Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
784 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 118 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 | C23×C5×D4 | C22 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C24×C5 ◁ C23×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#1390 | C2 | semidirect |
| 6. C22×C5×C22⋊C4 | C4 | semidirect |
| 7. C22×C5×C22⋊C4 | C4 | semidirect |
| 15. C5×#386 | C4 | semidirect |
| 20. #12854 | C5 | direct (N × H) |
| 54. #1390 | C2×C5 | semidirect |
| 106. C22×C22⋊C4 | C4×C5 | semidirect |
| 107. C22×C22⋊C4 | C4×C5 | semidirect |
| 115. #386 | C4×C5 | semidirect |
| 347. C5 | #12854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2308 | 2 |
| C5×#1783 | 2 |
| C5×#1781 | 2 |
| C5×#1390 | 2 |
| #12854 | 5 |