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×D5×Dic11 | C2 | semidirect |
| 4. C11×#685 | C2 | semidirect |
| 5. C5×Dic11⋊C4 | C2 | semidirect |
| 6. #11724886 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 16. #89169 | C4 | semidirect |
| 22. C2×D55 | C2×C4 | semidirect |
| 25. C2×D5×C11 | C2×C4 | semidirect |
| 27. Dic55 | D4 | semidirect |
| 29. C5×Dic11 | C2×C4 | semidirect |
| 36. Dic11⋊C4 | D5 | semidirect |
| 59. #685 | D11 | semidirect |
| 61. C5×C11 | C4×D4 | semidirect |
| 73. Dic11 | C4×D5 | semidirect |
| 96. C2×D5 | C4×D11 | semidirect |
| 109. C11 | #4039 | semidirect |
| 125. C5 | (C22⋊D11)⋊C4 | 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×#89169 | 2 |
| C2×D5×Dic11 | 2 |
| C11×#685 | 2 |
| C5×Dic11⋊C4 | 2 |
| #11724886 | 2 |
| Dic5×Dic11 | 2 |
| (C22⋊D11)⋊C4 | 5 |
| #4039 | 11 |