Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D5 |
| commutator, socle | C22×C5 | C23×C4 |
| Fitting, prime radical | C5×#532 | C2 |
| cosocle | C2×C4×C5 | C24 |
| hypercenter | #532 | D5 |
| hypocenter | C5 | #2931 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#4094 | C2 | semidirect |
| 3. #65523 | C2 | semidirect |
| 4. #65301 | C2 | semidirect |
| 5. D4×#168 | C2 | semidirect |
| 6. #65213 | C2 | semidirect |
| 7. C2×C4×#168 | C2 | semidirect |
| 44. C2×#168 | D4 | semidirect |
| 101. C4×C5 | #131 | semidirect |
| 151. C5 | #2931 | semidirect |
| 160. C4 | #4094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| C2×#4094 | 2 |
| #65523 | 2 |
| #65301 | 2 |
| D4×#168 | 2 |
| #65213 | 2 |
| C2×C4×#168 | 2 |
| #2931 | 5 |