Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×Dic55 | C2 | semidirect |
| 3. C2×D5×Dic11 | C2 | semidirect |
| 4. C5×C22⋊Dic11 | C2 | semidirect |
| 5. #11724889 | C2 | semidirect |
| 6. #11724885 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 13. C11×C22⋊D5 | C4 | semidirect |
| 21. C22×C5×C11 | C2×C4 | semidirect |
| 25. C2×D5×C11 | C2×C4 | semidirect |
| 27. Dic55 | D4 | semidirect |
| 30. C11×Dic5 | C2×C4 | semidirect |
| 35. C22⋊Dic11 | D5 | semidirect |
| 61. C5×C11 | C4×D4 | semidirect |
| 67. C22×C11 | C4×D5 | semidirect |
| 78. C22⋊D5 | Dic11 | semidirect |
| 92. C22×C5 | C2×Dic11 | semidirect |
| 96. C2×D5 | C2×Dic11 | semidirect |
| 101. Dic5 | C2×Dic11 | semidirect |
| 109. C11 | #4027 | semidirect |
| 125. C5 | D4×Dic11 | semidirect |
| 131. C22 | D5×Dic11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic55 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C2×D5×Dic11 | 2 |
| C5×C22⋊Dic11 | 2 |
| #11724889 | 2 |
| #11724885 | 2 |
| Dic5×Dic11 | 2 |
| D4×Dic11 | 5 |
| #4027 | 11 |