Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
6374 conjugacy classes of subgroups; only the 3275 normal subgroups are shown.
This group has 6374 conjugacy classes of subgroups — too many to draw. Only its 3275 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×C5×#564 | C2 | semidirect |
| 2. D5×#564 | C2 | direct (N × H) |
| 4. C2×C5⋊#564 | C2 | semidirect |
| 5. C5×#564 | C22 | semidirect |
| 8. C5⋊#564 | C22 | semidirect |
| 29. C2×#564 | D5 | direct (N × H) |
| 42. #564 | C2×D5 | direct (N × H) |
| 72. C2×D5 | #564 | direct (N × H) |
| 86. C2×C5 | C2×#564 | semidirect |
| 88. D5 | C2×#564 | direct (N × H) |
| 97. C5 | C22×#564 | semidirect |
| 105. C2 | D5×#564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#564 | 2 |
| D5×#564 | 2 |
| C2×D5×#125 | 2 |
| C2×C5⋊#564 | 2 |
| C22×#564 | 5 |