Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | H(3,ℤ/4) |
| commutator | C2×C8 | C42×C5 |
| Frattini, cosocle | C4×M16 | C22×C5 |
| socle | C2×C5 | #1288 |
| prime radical | C23×C5 | #104 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C5×#347 | C4 | semidirect |
| 14. C5×#322 | C4 | semidirect |
| 15. C5×C82 | C4 | semidirect |
| 16. #7226 | C5 | direct (N × H) |
| 58. #347 | C4×C5 | semidirect |
| 64. #322 | C4×C5 | semidirect |
| 65. C82 | C4×C5 | semidirect |
| 144. C5 | #7226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2165 | 2 |
| C5×#1841 | 2 |
| C5×#1453 | 2 |
| #7226 | 5 |