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. C3×#64766 | C2 | semidirect |
| 5. C3×Q8⋊#168 | C2 | semidirect |
| 6. #10602732 | C3 | direct (N × H) |
| 19. C5×Q82 | C2×C3 | semidirect |
| 22. #64766 | C2×C3 | semidirect |
| 23. Q8⋊#168 | C2×C3 | semidirect |
| 40. C3×Q82 | D5 | semidirect |
| 61. C3×C5×Q8 | SD16 | semidirect |
| 99. Q82 | C3×D5 | semidirect |
| 133. C5×Q8 | C3×SD16 | semidirect |
| 162. C3×Q8 | #688 | semidirect |
| 198. C3×C5 | #1623 | semidirect |
| 215. Q8 | C3×#688 | semidirect |
| 229. C5 | C3×#1623 | semidirect |
| 239. C3 | #10602732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×Q82 | 2 |
| C3×#65374 | 2 |
| C3×#65316 | 2 |
| C3×#64766 | 2 |
| C3×Q8⋊#168 | 2 |
| #10602732 | 3 |
| C3×#1623 | 5 |