Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 440 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×#498 | C2 | semidirect |
| 2. C5×#5088 | C2 | semidirect |
| 3. C5×#5085 | C2 | semidirect |
| 5. C5×#4455 | C2 | semidirect |
| 16. #71336 | C5 | direct (N × H) |
| 17. C5×#498 | D3 | semidirect |
| 34. C3×#498 | C2×C5 | semidirect |
| 35. #5088 | C2×C5 | semidirect |
| 36. #5085 | C2×C5 | semidirect |
| 38. #4455 | C2×C5 | semidirect |
| 59. C3×C5×C8 | SD16 | semidirect |
| 82. #498 | C5×D3 | semidirect |
| 118. C5×C8 | #215 | semidirect |
| 142. C3×C8 | C5×SD16 | semidirect |
| 164. C3×C5 | #1715 | semidirect |
| 188. C8 | C5×#215 | semidirect |
| 193. C5 | #71336 | direct (N × H) |
| 202. 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×#498 | 2 |
| C5×#5088 | 2 |
| C5×#5085 | 2 |
| C5×#4695 | 2 |
| C5×#4455 | 2 |
| C5×#1715 | 3 |
| #71336 | 5 |