Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
334 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 334 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, socle | C2×C5 | #1390 |
| commutator | C2×D4 | C42×C5 |
| Frattini, cosocle | C2×#127 | C22×C5 |
| prime radical | C2×C5×#127 | C22 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C23×C5 ◁ C22×C4×C5 ◁ C2×C5×#127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C5×#518 | C4 | semidirect |
| 8. C2×C5×#100 | C4 | semidirect |
| 11. C5×#353 | C4 | semidirect |
| 14. C5×#331 | C4 | semidirect |
| 15. #7493 | C5 | direct (N × H) |
| 75. #518 | C4×C5 | semidirect |
| 78. C2×#100 | C4×C5 | semidirect |
| 81. #353 | C4×C5 | semidirect |
| 84. #331 | C4×C5 | semidirect |
| 238. C5 | #7493 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#353 | 2 |
| C5×#1887 | 2 |
| C5×#1555 | 2 |
| #7493 | 5 |