Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1296 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 202 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. #11752349 | C2 | semidirect |
| 3. C3×#65690 | C2 | semidirect |
| 4. #11751933 | C2 | semidirect |
| 9. #91763 | C4 | semidirect |
| 10. C5×#874 | C4 | semidirect |
| 12. #91451 | C4 | semidirect |
| 19. #65690 | D3 | semidirect |
| 24. C2×D60 | C2×C4 | semidirect |
| 25. C2×C5×D12 | C2×C4 | semidirect |
| 27. C2×#1203 | C2×C4 | semidirect |
| 31. C3×C42×C5 | C2×C4 | semidirect |
| 32. C3×C4×Dic5 | C2×C4 | semidirect |
| 67. #874 | AGL(1,𝔽5) | semidirect |
| 81. C42×C5 | C4×D3 | semidirect |
| 82. C4×Dic5 | C4×D3 | semidirect |
| 105. C2×D12 | C2×AGL(1,𝔽5) | semidirect |
| 108. C3×C42 | C2×AGL(1,𝔽5) | semidirect |
| 173. C42 | D3×AGL(1,𝔽5) | semidirect |
| 174. C3×C5 | #2380 | semidirect |
| 207. C5 | #74298 | semidirect |
| 218. C3 | #10617370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#874 | 2 |
| #11752349 | 2 |
| C3×#65690 | 2 |
| #11751933 | 2 |
| #10617370 | 3 |
| #74298 | 5 |