Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
238 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C2×D8 |
| commutator | C2×C8 | C22×C4×C5 |
| Frattini, cosocle | C4×C8 | C23×C5 |
| socle | C22×C5 | C4×D8 |
| prime radical | C2×C5×D16 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C4×C5×C8 ◁ C5×C82 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1589 | C2 | semidirect |
| 3. C5×#1371 | C2 | semidirect |
| 4. C5×#1331 | C2 | semidirect |
| 5. C5×C8×C16 | C2 | semidirect |
| 16. #12081 | C5 | direct (N × H) |
| 32. #1589 | C2×C5 | semidirect |
| 33. #1371 | C2×C5 | semidirect |
| 34. #1331 | C2×C5 | semidirect |
| 35. C8×C16 | C2×C5 | semidirect |
| 52. C5×C16 | M16 | semidirect |
| 76. C5×C8 | D16 | semidirect |
| 119. C16 | C5×M16 | semidirect |
| 137. C8 | C5×D16 | semidirect |
| 140. C5 | #12081 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D16 | 2 |
| C5×#1589 | 2 |
| C5×#1371 | 2 |
| C5×#1331 | 2 |
| C5×C8×C16 | 2 |
| #12081 | 5 |