Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| socle | C2×C5 | #2077 |
| prime radical | C2×C5×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2155 | C2 | semidirect |
| 5. C5×#1388 | C2 | semidirect |
| 6. C5×#1382 | C2 | semidirect |
| 7. C5×#1381 | C2 | semidirect |
| 21. #13503 | C5 | direct (N × H) |
| 52. #2155 | C2×C5 | semidirect |
| 56. #1388 | C2×C5 | semidirect |
| 57. #1382 | C2×C5 | semidirect |
| 58. #1381 | C2×C5 | semidirect |
| 243. C5 | #13503 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2155 | 2 |
| C2×C5×#350 | 2 |
| C5×#1814 | 2 |
| C5×#1813 | 2 |
| C5×#1388 | 2 |
| C5×#1382 | 2 |
| C5×#1381 | 2 |
| #13503 | 5 |