Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
586 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 586 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. #10615561 | C2 | semidirect |
| 2. C22×#3958 | C2 | semidirect |
| 3. C2×#65197 | C2 | semidirect |
| 4. C2×C5×#361 | C2 | semidirect |
| 5. #10601502 | C2 | semidirect |
| 6. C2×#64717 | C2 | semidirect |
| 7. #10598306 | C2 | semidirect |
| 64. C2×D40 | D4 | semidirect |
| 67. C5×M32 | D4 | semidirect |
| 78. C2×#672 | D4 | semidirect |
| 84. C2×#361 | D5 | semidirect |
| 248. M32 | C22⋊D5 | semidirect |
| 385. C5 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615561 | 2 |
| C22×#3958 | 2 |
| C2×#65197 | 2 |
| C2×C5×#361 | 2 |
| #10601502 | 2 |
| C2×#64717 | 2 |
| #10598306 | 2 |
| #13336 | 5 |