Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
374 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C2×D8 |
| commutator | C2×C8 | C22×C4×C5 |
| Frattini, cosocle | C22×C8 | C23×C5 |
| socle | C22×C5 | C2×#107 |
| prime radical | C24×C5 | Q16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C23×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#368 | C2 | semidirect |
| 4. C5×#1381 | C2 | semidirect |
| 14. #12838 | C5 | direct (N × H) |
| 32. C2×#368 | C2×C5 | semidirect |
| 34. #1381 | C2×C5 | semidirect |
| 152. C5 | #12838 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×M32 | 2 |
| C2×C5×#368 | 2 |
| C5×#1810 | 2 |
| C5×#1381 | 2 |
| #12838 | 5 |