Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
474 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #10604667 | C2 | semidirect |
| 4. #10604660 | C2 | semidirect |
| 6. #10598598 | C2 | semidirect |
| 7. #10598593 | C2 | semidirect |
| 21. C5×#477 | C4 | semidirect |
| 22. #65373 | C4 | semidirect |
| 23. #65310 | C4 | semidirect |
| 26. #65131 | C4 | semidirect |
| 150. #477 | AGL(1,𝔽5) | semidirect |
| 397. C5 | #9321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617204 | 2 |
| #10612840 | 2 |
| #10604667 | 2 |
| #10604660 | 2 |
| #10604456 | 2 |
| #10598598 | 2 |
| #10598593 | 2 |
| #9321 | 5 |