Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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×C11×#41 | C2 | semidirect |
| 2. C11×#709 | C2 | semidirect |
| 3. C11×#689 | C2 | semidirect |
| 4. C11×#688 | C2 | semidirect |
| 5. C11×#687 | C2 | semidirect |
| 6. C11×#686 | C2 | semidirect |
| 7. C2×C11×#168 | C2 | semidirect |
| 28. C11×#41 | D5 | semidirect |
| 34. #4096 | C11 | direct (N × H) |
| 50. C5×#41 | C2×C11 | semidirect |
| 51. #709 | C2×C11 | semidirect |
| 52. #689 | C2×C11 | semidirect |
| 53. #688 | C2×C11 | semidirect |
| 54. #687 | C2×C11 | semidirect |
| 55. #686 | C2×C11 | semidirect |
| 56. C2×#168 | C2×C11 | semidirect |
| 57. C5×C11 | #135 | semidirect |
| 89. #41 | D5×C11 | semidirect |
| 95. C11 | #4096 | direct (N × H) |
| 111. C5 | C11×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×#41 | 2 |
| C11×#709 | 2 |
| C11×#689 | 2 |
| C11×#688 | 2 |
| C11×#687 | 2 |
| C11×#686 | 2 |
| C2×C11×#168 | 2 |
| C11×#135 | 5 |
| #4096 | 11 |