Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#64713 | C2 | semidirect |
| 4. #10601452 | C2 | semidirect |
| 6. C5×#1382 | C2 | semidirect |
| 7. #10598295 | C2 | semidirect |
| 21. #64712 | C4 | semidirect |
| 22. #64712 | C4 | semidirect |
| 23. #64711 | C4 | semidirect |
| 24. #64711 | C4 | semidirect |
| 66. #1382 | D5 | semidirect |
| 284. C5 | #13134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64730 | 2 |
| #10601489 | 2 |
| C2×#64713 | 2 |
| #10601452 | 2 |
| #10601444 | 2 |
| C5×#1382 | 2 |
| #10598295 | 2 |
| #13134 | 5 |