Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
560 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 146 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×#493 | C2 | semidirect |
| 2. C5×#5073 | C2 | semidirect |
| 3. C5×#4695 | C2 | semidirect |
| 4. C5×C8×C3⋊C8 | C2 | semidirect |
| 13. #71276 | C5 | direct (N × H) |
| 16. C5×#493 | D3 | semidirect |
| 28. C3×#493 | C2×C5 | semidirect |
| 29. #5073 | C2×C5 | semidirect |
| 30. #4695 | C2×C5 | semidirect |
| 31. C8×C3⋊C8 | C2×C5 | semidirect |
| 48. C3×C5×C8 | D8 | semidirect |
| 49. C5×C3⋊C8 | D8 | semidirect |
| 69. #493 | C5×D3 | semidirect |
| 97. C5×C8 | #213 | semidirect |
| 117. C3×C8 | C5×D8 | semidirect |
| 118. C3⋊C8 | C5×D8 | semidirect |
| 136. C3×C5 | #1712 | semidirect |
| 157. C8 | C5×#213 | semidirect |
| 162. C5 | #71276 | direct (N × H) |
| 170. C3 | C5×#1712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C5×#5073 | 2 |
| C5×#4695 | 2 |
| C5×C8×C3⋊C8 | 2 |
| C5×#1712 | 3 |
| #71276 | 5 |