Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D5×C11 | C2 | semidirect |
| 2. C22×D5×D11 | C2 | semidirect |
| 3. C2×C22⋊D55 | C2 | semidirect |
| 4. C2×C5×C22⋊D11 | C2 | semidirect |
| 5. D5×C22⋊D11 | C2 | direct (N × H) |
| 6. C2×#89169 | C2 | semidirect |
| 7. C2×#89167 | C2 | semidirect |
| 8. C2×D5×Dic11 | C2 | semidirect |
| 9. C23×C5×C11 | C22 | semidirect |
| 10. C22×D55 | C22 | semidirect |
| 13. C22×D5×C11 | C22 | semidirect |
| 14. C22×D5×C11 | C22 | semidirect |
| 15. C22×C5×D11 | C22 | semidirect |
| 17. C2×D5×D11 | C22 | semidirect |
| 18. C22⋊D55 | C22 | semidirect |
| 19. C2×Dic55 | C22 | semidirect |
| 20. C5×C22⋊D11 | C22 | semidirect |
| 21. C2×C5×Dic11 | C22 | semidirect |
| 22. #89169 | C22 | semidirect |
| 23. #89167 | C22 | semidirect |
| 24. D5×Dic11 | C22 | semidirect |
| 28. C22×C5×C11 | C23 | semidirect |
| 30. C2×D55 | C23 | semidirect |
| 33. C2×D5×C11 | D4 | semidirect |
| 35. C2×D5×C11 | C23 | semidirect |
| 37. C2×C5×D11 | C23 | semidirect |
| 39. Dic55 | C23 | semidirect |
| 40. C5×Dic11 | C23 | semidirect |
| 47. C2×C22⋊D11 | D5 | direct (N × H) |
| 51. C2×C5×C11 | C2×D4 | semidirect |
| 56. D5×C11 | C2×D4 | semidirect |
| 61. C23×C11 | C2×D5 | semidirect |
| 65. C22×D11 | C2×D5 | semidirect |
| 69. C22⋊D11 | C2×D5 | direct (N × H) |
| 72. C2×Dic11 | C2×D5 | semidirect |
| 74. C23×D5 | D11 | semidirect |
| 81. C5×C11 | C22×D4 | semidirect |
| 89. C22×C11 | C22×D5 | semidirect |
| 94. C2×D11 | C22×D5 | semidirect |
| 96. Dic11 | C22×D5 | semidirect |
| 98. C23×C5 | C2×D11 | semidirect |
| 104. C22×D5 | C2×D11 | semidirect |
| 105. C22×D5 | C2×D11 | semidirect |
| 117. C2×C11 | D4×D5 | semidirect |
| 125. C22×C5 | C22×D11 | semidirect |
| 131. C2×D5 | C22⋊D11 | direct (N × H) |
| 133. C2×D5 | C22×D11 | semidirect |
| 144. C11 | C2×D4×D5 | semidirect |
| 147. C2×C5 | C2×C22⋊D11 | semidirect |
| 151. D5 | C2×C22⋊D11 | direct (N × H) |
| 160. C23 | D5×D11 | semidirect |
| 168. C5 | C22×C22⋊D11 | semidirect |
| 181. C22 | C2×D5×D11 | semidirect |
| 189. C2 | D5×C22⋊D11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D5×C11 | 2 |
| C22×D5×D11 | 2 |
| C2×C22⋊D55 | 2 |
| C2×C5×C22⋊D11 | 2 |
| D5×C22⋊D11 | 2 |
| C2×#89169 | 2 |
| C2×#89167 | 2 |
| C2×D5×Dic11 | 2 |
| C22×C22⋊D11 | 5 |
| C2×D4×D5 | 11 |