Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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. C4⋊Dic55 | C2 | semidirect |
| 2. C11×#683 | C2 | semidirect |
| 4. #11724888 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 50. #683 | D11 | semidirect |
| 52. C5×C11 | #126 | semidirect |
| 92. C11 | #4025 | semidirect |
| 104. C5 | #66951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Dic55 | 2 |
| C11×#683 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| #11724888 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| Dic5×Dic11 | 2 |
| #66951 | 5 |
| #4025 | 11 |