Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×C5×#367 | C2 | semidirect |
| 3. C2×#64730 | C2 | semidirect |
| 4. C2×#64728 | C2 | semidirect |
| 5. #10601439 | C2 | semidirect |
| 6. #10601391 | C2 | semidirect |
| 7. #10598214 | C2 | semidirect |
| 55. C2×C5×C16 | D4 | semidirect |
| 70. C2×#367 | D5 | semidirect |
| 214. C2×C16 | D20 | semidirect |
| 340. C5 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610881 | 2 |
| C2×C5×#367 | 2 |
| C2×#64730 | 2 |
| C2×#64728 | 2 |
| #10601439 | 2 |
| #10601391 | 2 |
| #10598214 | 2 |
| #13385 | 5 |