Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 2. C5×#1953 | C2 | semidirect |
| 3. #10601483 | C2 | semidirect |
| 4. #10601480 | C2 | semidirect |
| 5. C2×#64715 | C2 | semidirect |
| 6. C2×#64715 | C2 | semidirect |
| 7. #10598163 | C2 | semidirect |
| 60. C5×#108 | D4 | semidirect |
| 74. #1953 | D5 | semidirect |
| 217. #108 | D20 | semidirect |
| 326. C5 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610296 | 2 |
| C5×#1953 | 2 |
| #10601483 | 2 |
| #10601480 | 2 |
| C2×#64715 | 2 |
| #10598163 | 2 |
| #13417 | 5 |