Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
480 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Fitting | C5×#400 | C2 |
| prime radical | C22×D20 | C22 |
| hypercenter | #400 | D5 |
| hypocenter | C5 | #2804 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#400 | C2 | semidirect |
| 2. #65278 | C2 | semidirect |
| 4. #65275 | C2 | semidirect |
| 5. #64962 | C2 | semidirect |
| 6. #64962 | C2 | semidirect |
| 7. #64957 | C2 | semidirect |
| 9. #64935 | C2 | semidirect |
| 43. C2×D20 | Q8 | semidirect |
| 61. #400 | D5 | semidirect |
| 210. C5 | #2804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#400 | 2 |
| #65278 | 2 |
| #65277 | 2 |
| #65275 | 2 |
| #64962 | 2 |
| #64957 | 2 |
| #64954 | 2 |
| #64935 | 2 |
| #2804 | 5 |