Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C5×#500 | C2 | semidirect |
| 4. #10598213 | C2 | semidirect |
| 5. #10598148 | C2 | semidirect |
| 33. C2×D40 | Q8 | semidirect |
| 43. C2×#500 | D5 | semidirect |
| 250. C5 | #13363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#500 | 2 |
| C2×#64711 | 2 |
| #10600569 | 2 |
| #10598213 | 2 |
| #10598148 | 2 |
| #13363 | 5 |