Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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. C2×Dic110 | C2 | semidirect |
| 3. C2×C5×Dic22 | C2 | semidirect |
| 4. C2×#89170 | C2 | semidirect |
| 6. D5×Dic22 | C2 | direct (N × H) |
| 10. Dic110 | C22 | semidirect |
| 14. C5×Dic22 | C22 | semidirect |
| 15. #89170 | C22 | semidirect |
| 19. C2×D5×C11 | Q8 | semidirect |
| 30. C2×Dic22 | D5 | direct (N × H) |
| 32. C2×C5×C11 | C2×Q8 | semidirect |
| 34. D5×C11 | C2×Q8 | semidirect |
| 44. Dic22 | C2×D5 | direct (N × H) |
| 51. C5×C11 | C22×Q8 | semidirect |
| 71. C2×C11 | Q8×D5 | semidirect |
| 74. C2×D5 | Dic22 | direct (N × H) |
| 86. C11 | C2×Q8×D5 | semidirect |
| 87. C2×C5 | C2×Dic22 | semidirect |
| 89. D5 | C2×Dic22 | direct (N × H) |
| 100. C5 | C22×Dic22 | semidirect |
| 109. C2 | D5×Dic22 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic110 | 2 |
| C2×C4×D5×C11 | 2 |
| C2×C5×Dic22 | 2 |
| C2×#89170 | 2 |
| C2×D5×Dic11 | 2 |
| D5×Dic22 | 2 |
| C22×Dic22 | 5 |
| C2×Q8×D5 | 11 |