Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×#64910 | C2 | semidirect |
| 4. #10604832 | C2 | semidirect |
| 6. #10598632 | C2 | semidirect |
| 7. #10598628 | C2 | semidirect |
| 21. C5×#473 | C4 | semidirect |
| 23. #65481 | C4 | semidirect |
| 24. #65432 | C4 | semidirect |
| 25. #65185 | C4 | semidirect |
| 174. #473 | AGL(1,𝔽5) | semidirect |
| 410. C5 | #13069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617413 | 2 |
| D5×#473 | 2 |
| C2×#64910 | 2 |
| #10604832 | 2 |
| #10604779 | 2 |
| #10598632 | 2 |
| #10598628 | 2 |
| #13069 | 5 |