Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×C4×D55 | C2 | semidirect |
| 3. C2×Dic5×D11 | C2 | semidirect |
| 4. C11×#683 | C2 | semidirect |
| 5. C5×(C2×D11)⋊C4 | C2 | semidirect |
| 6. #11724886 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 16. #89168 | C4 | semidirect |
| 22. C2×D55 | C2×C4 | semidirect |
| 25. C2×C5×D11 | C2×C4 | semidirect |
| 27. Dic55 | D4 | semidirect |
| 30. C11×Dic5 | C2×C4 | semidirect |
| 36. (C2×D11)⋊C4 | D5 | semidirect |
| 59. #683 | D11 | semidirect |
| 61. C5×C11 | C4×D4 | semidirect |
| 68. C2×D11 | C4×D5 | semidirect |
| 101. Dic5 | C4×D11 | semidirect |
| 109. C11 | #4027 | semidirect |
| 125. C5 | #66946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D55 | 2 |
| C2×#89168 | 2 |
| C2×Dic5×D11 | 2 |
| C11×#683 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| #11724886 | 2 |
| Dic5×Dic11 | 2 |
| #66946 | 5 |
| #4027 | 11 |