Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
258 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5×C16 | D4 |
| commutator | C4 | C22×C5×C16 |
| Frattini, cosocle | C4×C8 | C23×C5 |
| socle | C22×C5 | C8×D4 |
| prime radical | C2×C5×D8 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C16 ◁ C4×C5×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×D4×C16 | C2 | semidirect |
| 3. C5×#1370 | C2 | semidirect |
| 4. C5×D4⋊C16 | C2 | semidirect |
| 5. C5×C8×C16 | C2 | semidirect |
| 16. C16×D8 | C5 | direct (N × H) |
| 32. D4×C16 | C2×C5 | semidirect |
| 34. #1370 | C2×C5 | semidirect |
| 35. D4⋊C16 | C2×C5 | semidirect |
| 36. C8×C16 | C2×C5 | semidirect |
| 39. C5×D8 | C16 | direct (N × H) |
| 54. C5×C16 | D8 | direct (N × H) |
| 67. C5×D4 | C2×C16 | semidirect |
| 78. C5×C8 | C2×C16 | semidirect |
| 108. D8 | C5×C16 | direct (N × H) |
| 123. C16 | C5×D8 | direct (N × H) |
| 130. D4 | C2×C5×C16 | semidirect |
| 141. C8 | C2×C5×C16 | semidirect |
| 144. C5 | C16×D8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C16 | 2 |
| C5×C8×D8 | 2 |
| C5×#1370 | 2 |
| C5×D4⋊C16 | 2 |
| C5×C8×C16 | 2 |
| C16×D8 | 5 |