Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2550 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C5 | C24 |
| commutator | C22 | C24×C4×C5 |
| Frattini, cosocle | C23 | C25×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2356 | C2 | direct (N × H) |
| 11. C2×C4×C5×Q8 | C4 | semidirect |
| 35. C2×#2356 | C5 | direct (N × H) |
| 48. C4×C5×Q8 | C2×C4 | semidirect |
| 73. #2356 | C2×C5 | direct (N × H) |
| 124. C2×C4×Q8 | C4×C5 | semidirect |
| 196. C4×Q8 | C2×C4×C5 | semidirect |
| 280. C2×C5 | #2356 | direct (N × H) |
| 322. C5 | C2×#2356 | direct (N × H) |
| 341. C2 | C5×#2356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×Q8 | 2 |
| C5×#2356 | 2 |
| C2×C5×#391 | 2 |
| C2×C5×#387 | 2 |
| C2×C5×#383 | 2 |
| C2×C5×#382 | 2 |
| C2×C4×C5×C4⋊C4 | 2 |
| C2×C5×#376 | 2 |
| C2×#2356 | 5 |