Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 56 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×C5×Dic22 | C2 | semidirect |
| 3. C4⋊Dic55 | C2 | semidirect |
| 4. #11724888 | C2 | semidirect |
| 17. C2×D5×C11 | Q8 | semidirect |
| 23. C2×Dic22 | D5 | semidirect |
| 44. C5×C11 | C22⋊Q8 | semidirect |
| 68. C2×D5 | Dic22 | semidirect |
| 78. C11 | #4092 | semidirect |
| 90. C5 | #66977 | 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×C5×Dic22 | 2 |
| C4⋊Dic55 | 2 |
| #11724888 | 2 |
| #11724885 | 2 |
| #66977 | 5 |
| #4092 | 11 |