Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 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. #10615536 | C2 | semidirect |
| 2. C2×#65431 | C2 | semidirect |
| 3. C2×#65197 | C2 | semidirect |
| 4. C5×#2115 | C2 | semidirect |
| 5. #10602241 | C2 | semidirect |
| 6. C2×#64736 | C2 | semidirect |
| 7. #10598312 | C2 | semidirect |
| 87. #2115 | D5 | semidirect |
| 393. C5 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615536 | 2 |
| C2×#65431 | 2 |
| C2×#65197 | 2 |
| C5×#2115 | 2 |
| #10602241 | 2 |
| C2×#64736 | 2 |
| #10598312 | 2 |
| #13323 | 5 |