Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 4. #10598030 | C2 | direct (N × H) |
| 6. C2×#4016 | C4 | semidirect |
| 13. #65360 | C4 | semidirect |
| 15. C2×#3935 | C4 | semidirect |
| 37. #4016 | C2×C4 | semidirect |
| 47. #3935 | C2×C4 | semidirect |
| 230. C2×C5 | #1412 | semidirect |
| 267. C5 | C2×#1412 | semidirect |
| 297. C2 | #10598030 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65360 | 2 |
| C2×C5×#353 | 2 |
| C2×#64765 | 2 |
| #10598030 | 2 |
| C2×#1412 | 5 |