Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
616 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C2×#99 |
| commutator | C24 | C22×C4×C5 |
| Frattini, cosocle | C22×D4 | C23×C5 |
| prime radical | C22×C5×D4 | C23 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C23×C5×Q8 | C4 | semidirect |
| 15. C5×#385 | C4 | semidirect |
| 16. C5×#380 | C4 | semidirect |
| 20. #13296 | C5 | direct (N × H) |
| 48. C5×#99 | Q8 | semidirect |
| 103. C23×Q8 | C4×C5 | semidirect |
| 113. #385 | C4×C5 | semidirect |
| 114. #380 | C4×C5 | semidirect |
| 190. #99 | C5×Q8 | semidirect |
| 318. C5 | #13296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2409 | 2 |
| C5×#1800 | 2 |
| C4×C5×#99 | 2 |
| C5×#1390 | 2 |
| #13296 | 5 |