | 2 | 1 | |
| Y16 | (TI,S2R), P | 4 | 144 | |
| Y17 | (I,SR), P | 4 | 144 | |
| Y18 | (IQ,SRF), P | 4 | 48 | |
| Y19 | (T3IQ,S4RF), P | 4 | 48 | |
| Y20 | (T2Q,S2F), P | 4 | 72 | |
| Y21 | (Q,F), P | 4 | 72 | |
| Y22 | (I,SR), (T6Q,S6F) | 4 | 36 | |
| Y23 | (TI,R), (T3IQ,S6) | 4 | 72 | |
| Y24 | (TI,R), (T3IQ,S6R) | 4 | 72 | |
| Y25 | (TI,S6), (T6,R) | 4 | 36 | |
| Y26 | (TI,R), (T3IQ,S2F) | 4 | 36 | |
| Y27 | (T6,S6), P | 4 | 24 | |
| Y28 | (T2Q,R), (T3IQ,S2F) | 4 | 72 | |
| Y29 | (T3IQ,R), (T6,S10RF) | 4 | 24 | |
| Y30 | (T6,R), (TI,S2F) | 4 | 72 | |
| Y31 | (T6,R), (T3IQ,S2F) | 4 | 24 | |
| Y32 | (TI,S6), (T6,S4RF) | 4 | 24 | |
| Y33 | (T3IQ,R), (T2Q,S2F) | 4 | 36 | |
| Y34 | (T6Q,S4R), (Q,F) | 4 | 36 | |
| Y35 | (T3I,S6), (Q,F) | 4 | 36 | |
| Y36 | (TI,S4RF), (T10Q,S6) | 4 | 24 | |
| Y37 | (TI,R), (T6,S6) | 4 | 18 | |
| Y38 | (TQ,SF) | 4 | 18 | |
| Y39 | (TI,S2F), (T10Q,R) | 4 | 36 | |
| Y40 | (T,SR) o P | 4 | 144 | |
| Y41 | (T6,S6), (TI,S4RF) | 4 | 12 | |
| Y42 | (T3I,S4RF), (Q,F) | 4 | 36 | |
| Y43 | (T3,SF) | 4 | 12 | |
| Y44 | (TI,R), (T10Q,S2F) | 4 | 36 | |
| Y45 | (T2Q,S2F) o P | 4 | 72 | |
| Y46 | (T3IQ,S0) o P | 4 | 48 | |
| Y47 | (T4,S4), (Q,F) o P | 6 | 16 | |
| Y48 | (T4,S4), (T2Q,R) | 6 | 24 | |
| Y49 | (I,SR), (T6Q,S6F), P | 8 | 72 | |
| Y50 | (TI,R), (T4Q,S8F), P | 8 | 72 | |
| Y51 | (I,SR), (Q,F), P | 8 | 72 | |
| Y52 | (TI,R), (T10Q,S2F), (I,SR) o P | 8 | 72 | |
| Y53 | (TI,S6), (T6,R), (I,SR) o P | 8 | 144 | |
| Y54 | (TI,R), (T6,S6), (I,SR) o P | 8 | 36 | |
| Y55 | (T3Q,S3F), (I,SR) o P | 8 | 36 | |
| Y56 | (T3IQ,R), (IQ,S3R) o P | 8 | 144 | |
| Y57 | (TI,R), (T3IQ,S2F), (T,SR) o P | 8 | 144 | |
| Y58 | (T6,S6), (IQ,SRF), P | 8 | 12 | |
| Y59 | (T3I,S4RF), (Q,F), P | 8 | 144 | |
| Y60 | (TI,S6), (T3IQ,S10RF), P | 8 | 48 | |
| Y61 | (T6,S2F), P | 8 | 72 | |
| Y62 | (TI,S2F), (T10Q,R), (I,SR) o P | 8 | 144 | |
| Y63 | (TQ,SF), P | 8 | 72 | |
| Y64 | (T6,S4R), (T9I,S6F), (Q,F) | 8 | 72 | |
| Y65 | (TI,R), (T6,S6), (Q,F) o P | 8 | 72 | |
| Y66 | (T6,R), (TI,S6), (T4Q,S8F) | 8 | 36 | |
| Y67 | (TQ,S3), (TI,S4RF) | 8 | 24 | |
| Y68 | (TI,R), (TQ,S5F) | 8 | 36 | |
| Y69 | (TI,R), (T4Q,S8F), (T3Q,S5) o P | 8 | 72 | |
| Y70 | (T3IQ,S6), (T6Q,S4R), (Q,F) | 8 | 36 | |
| Y71 | (T3,SF), (I,S5R) | 8 | 72 | |
| Y72 | (TI,R), (T4,S4), (I,SR) o P | 12 | 96 | |
| Y73 | (T4,S4), (IQ,SRF), (I,SR) o P | 12 | 16 | |
| Y74 | (T2,RF), (TI,S2F) | 12 | 48 | |
| Y75 | (T6,S6), (I,SR), (Q,F), P | 16 | 18 | |
| Y76 | (T3IQ,S6), (T6Q,S4R), (Q,F), (T6,S6) o P | 16 | 72 | |
| Y77 | (T3I,S4R), (T6,S6F), (Q,F), P | 16 | 72 | |
| Y78 | (TI,R), (TQ,S5F), (I,SR) o P | 16 | 72 | |
| Y79 | (T6,R), (TI,S6), (T4Q,S8F), (I,SR) o P | 16 | 72 | |
| Y80 | (T6,S6), (T3I,S4R), (Q,F), P | 16 | 18 | |
| Y81 | (T3,S3), (Q,F), (I,SR) o P | 16 | 18 | |
| Y82 | (T3,S3), (I,SR), P | 16 | 72 | |
| Y83 | (T3Q,S3F), (I,SR), P | 16 | 72 | |
| Y84 | (T6,S6), (T3I,S4RF), (Q,F), P | 16 | 36 | |
| Y85 | (T3,S3F), (Q,F), (I,SR) o P | 16 | 36 | |
| Y86 | (I,SR), (T2IQ,S3RF), P | 24 | 48 | |
| Y87 | (T7IQ,S2RF), (T2Q,S4R), (I,SR) o P | 24 | 48 | |
| Y88 | (T7IQ,S2RF), (TI,R), (I,SR) o P | 24 | 48 | |
| Y89 | (T3,SF), (I,S5R), (Q,S4F), (TIQ,R) o P | 32 | 36 | |
| Y90 | (T3,S3), (I,SR), (Q,F), P | 32 | 36 | |
| Y91 | (T2,S2), (TI,R), (TQ,S5F), (T2,S0) o P | 48 | 24 | |
| Y92 | (T2,RF), (TI,S2F), (Q,S4F), (I,SR) o P | 48 | 48 | |
| Y93 | (T,S), (I,SR), (Q,F), P | 96 | 24 |