Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
636 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 138 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 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C2×C5×#127 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C43×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1745 | C2 | semidirect |
| 3. C5×#1270 | C2 | semidirect |
| 14. #7637 | C5 | direct (N × H) |
| 33. #1745 | C2×C5 | semidirect |
| 34. #1270 | C2×C5 | semidirect |
| 192. C5 | #7637 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#127 | 2 |
| C5×#1745 | 2 |
| C5×#1270 | 2 |
| #7637 | 5 |