Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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. Q8×D5×C11 | C2 | semidirect |
| 3. C5×C11×SD16 | C2 | semidirect |
| 4. C11×#689 | C2 | semidirect |
| 5. C11×#687 | C2 | semidirect |
| 6. C11×Dic20 | C2 | semidirect |
| 7. C11×#676 | C2 | semidirect |
| 32. C11×SD16 | D5 | semidirect |
| 34. #4061 | C11 | direct (N × H) |
| 49. Q8×D5 | C2×C11 | semidirect |
| 51. C5×SD16 | C2×C11 | semidirect |
| 52. #689 | C2×C11 | semidirect |
| 53. #687 | C2×C11 | semidirect |
| 54. Dic20 | C2×C11 | semidirect |
| 55. #676 | C2×C11 | semidirect |
| 56. C5×C11 | #137 | semidirect |
| 91. SD16 | D5×C11 | semidirect |
| 93. C11 | #4061 | direct (N × H) |
| 108. C5 | C11×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D5×C11 | 2 |
| C11×#711 | 2 |
| C5×C11×SD16 | 2 |
| C11×#689 | 2 |
| C11×#687 | 2 |
| C11×Dic20 | 2 |
| C11×#676 | 2 |
| C11×#137 | 5 |
| #4061 | 11 |