Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C22×C5 | C23×C4 |
| Fitting | C5×#381 | C2 |
| socle, cosocle | C23×C5 | C24 |
| prime radical | C2×#4076 | C2 |
| hypercenter | #381 | D5 |
| hypocenter | C5 | #2377 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#381 | C2 | semidirect |
| 3. #65501 | C2 | semidirect |
| 4. #65246 | C2 | semidirect |
| 5. #65245 | C2 | semidirect |
| 6. #64959 | C2 | semidirect |
| 7. #64957 | C2 | semidirect |
| 8. #64954 | C2 | semidirect |
| 9. #64943 | C2 | semidirect |
| 17. #4076 | C4 | semidirect |
| 36. C22×C4×C5 | C2×C4 | semidirect |
| 43. C2×C22⋊D5 | C2×C4 | semidirect |
| 58. #685 | C2×C4 | semidirect |
| 60. C4⋊Dic5 | C2×C4 | semidirect |
| 70. #381 | D5 | semidirect |
| 168. C22×C4 | C4×D5 | semidirect |
| 227. C5 | #2377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4076 | 2 |
| C5×#381 | 2 |
| #65501 | 2 |
| #65246 | 2 |
| #65245 | 2 |
| #64959 | 2 |
| #64957 | 2 |
| #64954 | 2 |
| #64943 | 2 |
| #2377 | 5 |