Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 106 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×#442 | C2 | semidirect |
| 3. C3×#65006 | C2 | semidirect |
| 4. C3×#64783 | C2 | semidirect |
| 5. C3×#64708 | C2 | semidirect |
| 6. C3×#64707 | C2 | semidirect |
| 7. C3×#64686 | C2 | semidirect |
| 8. #10601711 | C3 | direct (N × H) |
| 16. C3×#3959 | C4 | semidirect |
| 17. C3×#3958 | C4 | semidirect |
| 23. C5×#442 | C2×C3 | semidirect |
| 25. #65006 | C2×C3 | semidirect |
| 26. #64783 | C2×C3 | semidirect |
| 27. #64708 | C2×C3 | semidirect |
| 28. #64707 | C2×C3 | semidirect |
| 29. #64686 | C2×C3 | semidirect |
| 41. C3×Dic20 | C2×C4 | semidirect |
| 42. C3×D40 | C2×C4 | semidirect |
| 47. C3×#672 | C2×C4 | semidirect |
| 50. C3×#442 | D5 | semidirect |
| 62. #3959 | C3×C4 | semidirect |
| 63. #3958 | C3×C4 | semidirect |
| 108. Dic20 | C2×C3×C4 | semidirect |
| 109. D40 | C2×C3×C4 | semidirect |
| 114. #672 | C2×C3×C4 | semidirect |
| 117. #442 | C3×D5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | C3×AGL(1,ℤ/16) | semidirect |
| 270. C3 | #10601711 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#442 | 2 |
| C3×#65436 | 2 |
| C3×#65006 | 2 |
| C3×#64783 | 2 |
| C3×#64708 | 2 |
| C3×#64707 | 2 |
| C3×#64686 | 2 |
| #10601711 | 3 |
| C3×AGL(1,ℤ/16) | 5 |