Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
458 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×C5×#365 | C2 | semidirect |
| 3. C2×#64736 | C2 | semidirect |
| 4. C2×#64734 | C2 | semidirect |
| 5. #10601505 | C2 | semidirect |
| 6. C2×#64715 | C2 | semidirect |
| 7. #10598211 | C2 | semidirect |
| 50. C5×M32 | D4 | semidirect |
| 64. C2×#365 | D5 | semidirect |
| 197. M32 | D20 | semidirect |
| 317. C5 | #13398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65154 | 2 |
| C2×C5×#365 | 2 |
| C2×#64736 | 2 |
| C2×#64734 | 2 |
| #10601505 | 2 |
| C2×#64715 | 2 |
| #10598211 | 2 |
| #13398 | 5 |