Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 122 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×#486 | C2 | semidirect |
| 2. C5×#5085 | C2 | semidirect |
| 3. C5×#5080 | C2 | semidirect |
| 5. C5×#5070 | C2 | semidirect |
| 6. C5×#4693 | C2 | semidirect |
| 7. C5×#4454 | C2 | semidirect |
| 22. #71185 | C5 | direct (N × H) |
| 28. C5×#486 | D3 | semidirect |
| 49. C3×#486 | C2×C5 | semidirect |
| 50. #5085 | C2×C5 | semidirect |
| 51. #5080 | C2×C5 | semidirect |
| 53. #5070 | C2×C5 | semidirect |
| 54. #4693 | C2×C5 | semidirect |
| 55. #4454 | C2×C5 | semidirect |
| 87. C5×C3⋊C8 | SD16 | semidirect |
| 125. #486 | C5×D3 | semidirect |
| 211. C3⋊C8 | C5×SD16 | semidirect |
| 243. C3×C5 | #1715 | semidirect |
| 284. C5 | #71185 | direct (N × H) |
| 297. C3 | C5×#1715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#486 | 2 |
| C5×#5085 | 2 |
| C5×#5080 | 2 |
| C5×#5073 | 2 |
| C5×#5070 | 2 |
| C5×#4693 | 2 |
| C5×#4454 | 2 |
| C5×#1715 | 3 |
| #71185 | 5 |