Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
488 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 113 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×#3930 | C2 | semidirect |
| 3. C2×#64730 | C2 | semidirect |
| 4. #10601504 | C2 | semidirect |
| 5. C2×#64717 | C2 | semidirect |
| 6. C5×#1382 | C2 | semidirect |
| 7. #10598215 | C2 | semidirect |
| 55. C2×C5×C16 | D4 | semidirect |
| 65. C2×#672 | D4 | semidirect |
| 75. #1382 | D5 | semidirect |
| 214. C2×C16 | D20 | semidirect |
| 336. C5 | #13064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3930 | 2 |
| #10610911 | 2 |
| C2×#64730 | 2 |
| #10601504 | 2 |
| C2×#64717 | 2 |
| C5×#1382 | 2 |
| #10598215 | 2 |
| #13064 | 5 |