Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C3×C5×Q32 | C2 | semidirect |
| 4. C2×C5×#829 | C2 | semidirect |
| 5. C5×#4564 | C2 | semidirect |
| 7. C5×#4503 | C2 | semidirect |
| 24. #71502 | C5 | direct (N × H) |
| 27. C2×C5×Q32 | D3 | semidirect |
| 57. C2×C3×Q32 | C2×C5 | semidirect |
| 59. C2×#829 | C2×C5 | semidirect |
| 60. #4564 | C2×C5 | semidirect |
| 62. #4503 | C2×C5 | semidirect |
| 140. C2×Q32 | C5×D3 | semidirect |
| 148. C2×C5×D3 | Q32 | semidirect |
| 274. C3×C5 | #2188 | semidirect |
| 278. C2×D3 | C5×Q32 | semidirect |
| 314. C5 | #71502 | direct (N × H) |
| 326. C3 | C5×#2188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q16 | 2 |
| C2×C3×C5×Q32 | 2 |
| C5×#5188 | 2 |
| C2×C5×#829 | 2 |
| C5×#4564 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C5×#4503 | 2 |
| C5×#2188 | 3 |
| #71502 | 5 |