Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 130 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×Q82 | C2 | semidirect |
| 4. C5×#4546 | C2 | semidirect |
| 5. C5×#4535 | C2 | semidirect |
| 18. #71939 | C5 | direct (N × H) |
| 19. C5×Q82 | D3 | semidirect |
| 40. C3×Q82 | C2×C5 | semidirect |
| 43. #4546 | C2×C5 | semidirect |
| 44. #4535 | C2×C5 | semidirect |
| 61. C3×C5×Q8 | SD16 | semidirect |
| 99. Q82 | C5×D3 | semidirect |
| 133. C5×Q8 | #215 | semidirect |
| 162. C3×Q8 | C5×SD16 | semidirect |
| 198. C3×C5 | #1623 | semidirect |
| 215. Q8 | C5×#215 | semidirect |
| 229. C5 | #71939 | direct (N × H) |
| 239. C3 | C5×#1623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×Q82 | 2 |
| C5×#5085 | 2 |
| C5×#5027 | 2 |
| C5×#4546 | 2 |
| C5×#4535 | 2 |
| C5×#1623 | 3 |
| #71939 | 5 |