Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10604727 | C2 | semidirect |
| 3. #10604713 | C2 | semidirect |
| 4. #10598600 | C2 | semidirect |
| 5. #10598599 | C2 | semidirect |
| 6. C2×#4050 | C4 | semidirect |
| 12. C2×C5×#106 | C4 | semidirect |
| 14. #65157 | C4 | semidirect |
| 16. #65154 | C4 | semidirect |
| 127. C2×#106 | AGL(1,𝔽5) | semidirect |
| 317. C5 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610851 | 2 |
| #10604727 | 2 |
| #10604713 | 2 |
| #10598600 | 2 |
| #10598599 | 2 |
| #11867 | 5 |