Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×C5×Q32 | C2 | semidirect |
| 3. #10615605 | C2 | semidirect |
| 5. #10602854 | C2 | semidirect |
| 6. #10602291 | C2 | semidirect |
| 7. #10602290 | C2 | semidirect |
| 9. #10602194 | C2 | semidirect |
| 79. C22×Q32 | D5 | semidirect |
| 325. C5 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Q32 | 2 |
| #10615612 | 2 |
| #10615605 | 2 |
| C2×#65468 | 2 |
| #10602854 | 2 |
| #10602291 | 2 |
| #10602290 | 2 |
| #10602205 | 2 |
| #10602194 | 2 |
| #33588 | 5 |