Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1146 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1146 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. C2×#64984 | C2 | semidirect |
| 2. C2×#64984 | C2 | semidirect |
| 3. C2×#64982 | C2 | semidirect |
| 4. C2×#64983 | C2 | semidirect |
| 5. C2×C5×#322 | C2 | semidirect |
| 6. #10598887 | C2 | direct (N × H) |
| 18. #64984 | C22 | semidirect |
| 19. #64984 | C22 | semidirect |
| 21. #64983 | C22 | semidirect |
| 23. #64982 | C22 | semidirect |
| 24. C5×#322 | C22 | semidirect |
| 62. C2×#322 | D5 | semidirect |
| 87. C2×C5×C8 | D8 | semidirect |
| 115. #322 | C2×D5 | semidirect |
| 145. C5×C8 | C2×D8 | semidirect |
| 219. C2×C8 | D40 | semidirect |
| 227. C2×C5 | #1721 | semidirect |
| 261. C8 | C2×D40 | semidirect |
| 262. C5 | C2×#1721 | semidirect |
| 280. C2 | #10598887 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64984 | 2 |
| C2×#64982 | 2 |
| C2×#64983 | 2 |
| C2×C5×#322 | 2 |
| #10598887 | 2 |
| C2×#1721 | 5 |