Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1022 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 267 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×#64984 | C2 | semidirect |
| 3. C2×C4×C5×C16 | C2 | semidirect |
| 4. #10599853 | C2 | direct (N × H) |
| 11. C2×D80 | C22 | semidirect |
| 13. #64984 | C22 | semidirect |
| 14. C4×C5×C16 | C22 | semidirect |
| 28. C2×C5×C16 | D4 | semidirect |
| 36. C2×C4×C16 | D5 | semidirect |
| 56. C5×C16 | C2×D4 | semidirect |
| 66. C4×C16 | C2×D5 | semidirect |
| 71. C2×C4×C5 | D16 | semidirect |
| 97. C2×C16 | D20 | semidirect |
| 108. C4×C5 | C2×D16 | semidirect |
| 130. C16 | C2×D20 | semidirect |
| 131. C2×C5 | #2246 | semidirect |
| 143. C2×C4 | D80 | semidirect |
| 152. C5 | C2×#2246 | semidirect |
| 160. C4 | C2×D80 | semidirect |
| 164. C2 | #10599853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D80 | 2 |
| C2×#64984 | 2 |
| C2×C4×C5×C16 | 2 |
| #10599853 | 2 |
| C2×#2246 | 5 |