Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 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. C5×#1833 | C2 | semidirect |
| 5. #10598220 | C2 | semidirect |
| 6. #10598216 | C2 | semidirect |
| 7. #10598162 | C2 | semidirect |
| 57. #1833 | D5 | semidirect |
| 253. C5 | #13489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1833 | 2 |
| #10601480 | 2 |
| #10601444 | 2 |
| #10600690 | 2 |
| #10598220 | 2 |
| #10598216 | 2 |
| #10598162 | 2 |
| #13489 | 5 |