Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3694 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 3694 conjugacy classes of subgroups — too many to draw. Only its 827 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 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C2×C5×#376 | C2 |
| hypercenter | C2×#376 | D5 |
| hypocenter | C5 | #34641 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#65811 | C2 | semidirect |
| 2. C2×C5×#376 | C2 | semidirect |
| 3. #10605163 | C2 | semidirect |
| 4. #10605162 | C2 | semidirect |
| 5. #10605149 | C2 | semidirect |
| 6. #10605112 | C2 | semidirect |
| 29. C2×C42×C5 | D4 | semidirect |
| 45. C2×#376 | D5 | semidirect |
| 111. C2×C42 | D20 | semidirect |
| 166. C5 | #34641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65811 | 2 |
| C2×C5×#376 | 2 |
| #10605163 | 2 |
| #10605162 | 2 |
| #10605149 | 2 |
| #10605112 | 2 |
| #34641 | 5 |