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