Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 98 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×#443 | C2 | semidirect |
| 2. C3×#65484 | C2 | semidirect |
| 4. C3×#64985 | C2 | semidirect |
| 5. C3×#64716 | C2 | semidirect |
| 6. C3×#64715 | C2 | semidirect |
| 7. C3×#64683 | C2 | semidirect |
| 8. #10601718 | C3 | direct (N × H) |
| 25. C5×#443 | C2×C3 | semidirect |
| 26. #65484 | C2×C3 | semidirect |
| 28. #64985 | C2×C3 | semidirect |
| 29. #64716 | C2×C3 | semidirect |
| 30. #64715 | C2×C3 | semidirect |
| 31. #64683 | C2×C3 | semidirect |
| 56. C3×#443 | D5 | semidirect |
| 132. #443 | C3×D5 | semidirect |
| 249. C3×C5 | #2212 | semidirect |
| 284. C5 | C3×#2212 | semidirect |
| 294. C3 | #10601718 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#443 | 2 |
| C3×#65484 | 2 |
| C3×#65482 | 2 |
| C3×#64985 | 2 |
| C3×#64716 | 2 |
| C3×#64715 | 2 |
| C3×#64683 | 2 |
| #10601718 | 3 |
| C3×#2212 | 5 |