Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 456 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 | #1304 |
| commutator | C22×C4 | C42×C5 |
| Frattini, cosocle | C22×#41 | C22×C5 |
| prime radical | C22×C5×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C23×C5 ◁ C22×C5×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C5×#407 | C4 | semidirect |
| 9. #7319 | C5 | direct (N × H) |
| 53. #407 | C4×C5 | semidirect |
| 157. C5 | #7319 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1785 | 2 |
| C5×#1782 | 2 |
| #7319 | 5 |