Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C5 |
| prime radical | C5×#1667 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C42×C5 ◁ C5×C8×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2248 | C2 | semidirect |
| 2. C5×D4×C16 | C2 | semidirect |
| 3. C5×#1669 | C2 | semidirect |
| 5. C5×#1372 | C2 | semidirect |
| 6. C5×#1362 | C2 | semidirect |
| 7. C5×#1361 | C2 | semidirect |
| 23. #12432 | C5 | direct (N × H) |
| 47. #2248 | C2×C5 | semidirect |
| 48. D4×C16 | C2×C5 | semidirect |
| 49. #1669 | C2×C5 | semidirect |
| 51. #1372 | C2×C5 | semidirect |
| 52. #1362 | C2×C5 | semidirect |
| 53. #1361 | C2×C5 | semidirect |
| 81. C5×C16 | D8 | semidirect |
| 107. C5×D4 | SD32 | semidirect |
| 185. C16 | C5×D8 | semidirect |
| 201. D4 | C5×SD32 | semidirect |
| 215. C5 | #12432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2248 | 2 |
| C5×D4×C16 | 2 |
| C5×#1669 | 2 |
| C5×#1667 | 2 |
| C5×#1372 | 2 |
| C5×#1362 | 2 |
| C5×#1361 | 2 |
| #12432 | 5 |