Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
252 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #476 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| prime radical | C23×C5 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. #13542 | C5 | direct (N × H) |
| 153. C5 | #13542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1945 | 2 |
| C5×#1846 | 2 |
| C5×#1386 | 2 |
| C5×#1383 | 2 |
| C5×#1376 | 2 |
| #13542 | 5 |