Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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. C5×#4343 | C2 | semidirect |
| 2. #11724990 | C2 | semidirect |
| 3. #11724935 | C2 | semidirect |
| 4. C11×#689 | C2 | semidirect |
| 5. #11724874 | C2 | semidirect |
| 6. #11724872 | C2 | semidirect |
| 7. D11×#168 | C2 | semidirect |
| 28. #4343 | D5 | semidirect |
| 52. #689 | D11 | semidirect |
| 57. C5×C11 | #135 | semidirect |
| 95. C11 | #4096 | semidirect |
| 111. C5 | #66972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4343 | 2 |
| #11724990 | 2 |
| #11724935 | 2 |
| C11×#689 | 2 |
| #11724874 | 2 |
| #11724872 | 2 |
| D11×#168 | 2 |
| #66972 | 5 |
| #4096 | 11 |