Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×AGL(1,𝔽5) |
| commutator, socle | C2×C5 | C23×C8 |
| Fitting | C5×#131 | C4 |
| prime radical | D5×#41 | C4 |
| cosocle | #168 | C24 |
| hypercenter | #131 | AGL(1,𝔽5) |
| hypocenter | C5 | #3407 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C4 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #65791 | C2 | semidirect |
| 3. #65725 | C2 | semidirect |
| 4. D5⋊M32 | C2 | semidirect |
| 5. C2×#3990 | C2 | semidirect |
| 13. #3998 | C22 | semidirect |
| 14. C2×#674 | C22 | semidirect |
| 17. #3990 | C22 | semidirect |
| 18. D5⋊C16 | C22 | semidirect |
| 118. C5 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#131 | 2 |
| #65791 | 2 |
| #65725 | 2 |
| D5⋊M32 | 2 |
| C2×#3990 | 2 |
| #3407 | 5 |