Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
914 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 914 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×#64988 | C2 | semidirect |
| 4. C2×#64971 | C2 | semidirect |
| 5. C2×C5×#322 | C2 | semidirect |
| 6. #10598891 | C2 | direct (N × H) |
| 17. #64988 | C22 | semidirect |
| 23. #64971 | C22 | semidirect |
| 24. C5×#322 | C22 | semidirect |
| 61. C2×#322 | D5 | semidirect |
| 111. #322 | C2×D5 | semidirect |
| 210. C2×C5 | #1722 | semidirect |
| 238. C5 | C2×#1722 | semidirect |
| 252. C2 | #10598891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64988 | 2 |
| C2×#64982 | 2 |
| C2×#64983 | 2 |
| C2×#64971 | 2 |
| C2×C5×#322 | 2 |
| #10598891 | 2 |
| C2×#1722 | 5 |