Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C5×C11×C4⋊C4 | C2 | semidirect |
| 4. C11×C4⋊Dic5 | C2 | semidirect |
| 5. C4×C11×Dic5 | C2 | semidirect |
| 11. C4×D5×C11 | C4 | semidirect |
| 23. C11×C4⋊C4 | D5 | semidirect |
| 26. #4038 | C11 | direct (N × H) |
| 38. C5×C4⋊C4 | C2×C11 | semidirect |
| 40. C4⋊Dic5 | C2×C11 | semidirect |
| 41. C4×Dic5 | C2×C11 | semidirect |
| 42. C5×C11 | #117 | semidirect |
| 56. C4×D5 | C4×C11 | semidirect |
| 72. C4⋊C4 | D5×C11 | semidirect |
| 75. C11 | #4038 | direct (N × H) |
| 86. C5 | C11×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5×C11 | 2 |
| C5×C11×C4⋊C4 | 2 |
| C11×#685 | 2 |
| C11×C4⋊Dic5 | 2 |
| C4×C11×Dic5 | 2 |
| C11×#117 | 5 |
| #4038 | 11 |