Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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. C5×#4707 | C2 | semidirect |
| 3. C3×C5×#329 | C2 | semidirect |
| 4. C5×#4540 | C2 | semidirect |
| 5. C5×#4464 | C2 | semidirect |
| 20. #68342 | C5 | direct (N × H) |
| 25. C5×#329 | D3 | semidirect |
| 49. #4707 | C2×C5 | semidirect |
| 50. C3×#329 | C2×C5 | semidirect |
| 51. #4540 | C2×C5 | semidirect |
| 52. #4464 | C2×C5 | semidirect |
| 128. #329 | C5×D3 | semidirect |
| 261. C3×C5 | #1525 | semidirect |
| 307. C5 | #68342 | direct (N × H) |
| 321. C3 | C5×#1525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5668 | 2 |
| C5×#4707 | 2 |
| C3×C5×#329 | 2 |
| C5×#4540 | 2 |
| C5×#4464 | 2 |
| C5×#1525 | 3 |
| #68342 | 5 |