Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
334 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×D5×D16 | C2 | semidirect |
| 2. C2×C5×D32 | C2 | semidirect |
| 3. #10602262 | C2 | semidirect |
| 4. C2×#64739 | C2 | semidirect |
| 5. #10598315 | C2 | semidirect |
| 6. #10598087 | C2 | semidirect |
| 7. #10598085 | C2 | semidirect |
| 10. C2×C5×D16 | C22 | semidirect |
| 18. C2×C5×C32 | C22 | semidirect |
| 21. #64724 | C22 | semidirect |
| 22. C2×#3926 | C22 | semidirect |
| 36. C5×D16 | D4 | semidirect |
| 43. D80 | D4 | semidirect |
| 50. C2×D32 | D5 | semidirect |
| 86. C2×D16 | C2×D5 | semidirect |
| 92. C2×C32 | C2×D5 | semidirect |
| 133. D16 | C22⋊D5 | semidirect |
| 155. C2×D5 | D32 | semidirect |
| 215. C5 | #13661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D16 | 2 |
| C2×C5×D32 | 2 |
| #10602262 | 2 |
| C2×#64739 | 2 |
| #10598315 | 2 |
| #10598087 | 2 |
| #10598085 | 2 |
| #13661 | 5 |