Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
300 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 120 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 | C2×D4 |
| commutator | C2×C4 | C22×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C5 |
| prime radical | C24×C5 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#340 | C2 | semidirect |
| 5. C5×#340 | C2 | semidirect |
| 9. C5×#117 | C4 | semidirect |
| 18. #1825 | C5 | direct (N × H) |
| 41. #340 | C2×C5 | semidirect |
| 42. #340 | C2×C5 | semidirect |
| 68. #117 | C4×C5 | semidirect |
| 140. C5 | #1825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#117 | 2 |
| C2×C5×C22⋊C8 | 2 |
| C5×#380 | 2 |
| C5×#340 | 2 |
| #1825 | 5 |