Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
172 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #1675 |
| commutator, Frattini, cosocle | C4×C8 | C23×C5 |
| prime radical | C5×#135 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2253 | C2 | semidirect |
| 4. C5×#1373 | C2 | semidirect |
| 5. C5×#1366 | C2 | semidirect |
| 17. #12464 | C5 | direct (N × H) |
| 32. #2253 | C2×C5 | semidirect |
| 35. #1373 | C2×C5 | semidirect |
| 36. #1366 | C2×C5 | semidirect |
| 130. C5 | #12464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2253 | 2 |
| C5×#2231 | 2 |
| C5×#2170 | 2 |
| C5×#1373 | 2 |
| C5×#1366 | 2 |
| #12464 | 5 |