Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
184 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. C4⋊Dic55 | C2 | semidirect |
| 4. C11×C4⋊Dic5 | C2 | semidirect |
| 5. Dic11⋊Dic5 | C2 | semidirect |
| 11. C4×C5×D11 | C4 | semidirect |
| 18. C4×C5×C11 | C2×C4 | semidirect |
| 20. C5×Dic11 | C2×C4 | semidirect |
| 31. C5×D11 | C4⋊C4 | semidirect |
| 38. C4×D11 | Dic5 | semidirect |
| 43. C4⋊Dic5 | D11 | direct (N × H) |
| 44. C5×C11 | C2×C4⋊C4 | semidirect |
| 50. C4×C11 | C2×Dic5 | semidirect |
| 52. Dic11 | C2×Dic5 | semidirect |
| 64. D11 | C4⋊Dic5 | direct (N × H) |
| 70. C4×C5 | C4×D11 | semidirect |
| 78. C11 | C2×C4⋊Dic5 | semidirect |
| 90. C5 | C4⋊C4×D11 | semidirect |
| 98. C4 | Dic5×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D11 | 2 |
| C2×Dic5×D11 | 2 |
| C4⋊Dic55 | 2 |
| C11×C4⋊Dic5 | 2 |
| Dic11⋊Dic5 | 2 |
| C4⋊C4×D11 | 5 |
| C2×C4⋊Dic5 | 11 |