Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 88 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. C5×#4831 | C2 | semidirect |
| 2. #11747078 | C2 | semidirect |
| 3. #11747068 | C2 | semidirect |
| 5. #11746306 | C2 | semidirect |
| 6. C3×#64705 | C2 | semidirect |
| 7. #11745866 | C2 | semidirect |
| 30. #64705 | D3 | semidirect |
| 55. #4831 | D5 | semidirect |
| 98. C5×C3⋊C8 | SD16 | semidirect |
| 242. C3⋊C8 | #688 | semidirect |
| 277. C3×C5 | #1688 | semidirect |
| 326. C5 | #68413 | semidirect |
| 341. C3 | #10601752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4831 | 2 |
| #11747078 | 2 |
| #11747068 | 2 |
| #11747035 | 2 |
| #11746306 | 2 |
| C3×#64705 | 2 |
| #11745866 | 2 |
| #10601752 | 3 |
| #68413 | 5 |