Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2942 conjugacy classes of subgroups; only the 1179 normal subgroups are shown.
This group has 2942 conjugacy classes of subgroups — too many to draw. Only its 1179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C22×C5×#95 | C2 |
| socle, prime radical | C25×C5 | C23 |
| hypercenter | C22×#95 | D5 |
| hypocenter | C5 | C22×#401 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C25 ◁ C22×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C5⋊#401 | C2 | direct (N × H) |
| 11. C5⋊#401 | C22 | direct (N × H) |
| 82. C22×C5 | #401 | semidirect |
| 108. C2×C5 | C2×#401 | semidirect |
| 128. C5 | C22×#401 | semidirect |
| 129. C22 | C5⋊#401 | direct (N × H) |
| 139. C2 | C2×C5⋊#401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#95 | 2 |
| C22×#3963 | 2 |
| C2×C5⋊#401 | 2 |
| C22×#401 | 5 |