Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×C5×#985 | C2 | semidirect |
| 2. C2×C5×#983 | C2 | semidirect |
| 3. C5×#548⋊C3 | C2 | semidirect |
| 4. C5×#5427 | C2 | semidirect |
| 5. C5×#5421 | C2 | semidirect |
| 6. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 7. C5×#5388 | C2 | semidirect |
| 19. #85385 | C5 | direct (N × H) |
| 23. C5×#548 | D3 | semidirect |
| 44. C5×#226 | D4 | semidirect |
| 48. C2×#985 | C2×C5 | semidirect |
| 49. C2×#983 | C2×C5 | semidirect |
| 50. #548⋊C3 | C2×C5 | semidirect |
| 51. #5427 | C2×C5 | semidirect |
| 52. #5421 | C2×C5 | semidirect |
| 53. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 54. #5388 | C2×C5 | semidirect |
| 178. #548 | C5×D3 | semidirect |
| 213. #226 | C5×D4 | semidirect |
| 461. C5 | #85385 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#985 | 2 |
| C2×C5×#983 | 2 |
| C5×#548⋊C3 | 2 |
| C5×#5427 | 2 |
| C5×#5421 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×#5388 | 2 |
| C5×#3271 | 3 |
| C5×#884 | 4 |
| #85385 | 5 |