Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10605088 | C2 | semidirect |
| 5. #10598169 | C2 | semidirect |
| 6. #10598167 | C2 | semidirect |
| 7. #10598103 | C2 | semidirect |
| 29. C22×C5×D4 | Q8 | semidirect |
| 38. C2×C5×C4⋊C4 | Q8 | semidirect |
| 214. C22×D4 | Dic10 | semidirect |
| 232. C2×C4⋊C4 | Dic10 | semidirect |
| 414. C5 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605088 | 2 |
| C2×C5×#327 | 2 |
| #10602479 | 2 |
| #10602468 | 2 |
| #10598169 | 2 |
| #10598167 | 2 |
| #10598103 | 2 |
| #10374 | 5 |