Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
504 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C5 |
| prime radical | C22×C5×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#398 | C2 | semidirect |
| 3. C5×#397 | C2 | semidirect |
| 5. C5×#389 | C2 | semidirect |
| 6. C5×#385 | C2 | semidirect |
| 22. #2724 | C5 | direct (N × H) |
| 45. #398 | C2×C5 | semidirect |
| 46. #397 | C2×C5 | semidirect |
| 48. #389 | C2×C5 | semidirect |
| 49. #385 | C2×C5 | semidirect |
| 151. C5 | #2724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#123 | 2 |
| C5×#398 | 2 |
| C5×#397 | 2 |
| C5×#390 | 2 |
| C5×#389 | 2 |
| C5×#385 | 2 |
| #2724 | 5 |