Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
154 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 154 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 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C5 |
| prime radical | C5×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#510 | C2 | semidirect |
| 3. C5×#495 | C2 | semidirect |
| 4. C5×#443 | C2 | semidirect |
| 5. C5×#364 | C2 | semidirect |
| 6. C5×#362 | C2 | semidirect |
| 7. C5×#361 | C2 | semidirect |
| 23. #2212 | C5 | direct (N × H) |
| 45. #510 | C2×C5 | semidirect |
| 47. #495 | C2×C5 | semidirect |
| 48. #443 | C2×C5 | semidirect |
| 49. #364 | C2×C5 | semidirect |
| 50. #362 | C2×C5 | semidirect |
| 51. #361 | C2×C5 | semidirect |
| 135. C5 | #2212 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#510 | 2 |
| C5×#509 | 2 |
| C5×#495 | 2 |
| C5×#443 | 2 |
| C5×#364 | 2 |
| C5×#362 | 2 |
| C5×#361 | 2 |
| #2212 | 5 |