Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1128 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 391 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 |
|---|---|---|
| 2. #10615515 | C2 | semidirect |
| 3. #10615511 | C2 | semidirect |
| 4. #10602869 | C2 | semidirect |
| 5. C2×#64786 | C2 | semidirect |
| 7. C5×#578 | C4 | semidirect |
| 9. C5×#576 | C4 | semidirect |
| 16. #65395 | C22 | semidirect |
| 17. C2×#3949 | C22 | semidirect |
| 18. C2×#3944 | C22 | semidirect |
| 19. #64786 | C22 | semidirect |
| 20. #64786 | C22 | semidirect |
| 33. C5×#135 | C2×C4 | semidirect |
| 35. C2×C5×Q16 | C2×C4 | semidirect |
| 37. C2×C5×D8 | C2×C4 | semidirect |
| 94. #578 | Dic5 | semidirect |
| 96. #576 | Dic5 | semidirect |
| 142. #135 | C2×Dic5 | semidirect |
| 144. C2×Q16 | C2×Dic5 | semidirect |
| 146. C2×D8 | C2×Dic5 | semidirect |
| 235. C5 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3584 | 2 |
| #10615515 | 2 |
| #10615511 | 2 |
| #10602869 | 2 |
| C2×#64786 | 2 |
| #33388 | 5 |