Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
268 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×C5×#430 | C2 | semidirect |
| 3. C5×#4553 | C2 | semidirect |
| 4. C5×#4495 | C2 | semidirect |
| 5. C5×#4494 | C2 | semidirect |
| 16. #70723 | C5 | direct (N × H) |
| 18. C5×#430 | D3 | semidirect |
| 35. C3×#430 | C2×C5 | semidirect |
| 37. #4553 | C2×C5 | semidirect |
| 38. #4495 | C2×C5 | semidirect |
| 39. #4494 | C2×C5 | semidirect |
| 86. #430 | C5×D3 | semidirect |
| 175. C3×C5 | #2238 | semidirect |
| 207. C5 | #70723 | direct (N × H) |
| 218. C3 | C5×#2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#430 | 2 |
| C5×#5135 | 2 |
| C5×#4553 | 2 |
| C5×#4495 | 2 |
| C5×#4494 | 2 |
| C5×#2238 | 3 |
| #70723 | 5 |