Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×D5×Dic11 | C2 | semidirect |
| 3. C4⋊Dic55 | C2 | semidirect |
| 4. C4×C5×Dic11 | C2 | semidirect |
| 5. #11724885 | C2 | semidirect |
| 9. C11×D20 | C4 | semidirect |
| 17. C2×D5×C11 | C2×C4 | semidirect |
| 18. C4×C5×C11 | C2×C4 | semidirect |
| 21. C5×Dic11 | D4 | semidirect |
| 26. C4×Dic11 | D5 | semidirect |
| 44. C5×C11 | C4×D4 | semidirect |
| 49. C4×C11 | C4×D5 | semidirect |
| 52. Dic11 | D20 | direct (N × H) |
| 58. D20 | Dic11 | direct (N × H) |
| 68. C2×D5 | C2×Dic11 | semidirect |
| 71. C4×C5 | C2×Dic11 | semidirect |
| 78. C11 | C4×D20 | semidirect |
| 90. C5 | D4×Dic11 | semidirect |
| 98. C4 | D5×Dic11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×D20 | 2 |
| C2×D5×Dic11 | 2 |
| C4⋊Dic55 | 2 |
| C4×C5×Dic11 | 2 |
| #11724885 | 2 |
| D4×Dic11 | 5 |
| C4×D20 | 11 |