Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 270 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 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C42×C5 |
| Frattini, cosocle | #532 | C22×C5 |
| socle | C2×C5 | #1390 |
| prime radical | C5×#532 | C22 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C5×#355 | C4 | semidirect |
| 14. C5×#331 | C4 | semidirect |
| 15. #7488 | C5 | direct (N × H) |
| 80. #355 | C4×C5 | semidirect |
| 83. #331 | C4×C5 | semidirect |
| 212. C5 | #7488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2132 | 2 |
| C5×#1884 | 2 |
| C5×#1543 | 2 |
| #7488 | 5 |