Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×D80 | C2 | semidirect |
| 2. C2×#65172 | C2 | semidirect |
| 3. C2×#64727 | C2 | semidirect |
| 4. C2×#64711 | C2 | semidirect |
| 5. C5×#1380 | C2 | semidirect |
| 32. C2×D40 | D4 | semidirect |
| 40. C2×C5×C16 | D4 | semidirect |
| 42. C5×#107 | D4 | semidirect |
| 51. #1380 | D5 | semidirect |
| 113. C22×D5 | D16 | semidirect |
| 158. C2×C16 | D20 | semidirect |
| 160. #107 | D20 | semidirect |
| 261. C5 | #13304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D80 | 2 |
| C2×#65172 | 2 |
| C2×#64727 | 2 |
| C2×#64711 | 2 |
| C5×#1380 | 2 |
| #13304 | 5 |