Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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×#399 | C2 |
| prime radical | C24×D5 | C22 |
| hypercenter | #399 | D5 |
| hypocenter | C5 | #2842 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#399 | C2 | semidirect |
| 2. #65283 | C2 | semidirect |
| 4. #65238 | C2 | semidirect |
| 5. #64965 | C2 | semidirect |
| 7. C2×C5×C4⋊C4 | C22 | semidirect |
| 12. C2×C4⋊Dic5 | C22 | semidirect |
| 13. C2×#683 | C22 | semidirect |
| 14. C5×#95 | C22 | semidirect |
| 15. #3963 | C22 | semidirect |
| 33. #399 | D5 | semidirect |
| 57. C2×C4⋊C4 | C2×D5 | semidirect |
| 63. #95 | C2×D5 | semidirect |
| 114. C5 | #2842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#399 | 2 |
| #65283 | 2 |
| #65244 | 2 |
| #65238 | 2 |
| #64965 | 2 |
| #2842 | 5 |