Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
716 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C24×C5 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2099 | C2 | semidirect |
| 4. C5×#2057 | C2 | semidirect |
| 20. #32786 | C5 | direct (N × H) |
| 43. #2099 | C2×C5 | semidirect |
| 45. #2057 | C2×C5 | semidirect |
| 214. C5 | #32786 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2857 | 2 |
| C5×#2099 | 2 |
| C5×#2075 | 2 |
| C5×#2057 | 2 |
| C5×#1817 | 2 |
| #32786 | 5 |