Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C5 |
| prime radical | C5×#493 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C42×C5 ◁ C5×C82 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2227 | C2 | semidirect |
| 4. C5×#1591 | C2 | semidirect |
| 5. C5×#1370 | C2 | semidirect |
| 6. C5×#1365 | C2 | semidirect |
| 23. #12486 | C5 | direct (N × H) |
| 46. #2227 | C2×C5 | semidirect |
| 49. #1591 | C2×C5 | semidirect |
| 50. #1370 | C2×C5 | semidirect |
| 51. #1365 | C2×C5 | semidirect |
| 200. C5 | #12486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2227 | 2 |
| C5×#2207 | 2 |
| C5×#1706 | 2 |
| C5×#1591 | 2 |
| C5×#1370 | 2 |
| C5×#1365 | 2 |
| C5×#1361 | 2 |
| #12486 | 5 |