36 basic regular quotient singularity types and
52 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [60] | 30 |
| [33, 4, 3] | 30 |
| [3, 5, 5, 2] | 30 |
| [5, 3, 3, 2] | 30 |
| [33, 2, 2, 5] | 30 |
| [35, 2, 2, 3] | 30 |
| [3, 4, 6, 4, 3] | 30 |
| [5, 2, 3, 5, 2] | 30 |
| [32, 2, 2, 5, 2] | 30 |
| [32, 3, 2, 3, 2] | 30 |
| [32, 5, 2, 2, 2] | 30 |
| [3, 4, 8, 2, 2, 3] | 30 |
| [5, 2, 2, 6, 4, 3] | 30 |
| [2, 2, 2, 9, 2, 2, 2] | 30 |
| [2, 3, 2, 5, 2, 3, 2] | 30 |
| [2, 3, 2, 7, 2, 2, 2] | 30 |
| [2, 5, 2, 3, 2, 5, 2] | 30 |
| [2, 5, 2, 4, 2, 3, 2] | 30 |
| [2, 5, 2, 6, 2, 2, 2] | 30 |
| [3, 2, 2, 10, 2, 2, 3] | 30 |
| [3, 4, 5, 2, 2, 5, 2] | 30 |
| [3, 4, 5, 3, 2, 3, 2] | 30 |
| [3, 4, 5, 5, 2, 2, 2] | 30 |
| [5, 2, 2, 6, 2, 2, 5] | 30 |
| [5, 2, 2, 8, 2, 2, 3] | 30 |
| [3, 2, 2, 7, 2, 2, 5, 2] | 30 |
| [3, 2, 2, 7, 3, 2, 3, 2] | 30 |
| [3, 2, 2, 7, 5, 2, 2, 2] | 30 |
| [5, 2, 2, 5, 2, 2, 5, 2] | 30 |
| [5, 2, 2, 5, 3, 2, 3, 2] | 30 |
| [5, 2, 2, 5, 5, 2, 2, 2] | 30 |
| [2, 2, 2, 5, 4, 5, 2, 2, 2] | 30 |
| [2, 3, 2, 3, 4, 3, 2, 3, 2] | 30 |
| [2, 3, 2, 3, 4, 5, 2, 2, 2] | 30 |
| [2, 5, 2, 2, 4, 2, 2, 5, 2] | 30 |
| [2, 5, 2, 2, 4, 3, 2, 3, 2] | 30 |
| [2, 5, 2, 2, 4, 5, 2, 2, 2] | 30 |
| [3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [3, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [32, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [3, 4, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [3, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [5, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 2, 2, 5, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 3, 2, 3, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 5, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [31, 31] | [31, 2, 31] | [31, 2, 2, 31] | 30 |
| [31, 4, 4, 3] | [31, 2, 4, 4, 3] | [31, 2, 2, 4, 4, 3] | 30 |
| [31, 4, 2, 2, 5] | [31, 2, 4, 2, 2, 5] | [31, 2, 2, 4, 2, 2, 5] | 30 |
| [31, 6, 2, 2, 3] | [31, 2, 6, 2, 2, 3] | [31, 2, 2, 6, 2, 2, 3] | 30 |
| [3, 4, 4, 4, 4, 3] | [3, 4, 4, 2, 4, 4, 3] | [3, 4, 4, 2, 2, 4, 4, 3] | 30 |
| [31, 3, 2, 2, 5, 2] | [31, 2, 3, 2, 2, 5, 2] | [31, 2, 2, 3, 2, 2, 5, 2] | 30 |
| [31, 3, 3, 2, 3, 2] | [31, 2, 3, 3, 2, 3, 2] | [31, 2, 2, 3, 3, 2, 3, 2] | 30 |
| [31, 3, 5, 2, 2, 2] | [31, 2, 3, 5, 2, 2, 2] | [31, 2, 2, 3, 5, 2, 2, 2] | 30 |
| [3, 4, 4, 6, 2, 2, 3] | [3, 4, 4, 2, 6, 2, 2, 3] | [3, 4, 4, 2, 2, 6, 2, 2, 3] | 30 |
| [5, 2, 2, 4, 4, 4, 3] | [5, 2, 2, 4, 2, 4, 4, 3] | [5, 2, 2, 4, 2, 2, 4, 4, 3] | 30 |
| [3, 2, 2, 6, 6, 2, 2, 3] | [3, 2, 2, 6, 2, 6, 2, 2, 3] | [3, 2, 2, 6, 2, 2, 6, 2, 2, 3] | 30 |
| [3, 4, 4, 3, 2, 2, 5, 2] | [3, 4, 4, 2, 3, 2, 2, 5, 2] | [3, 4, 4, 2, 2, 3, 2, 2, 5, 2] | 30 |
| [3, 4, 4, 3, 3, 2, 3, 2] | [3, 4, 4, 2, 3, 3, 2, 3, 2] | [3, 4, 4, 2, 2, 3, 3, 2, 3, 2] | 30 |
| [3, 4, 4, 3, 5, 2, 2, 2] | [3, 4, 4, 2, 3, 5, 2, 2, 2] | [3, 4, 4, 2, 2, 3, 5, 2, 2, 2] | 30 |
| [5, 2, 2, 4, 4, 2, 2, 5] | [5, 2, 2, 4, 2, 4, 2, 2, 5] | [5, 2, 2, 4, 2, 2, 4, 2, 2, 5] | 30 |
| [5, 2, 2, 4, 6, 2, 2, 3] | [5, 2, 2, 4, 2, 6, 2, 2, 3] | [5, 2, 2, 4, 2, 2, 6, 2, 2, 3] | 30 |
| [3, 2, 2, 6, 3, 2, 2, 5, 2] | [3, 2, 2, 6, 2, 3, 2, 2, 5, 2] | [3, 2, 2, 6, 2, 2, 3, 2, 2, 5, 2] | 30 |
| [3, 2, 2, 6, 3, 3, 2, 3, 2] | [3, 2, 2, 6, 2, 3, 3, 2, 3, 2] | [3, 2, 2, 6, 2, 2, 3, 3, 2, 3, 2] | 30 |
| [3, 2, 2, 6, 3, 5, 2, 2, 2] | [3, 2, 2, 6, 2, 3, 5, 2, 2, 2] | [3, 2, 2, 6, 2, 2, 3, 5, 2, 2, 2] | 30 |
| [5, 2, 2, 4, 3, 2, 2, 5, 2] | [5, 2, 2, 4, 2, 3, 2, 2, 5, 2] | [5, 2, 2, 4, 2, 2, 3, 2, 2, 5, 2] | 30 |
| [5, 2, 2, 4, 3, 3, 2, 3, 2] | [5, 2, 2, 4, 2, 3, 3, 2, 3, 2] | [5, 2, 2, 4, 2, 2, 3, 3, 2, 3, 2] | 30 |
| [5, 2, 2, 4, 3, 5, 2, 2, 2] | [5, 2, 2, 4, 2, 3, 5, 2, 2, 2] | [5, 2, 2, 4, 2, 2, 3, 5, 2, 2, 2] | 30 |
| [2, 2, 2, 5, 3, 3, 5, 2, 2, 2] | [2, 2, 2, 5, 3, 2, 3, 5, 2, 2, 2] | [2, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 2] | 30 |
| [2, 3, 2, 3, 3, 3, 3, 2, 3, 2] | [2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2] | [2, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 2] | 30 |
| [2, 3, 2, 3, 3, 3, 5, 2, 2, 2] | [2, 3, 2, 3, 3, 2, 3, 5, 2, 2, 2] | [2, 3, 2, 3, 3, 2, 2, 3, 5, 2, 2, 2] | 30 |
| [2, 5, 2, 2, 3, 3, 2, 2, 5, 2] | [2, 5, 2, 2, 3, 2, 3, 2, 2, 5, 2] | [2, 5, 2, 2, 3, 2, 2, 3, 2, 2, 5, 2] | 30 |
| [2, 5, 2, 2, 3, 3, 3, 2, 3, 2] | [2, 5, 2, 2, 3, 2, 3, 3, 2, 3, 2] | [2, 5, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2] | 30 |
| [2, 5, 2, 2, 3, 3, 5, 2, 2, 2] | [2, 5, 2, 2, 3, 2, 3, 5, 2, 2, 2] | [2, 5, 2, 2, 3, 2, 2, 3, 5, 2, 2, 2] | 30 |
| [31, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [31, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [31, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [3, 4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 4, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 4, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [3, 2, 2, 6, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 6, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 6, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [5, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [5, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [5, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 2, 2, 5, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 5, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 5, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 3, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 3, 2, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 5, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 5, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 5, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 30 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87