Finite Group DatabasebetaFinite Group DatabasebetaOrder 20160.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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. D5040 | C2 | semidirect |
| 10. C5×C7×C9×C32 | C2 | semidirect |
| 14. C7×C9×C32 | D5 | semidirect |
| 18. C5×C9×C32 | D7 | semidirect |
| 23. C5×C7×C32 | D9 | semidirect |
| 50. C5×C7×C9 | D32 | semidirect |
| 52. C9×C32 | D35 | semidirect |
| 60. C7×C32 | D45 | semidirect |
| 69. C5×C32 | D63 | semidirect |
| 94. C7×C9 | D160 | semidirect |
| 101. C5×C9 | D224 | semidirect |
| 108. C5×C7 | D288 | semidirect |
| 110. C32 | D315 | semidirect |
| 131. C9 | D1120 | semidirect |
| 134. C7 | D1440 | semidirect |
| 137. C5 | D2016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5040 | 2 |
| D3360 | 3 |
| D2016 | 5 |
| D1440 | 7 |
| C5×C7×C9×C32 | 2 |