Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2334 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 747 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. C23×Dic20 | C2 | semidirect |
| 3. C23×C5×C16 | C2 | semidirect |
| 4. C22×#3932 | C2 | direct (N × H) |
| 9. C22×Dic20 | C22 | semidirect |
| 12. C22×C5×C16 | C22 | semidirect |
| 13. C2×#3932 | C22 | direct (N × H) |
| 25. C2×Dic20 | C23 | semidirect |
| 28. C2×C5×C16 | C23 | semidirect |
| 29. #3932 | C23 | direct (N × H) |
| 33. C23×C16 | D5 | semidirect |
| 47. Dic20 | C24 | semidirect |
| 50. C5×C16 | C24 | semidirect |
| 59. C22×C16 | C2×D5 | semidirect |
| 60. C23×C5 | SD32 | semidirect |
| 87. C2×C16 | C22×D5 | semidirect |
| 88. C22×C5 | C2×SD32 | semidirect |
| 111. C16 | C23×D5 | semidirect |
| 112. C2×C5 | C22×SD32 | semidirect |
| 117. C23 | #3932 | direct (N × H) |
| 128. C5 | C23×SD32 | semidirect |
| 131. C22 | C2×#3932 | direct (N × H) |
| 137. C2 | C22×#3932 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic20 | 2 |
| C23×D40 | 2 |
| C23×C5×C16 | 2 |
| C22×#3932 | 2 |
| C23×SD32 | 5 |