Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1806 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C2×C5×#384 | C2 |
| socle, prime radical | C24×C5 | C24 |
| hypercenter | C2×#384 | D5 |
| hypocenter | C5 | C2×#2843 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×#384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #10606085 | C2 | direct (N × H) |
| 34. C2×C42×C5 | Q8 | semidirect |
| 69. C42×C5 | C2×Q8 | semidirect |
| 121. C2×C42 | Dic10 | semidirect |
| 159. C42 | C2×Dic10 | semidirect |
| 160. C2×C5 | #2843 | semidirect |
| 183. C5 | C2×#2843 | semidirect |
| 195. C2 | #10606085 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#384 | 2 |
| C2×#65275 | 2 |
| C2×#65273 | 2 |
| C2×#65268 | 2 |
| C2×#65226 | 2 |
| #10606085 | 2 |
| C2×#2843 | 5 |