Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
448 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 448 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×#486 | C2 | semidirect |
| 2. C3×#65374 | C2 | semidirect |
| 3. C3×#65367 | C2 | semidirect |
| 4. C3×#65365 | C2 | semidirect |
| 6. C3×#64983 | C2 | semidirect |
| 7. C3×C8×#168 | C2 | semidirect |
| 8. #10601973 | C3 | direct (N × H) |
| 23. C5×#486 | C2×C3 | semidirect |
| 24. #65374 | C2×C3 | semidirect |
| 25. #65367 | C2×C3 | semidirect |
| 26. #65365 | C2×C3 | semidirect |
| 28. #64983 | C2×C3 | semidirect |
| 29. C8×#168 | C2×C3 | semidirect |
| 54. C3×#486 | D5 | semidirect |
| 86. C3×#168 | D8 | semidirect |
| 87. C3×#168 | SD16 | semidirect |
| 125. #486 | C3×D5 | semidirect |
| 174. #168 | C3×D8 | semidirect |
| 175. #168 | C3×SD16 | semidirect |
| 243. C3×C5 | #1706 | semidirect |
| 284. C5 | C3×#1706 | semidirect |
| 297. C3 | #10601973 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#486 | 2 |
| C3×#65374 | 2 |
| C3×#65367 | 2 |
| C3×#65365 | 2 |
| C3×#65362 | 2 |
| C3×#64983 | 2 |
| C3×C8×#168 | 2 |
| #10601973 | 3 |
| C3×#1706 | 5 |