Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11751669 | C2 | semidirect |
| 4. C16×ΓL(1,𝔽16) | C2 | semidirect |
| 5. C3×#64850 | C2 | semidirect |
| 6. #11746458 | C2 | semidirect |
| 19. #91084 | C4 | semidirect |
| 20. C5×#800 | C4 | semidirect |
| 22. #90945 | C4 | semidirect |
| 23. #90944 | C4 | semidirect |
| 30. #64850 | D3 | semidirect |
| 42. Dic60 | C2×C4 | semidirect |
| 44. C5×Dic12 | C2×C4 | semidirect |
| 50. C3×C5×C16 | C2×C4 | semidirect |
| 51. C3×#672 | C2×C4 | semidirect |
| 106. #800 | AGL(1,𝔽5) | semidirect |
| 125. C5×C16 | C4×D3 | semidirect |
| 126. #672 | C4×D3 | semidirect |
| 140. ΓL(1,𝔽16) | SD32 | semidirect |
| 160. Dic12 | C2×AGL(1,𝔽5) | semidirect |
| 165. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 253. C16 | D3×AGL(1,𝔽5) | semidirect |
| 254. C3×C5 | C4×SD32 | semidirect |
| 295. C5 | #69337 | semidirect |
| 309. C3 | AGL(1,𝔽5)×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751669 | 2 |
| #11751664 | 2 |
| D5×#800 | 2 |
| C16×ΓL(1,𝔽16) | 2 |
| C3×#64850 | 2 |
| #11746458 | 2 |
| #11746456 | 2 |
| AGL(1,𝔽5)×SD32 | 3 |
| #69337 | 5 |