Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
564 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 110 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. #10617089 | C2 | semidirect |
| 3. #10604290 | C2 | semidirect |
| 4. #10604270 | C2 | semidirect |
| 5. #10604270 | C2 | semidirect |
| 6. #10598774 | C2 | semidirect |
| 7. #10598773 | C2 | semidirect |
| 42. C2×D40 | C8 | semidirect |
| 93. C2×D20 | C2×C8 | semidirect |
| 108. C2×C5×C8 | C2×C8 | semidirect |
| 291. C2×C8 | D5⋊C8 | semidirect |
| 356. C5 | #9089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617089 | 2 |
| C2×#65158 | 2 |
| #10604290 | 2 |
| #10604270 | 2 |
| #10598774 | 2 |
| #10598773 | 2 |
| #9089 | 5 |