Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
508 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 508 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. C3×C5×#398 | C2 | semidirect |
| 3. C5×#4967 | C2 | semidirect |
| 4. C5×#4528 | C2 | semidirect |
| 5. C5×#4451 | C2 | semidirect |
| 20. #69712 | C5 | direct (N × H) |
| 23. C5×#398 | D3 | semidirect |
| 48. C3×#398 | C2×C5 | semidirect |
| 49. #4967 | C2×C5 | semidirect |
| 50. #4528 | C2×C5 | semidirect |
| 51. #4451 | C2×C5 | semidirect |
| 126. #398 | C5×D3 | semidirect |
| 266. C3×C5 | #1610 | semidirect |
| 317. C5 | #69712 | direct (N × H) |
| 332. C3 | C5×#1610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5510 | 2 |
| C3×C5×#398 | 2 |
| C5×#4967 | 2 |
| C5×#4528 | 2 |
| C5×#4451 | 2 |
| C5×#1610 | 3 |
| #69712 | 5 |