Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 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. C4×C5×D16 | C2 | semidirect |
| 3. C4×D80 | C2 | semidirect |
| 4. #10598315 | C2 | semidirect |
| 5. #10598068 | C2 | semidirect |
| 6. #10598066 | C2 | semidirect |
| 7. C4×#3926 | C2 | semidirect |
| 15. #64739 | C4 | direct (N × H) |
| 26. C5×D16 | C2×C4 | semidirect |
| 35. D80 | C2×C4 | semidirect |
| 37. #3926 | C2×C4 | semidirect |
| 40. C4×D16 | D5 | semidirect |
| 98. D16 | C4×D5 | semidirect |
| 117. C4×C5 | D32 | semidirect |
| 160. C5 | C4×D32 | semidirect |
| 171. C4 | #64739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D16 | 2 |
| C2×#64739 | 2 |
| C4×D80 | 2 |
| #10598315 | 2 |
| #10598068 | 2 |
| #10598066 | 2 |
| C4×#3926 | 2 |
| C4×D32 | 5 |