Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
648 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11756822 | C2 | semidirect |
| 3. D5⋊#823 | C2 | semidirect |
| 4. #11751719 | C2 | semidirect |
| 5. #11751706 | C2 | semidirect |
| 6. #11746768 | C2 | semidirect |
| 7. C3×#64894 | C2 | semidirect |
| 18. C2×#6706 | C4 | semidirect |
| 19. C2×C5×D24 | C4 | semidirect |
| 21. C2×#6659 | C4 | semidirect |
| 22. C2×#6654 | C4 | semidirect |
| 35. #64894 | D3 | semidirect |
| 148. C2×D24 | AGL(1,𝔽5) | semidirect |
| 409. C3×C5 | #1903 | semidirect |
| 476. C5 | #69038 | semidirect |
| 495. C3 | #10604805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756822 | 2 |
| C2×#91250 | 2 |
| D5⋊#823 | 2 |
| #11751719 | 2 |
| #11751706 | 2 |
| #11746768 | 2 |
| C3×#64894 | 2 |
| #10604805 | 3 |
| #69038 | 5 |