| Σ | # | Presentation | Description | Related |
|---|
| 4 | 1 | ⟨a, b | aa=1, ab=1⟩ | Isomorphic to ℤ2 | 1990 iso |
| 5 | 4 | ⟨a, b | aa=a, ab=1⟩ | Isomorphic to ℤ1 | 2030 iso |
| 5 | 6 | ⟨a, b | aa=b, ab=1⟩ | Isomorphic to ℤ3 | 2029 iso |
| 5 | 7 | ⟨a, b | aa=b, bb=1⟩ | Isomorphic to ℤ4 | 1419 iso |
| 6 | 26 | ⟨a, b | aaa=1, abb=1⟩ | Isomorphic to ℤ6 | 1373 iso |
| 6 | 44 | ⟨a, b | aa=b, abb=1⟩ | Isomorphic to ℤ5 | 1132 iso |
| 7 | 116 | ⟨a, b | aaa=b, abb=1⟩ | Isomorphic to ℤ7 | 763 iso |
| 7 | 118 | ⟨a, b | aaa=b, bbb=1⟩ | Isomorphic to ℤ9 | 562 iso |
| 7 | 188 | ⟨a, b | aab=1, bbbb=1⟩ | Isomorphic to ℤ8 | 727 iso |
| 8 | 458 | ⟨a, b | aaaa=1, abbb=1⟩ | Isomorphic to ℤ12 | 325 iso |
| 8 | 507 | ⟨a, b | aaa=b, abbb=1⟩ | Isomorphic to ℤ10 | 536 iso |
| 9 | 1328 | ⟨a, b | aaaa=b, abbb=1⟩ | Isomorphic to ℤ13 | 189 iso |
| 9 | 1331 | ⟨a, b | aaaa=b, bbbb=1⟩ | Isomorphic to ℤ16 | 67 iso |
| 9 | 1472 | ⟨a, b | aaa=bb, abbb=1⟩ | Isomorphic to ℤ11 | 259 iso |
| 9 | 1751 | ⟨a, b | aaab=1, bbbbb=1⟩ | Isomorphic to ℤ15 | 138 iso |
| 10 | 3773 | ⟨a, b | aaaa=bb, abbb=1⟩ | Isomorphic to ℤ14 | 165 iso |
| 10 | 4212 | ⟨a, b | aaaaa=1, abbbb=1⟩ | Isomorphic to ℤ20 | 16 iso |
| 10 | 4375 | ⟨a, b | aaaa=b, abbbb=1⟩ | Isomorphic to ℤ17 | 39 iso |
| 10 | 5521 | ⟨a, b | aaab=1, bbbbbb=1⟩ | Isomorphic to ℤ18 | 33 iso |
| 11 | 11127 | ⟨a, b | aaaaa=b, abbbb=1⟩ | Isomorphic to ℤ21 | 13 iso |
| 11 | 11133 | ⟨a, b | aaaaa=b, bbbbb=1⟩ | Isomorphic to ℤ25 | 3 iso |
| 11 | 13340 | ⟨a, b | aaaab=1, abbbbb=1⟩ | Isomorphic to ℤ19 | 20 iso |
| 11 | 13372 | ⟨a, b | aaaab=1, bbbbbb=1⟩ | Isomorphic to ℤ24 | 8 iso |