Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 396 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×#500 | C2 | semidirect |
| 4. C3×#65370 | C2 | semidirect |
| 5. C3×#65368 | C2 | semidirect |
| 7. C3×#64675 | C2 | semidirect |
| 8. #10602156 | C3 | direct (N × H) |
| 23. C5×#500 | C2×C3 | semidirect |
| 26. #65370 | C2×C3 | semidirect |
| 27. #65368 | C2×C3 | semidirect |
| 29. #64675 | C2×C3 | semidirect |
| 48. C3×#500 | D5 | semidirect |
| 82. C3×C5×C8 | SD16 | semidirect |
| 116. #500 | C3×D5 | semidirect |
| 164. C5×C8 | C3×SD16 | semidirect |
| 199. C3×C8 | #688 | semidirect |
| 228. C3×C5 | #1714 | semidirect |
| 258. C8 | C3×#688 | semidirect |
| 263. C5 | C3×#1714 | semidirect |
| 274. C3 | #10602156 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C3×#65377 | 2 |
| C3×#65374 | 2 |
| C3×#65370 | 2 |
| C3×#65368 | 2 |
| C3×#64982 | 2 |
| C3×#64675 | 2 |
| #10602156 | 3 |
| C3×#1714 | 5 |