Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
558 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| prime radical | C5×#3150 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#510 | C2 | semidirect |
| 3. C2×C5×#360 | C2 | semidirect |
| 4. C5×#1971 | C2 | semidirect |
| 5. C5×#1377 | C2 | semidirect |
| 22. #13342 | C5 | direct (N × H) |
| 36. C2×C5×Q16 | D4 | semidirect |
| 53. C5×M32 | D4 | semidirect |
| 59. C2×#510 | C2×C5 | semidirect |
| 61. C2×#360 | C2×C5 | semidirect |
| 62. #1971 | C2×C5 | semidirect |
| 63. #1377 | C2×C5 | semidirect |
| 169. C2×Q16 | C5×D4 | semidirect |
| 186. M32 | C5×D4 | semidirect |
| 287. C5 | #13342 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#510 | 2 |
| C5×#3150 | 2 |
| C2×C5×#360 | 2 |
| C5×#1971 | 2 |
| C5×#1377 | 2 |
| #13342 | 5 |