Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
724 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 724 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. #11756837 | C2 | semidirect |
| 3. D5⋊#823 | C2 | semidirect |
| 4. #11751719 | C2 | semidirect |
| 5. #11751718 | C2 | semidirect |
| 6. #11746734 | C2 | semidirect |
| 7. C3×#64863 | C2 | semidirect |
| 18. #91764 | C4 | semidirect |
| 19. C5×#874 | C4 | semidirect |
| 22. #91451 | C4 | semidirect |
| 24. #91373 | C4 | semidirect |
| 35. #64863 | D3 | semidirect |
| 39. C2×Dic30 | C2×C4 | semidirect |
| 42. C2×C5×D12 | C2×C4 | semidirect |
| 59. C4×ΓL(1,𝔽16) | D4 | semidirect |
| 65. C3×C4×AGL(1,𝔽5) | D4 | semidirect |
| 69. C3×C42×C5 | C2×C4 | semidirect |
| 73. C3×C4×Dic5 | C2×C4 | semidirect |
| 153. #874 | AGL(1,𝔽5) | semidirect |
| 186. C4×AGL(1,𝔽5) | D12 | semidirect |
| 191. C42×C5 | C4×D3 | semidirect |
| 196. C4×Dic5 | C4×D3 | semidirect |
| 241. C2×D12 | C2×AGL(1,𝔽5) | semidirect |
| 254. C3×C42 | C2×AGL(1,𝔽5) | semidirect |
| 423. C42 | D3×AGL(1,𝔽5) | semidirect |
| 424. C3×C5 | #1911 | semidirect |
| 497. C5 | #68705 | semidirect |
| 519. C3 | #10604615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756837 | 2 |
| #11752733 | 2 |
| D5⋊#823 | 2 |
| #11751719 | 2 |
| #11751718 | 2 |
| #11746734 | 2 |
| C3×#64863 | 2 |
| #10604615 | 3 |
| #68705 | 5 |