Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C5 |
| Frattini, cosocle | C2×#41 | C23×C5 |
| socle | C2×C5 | #1867 |
| prime radical | C5×#532 | C22 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#1858 | C2 | semidirect |
| 5. C5×#1395 | C2 | semidirect |
| 17. C5×#356 | C4 | semidirect |
| 18. C5×#355 | C4 | semidirect |
| 21. #12974 | C5 | direct (N × H) |
| 54. #1858 | C2×C5 | semidirect |
| 55. #1395 | C2×C5 | semidirect |
| 105. #356 | C4×C5 | semidirect |
| 106. #355 | C4×C5 | semidirect |
| 252. C5 | #12974 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2980 | 2 |
| C5×#2132 | 2 |
| C5×#1884 | 2 |
| C5×#1858 | 2 |
| C5×#1395 | 2 |
| #12974 | 5 |