Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2046 conjugacy classes of subgroups; only the 1152 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C42×C8 |
| Frattini | C23 | C23×AGL(1,𝔽5) |
| Fitting | C43×C5 | C4 |
| socle | C23×C5 | C23×C4 |
| prime radical | C23×D5 | C22×C4 |
| cosocle | C22×Dic5 | C24 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C42×#170 | C2 | semidirect |
| 8. C4×D5⋊C8 | C4 | direct (N × H) |
| 22. C42×D5 | C8 | semidirect |
| 24. C4×#170 | C2×C4 | semidirect |
| 37. D5⋊C8 | C42 | direct (N × H) |
| 39. C42×C5 | C2×C8 | semidirect |
| 41. C4×Dic5 | C2×C8 | semidirect |
| 60. C4×D5 | C4×C8 | semidirect |
| 62. #170 | C2×C42 | semidirect |
| 80. C4×C5 | C2×C4×C8 | semidirect |
| 81. Dic5 | C2×C4×C8 | semidirect |
| 96. C42 | D5⋊C8 | direct (N × H) |
| 100. D5 | C42×C8 | semidirect |
| 113. C5 | C2×C42×C8 | semidirect |
| 120. C4 | C4×D5⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5⋊C8 | 2 |
| C43×D5 | 2 |
| C42×#170 | 2 |
| C2×C42×C8 | 5 |