Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
722 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 126 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. #10617497 | C2 | semidirect |
| 3. #10604932 | C2 | semidirect |
| 4. #10604922 | C2 | semidirect |
| 5. #10598696 | C2 | semidirect |
| 29. C5×#127 | C8 | semidirect |
| 51. C4⋊#170 | D4 | semidirect |
| 70. C2×C5×D4 | C2×C8 | semidirect |
| 89. C42×C5 | C2×C8 | semidirect |
| 165. #127 | #170 | semidirect |
| 225. C2×D4 | C2×#170 | semidirect |
| 256. C42 | C2×#170 | semidirect |
| 305. C5 | #8959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617497 | 2 |
| Dic5×#127 | 2 |
| #10604932 | 2 |
| #10604922 | 2 |
| #10598696 | 2 |
| #8959 | 5 |