Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 82 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×C3×C5×Q32 | C2 | semidirect |
| 3. C5×#4522 | C2 | semidirect |
| 4. C5×#4521 | C2 | semidirect |
| 5. C5×#4499 | C2 | semidirect |
| 16. #71493 | C5 | direct (N × H) |
| 18. C2×C5×Q32 | D3 | semidirect |
| 32. C2×C3×Q32 | C2×C5 | semidirect |
| 34. #4522 | C2×C5 | semidirect |
| 35. #4521 | C2×C5 | semidirect |
| 36. #4499 | C2×C5 | semidirect |
| 77. C2×Q32 | C5×D3 | semidirect |
| 145. C3×C5 | #2264 | semidirect |
| 168. C5 | #71493 | direct (N × H) |
| 175. C3 | C5×#2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q32 | 2 |
| C5×#4904 | 2 |
| C5×#4522 | 2 |
| C5×#4521 | 2 |
| C5×#4499 | 2 |
| C5×#2264 | 3 |
| #71493 | 5 |