Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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. C5×#578⋊C3 | C2 | semidirect |
| 2. C5×#504⋊C3 | C2 | semidirect |
| 3. C5×#3417 | C3 | semidirect |
| 7. #3417⋊C3 | C5 | direct (N × H) |
| 8. C5×#578 | C2×C3 | semidirect |
| 12. C5×#504 | C2×C3 | semidirect |
| 17. #578⋊C3 | C2×C5 | semidirect |
| 18. #504⋊C3 | C2×C5 | semidirect |
| 30. #3417 | C3×C5 | semidirect |
| 50. #578 | C2×C3×C5 | semidirect |
| 54. #504 | C2×C3×C5 | semidirect |
| 125. C5 | #3417⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#578⋊C3 | 2 |
| C5×#504⋊C3 | 2 |
| C5×#3417 | 3 |
| C3×C5×D16 | 4 |
| #3417⋊C3 | 5 |