Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 452 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×#563 | C2 | semidirect |
| 4. C5×#4541 | C2 | semidirect |
| 5. C5×#4539 | C2 | semidirect |
| 20. #71958 | C5 | direct (N × H) |
| 21. C5×#563 | D3 | semidirect |
| 50. C3×#563 | C2×C5 | semidirect |
| 53. #4541 | C2×C5 | semidirect |
| 54. #4539 | C2×C5 | semidirect |
| 125. #563 | C5×D3 | semidirect |
| 257. C3×C5 | #2201 | semidirect |
| 297. C5 | #71958 | direct (N × H) |
| 310. C3 | C5×#2201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#563 | 2 |
| C5×#5061 | 2 |
| C5×#5053 | 2 |
| C5×#4541 | 2 |
| C5×#4539 | 2 |
| C5×#2201 | 3 |
| #71958 | 5 |