Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 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×C5×Dic22 | C2 | semidirect |
| 3. #11724932 | C2 | semidirect |
| 4. C11×#685 | C2 | semidirect |
| 5. #11724886 | C2 | semidirect |
| 6. #11724885 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 31. C2×Dic22 | D5 | semidirect |
| 57. #685 | D11 | semidirect |
| 59. C5×C11 | #124 | semidirect |
| 106. C11 | #4093 | semidirect |
| 121. C5 | #66938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic22 | 2 |
| C2×#89169 | 2 |
| #11724932 | 2 |
| C11×#685 | 2 |
| #11724886 | 2 |
| #11724885 | 2 |
| Dic5×Dic11 | 2 |
| #66938 | 5 |
| #4093 | 11 |