Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1154 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 390 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C5 | C24 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C22×C4 | C24×C5 |
| socle | C23×C5 | C23×C4 |
| prime radical | C5×#2397 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#436 | C2 | semidirect |
| 3. C5×#1955 | C2 | semidirect |
| 4. C5×#1843 | C2 | semidirect |
| 5. C5×#1726 | C2 | semidirect |
| 16. #21684 | C5 | direct (N × H) |
| 31. C4×C5×C8 | D4 | semidirect |
| 33. C2×#436 | C2×C5 | semidirect |
| 35. #1955 | C2×C5 | semidirect |
| 36. #1843 | C2×C5 | semidirect |
| 37. #1726 | C2×C5 | semidirect |
| 94. C4×C8 | C5×D4 | semidirect |
| 140. C5 | #21684 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#436 | 2 |
| C5×#2397 | 2 |
| C5×#1955 | 2 |
| C5×#1843 | 2 |
| C5×#1726 | 2 |
| #21684 | 5 |