Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#509 | C2 | semidirect |
| 2. #10615648 | C2 | semidirect |
| 3. C2×#65449 | C2 | semidirect |
| 4. C2×#64787 | C2 | semidirect |
| 5. C2×#64782 | C2 | semidirect |
| 6. C2×#64735 | C2 | semidirect |
| 7. #10598308 | C2 | semidirect |
| 47. C2×C5×D8 | D4 | semidirect |
| 70. C5×M32 | D4 | semidirect |
| 76. #3951 | D4 | semidirect |
| 82. C2×#509 | D5 | semidirect |
| 237. C2×D8 | C22⋊D5 | semidirect |
| 256. M32 | C22⋊D5 | semidirect |
| 405. C5 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#509 | 2 |
| #10615648 | 2 |
| C2×#65449 | 2 |
| C2×#64787 | 2 |
| C2×#64782 | 2 |
| C2×#64735 | 2 |
| #10598308 | 2 |
| #13307 | 5 |