Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
| 2. C2×C4×D5×C11 | C2 | semidirect |
| 3. C2×C5×D44 | C2 | semidirect |
| 4. C2×#89167 | C2 | semidirect |
| 5. C2×Dic5×D11 | C2 | semidirect |
| 6. #11724982 | C2 | direct (N × H) |
| 11. Dic110 | C22 | semidirect |
| 13. C4×D5×C11 | C22 | semidirect |
| 14. C5×D44 | C22 | semidirect |
| 15. #89167 | C22 | semidirect |
| 16. Dic5×D11 | C22 | semidirect |
| 29. C2×D44 | D5 | semidirect |
| 33. C2×C5×C11 | #41 | semidirect |
| 44. D44 | C2×D5 | semidirect |
| 51. C2×C4×D5 | D11 | semidirect |
| 53. C5×C11 | C2×#41 | semidirect |
| 70. C4×D5 | C2×D11 | semidirect |
| 74. C2×C11 | #711 | semidirect |
| 91. C11 | C2×#711 | semidirect |
| 93. C2×C5 | #4339 | semidirect |
| 106. C5 | C2×#4339 | semidirect |
| 117. C2 | #11724982 | 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×D44 | 2 |
| C2×#89167 | 2 |
| C2×Dic5×D11 | 2 |
| #11724982 | 2 |
| C2×#4339 | 5 |
| C2×#711 | 11 |