Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
490 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C5 |
| prime radical | C23×C5 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2227 | C2 | semidirect |
| 4. C5×#2209 | C2 | semidirect |
| 20. #33815 | C5 | direct (N × H) |
| 44. #2227 | C2×C5 | semidirect |
| 46. #2209 | C2×C5 | semidirect |
| 96. C2×C4×C5 | Q32 | semidirect |
| 176. C2×C4 | C5×Q32 | semidirect |
| 185. C5 | #33815 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3170 | 2 |
| C5×#2227 | 2 |
| C5×#2216 | 2 |
| C5×#2209 | 2 |
| C2×C5×C4⋊C16 | 2 |
| #33815 | 5 |