Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11751670 | C2 | semidirect |
| 4. #11746716 | C2 | semidirect |
| 5. C3×ΓL(1,𝔽81) | C2 | semidirect |
| 6. #11746470 | C2 | semidirect |
| 19. Dic120 | C4 | semidirect |
| 20. C5×#800 | C4 | semidirect |
| 22. #90948 | C4 | semidirect |
| 23. #90944 | C4 | semidirect |
| 30. ΓL(1,𝔽81) | D3 | semidirect |
| 104. #800 | AGL(1,𝔽5) | semidirect |
| 238. C3×C5 | #2180 | semidirect |
| 269. C5 | #69309 | semidirect |
| 279. C3 | #10604131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751687 | 2 |
| #11751670 | 2 |
| #11746828 | 2 |
| #11746716 | 2 |
| C3×ΓL(1,𝔽81) | 2 |
| #11746470 | 2 |
| #11746464 | 2 |
| #10604131 | 3 |
| #69309 | 5 |