Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 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×#89170 | C2 | semidirect |
| 3. #11724932 | C2 | semidirect |
| 4. C4×C11×Dic5 | C2 | semidirect |
| 5. C5×(C2×D11)⋊C4 | C2 | semidirect |
| 6. #11724886 | C2 | semidirect |
| 7. (C2×D11)⋊Dic5 | C2 | semidirect |
| 36. (C2×D11)⋊C4 | D5 | semidirect |
| 58. C4×Dic5 | D11 | semidirect |
| 59. C5×C11 | #124 | semidirect |
| 106. C11 | #4031 | semidirect |
| 121. C5 | #66928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89170 | 2 |
| C2×#89168 | 2 |
| #11724932 | 2 |
| C4×C11×Dic5 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| #11724886 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| #66928 | 5 |
| #4031 | 11 |