Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C5 |
| prime radical | C5×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×SD32 | C2 | semidirect |
| 2. C5×#504 | C2 | semidirect |
| 3. C5×#473 | C2 | semidirect |
| 5. C5×#368 | C2 | semidirect |
| 6. C5×#362 | C2 | semidirect |
| 7. C5×#361 | C2 | semidirect |
| 23. #2223 | C5 | direct (N × H) |
| 44. C2×SD32 | C2×C5 | semidirect |
| 45. #504 | C2×C5 | semidirect |
| 46. #473 | C2×C5 | semidirect |
| 48. #368 | C2×C5 | semidirect |
| 49. #362 | C2×C5 | semidirect |
| 50. #361 | C2×C5 | semidirect |
| 130. C5 | #2223 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×SD32 | 2 |
| C5×#504 | 2 |
| C5×#473 | 2 |
| C5×#472 | 2 |
| C5×#368 | 2 |
| C5×#362 | 2 |
| C5×#361 | 2 |
| #2223 | 5 |