Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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 | H(3,ℤ/4) |
| commutator | C2×C8 | C42×C5 |
| Frattini, cosocle | C2×#131 | C22×C5 |
| socle | C2×C5 | #1289 |
| prime radical | C2×C5×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C5×M32 | C4 | semidirect |
| 5. C22×C5×C16 | C4 | semidirect |
| 9. C5×H(3,ℤ/4) | C4 | semidirect |
| 10. #7228 | C5 | direct (N × H) |
| 51. C2×M32 | C4×C5 | semidirect |
| 52. C22×C16 | C4×C5 | semidirect |
| 56. H(3,ℤ/4) | C4×C5 | semidirect |
| 142. C5 | #7228 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2113 | 2 |
| C5×#1812 | 2 |
| #7228 | 5 |