Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
184 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 4. #11724930 | C2 | semidirect |
| 5. C5×Dic11⋊C4 | C2 | semidirect |
| 6. #11724888 | C2 | semidirect |
| 7. Dic11⋊Dic5 | C2 | semidirect |
| 17. D5×Dic11 | C4 | semidirect |
| 25. Dic55 | C2×C4 | semidirect |
| 27. C5×Dic11 | C2×C4 | semidirect |
| 35. Dic11⋊C4 | D5 | direct (N × H) |
| 40. D5×C11 | C4⋊C4 | semidirect |
| 58. C5×C11 | C2×C4⋊C4 | semidirect |
| 68. Dic11 | C4×D5 | semidirect |
| 101. C11 | D5×C4⋊C4 | semidirect |
| 105. D5 | Dic11⋊C4 | direct (N × H) |
| 116. C5 | C2×Dic11⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5×C11 | 2 |
| C2×D5×Dic11 | 2 |
| #11724930 | 2 |
| C5×Dic11⋊C4 | 2 |
| #11724888 | 2 |
| Dic11⋊Dic5 | 2 |
| C2×Dic11⋊C4 | 5 |
| D5×C4⋊C4 | 11 |