Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 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 | C2×C4 | C23×D5 |
| commutator, socle | C22×C5 | C23×C4 |
| Fitting | C5×#408 | C2 |
| prime radical | C2×C5×#41 | C22 |
| cosocle | C2×C4×C5 | C24 |
| hypercenter | #408 | D5 |
| hypocenter | C5 | #2923 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #65408 | C2 | semidirect |
| 5. M16×Dic5 | C2 | semidirect |
| 6. #65391 | C2 | semidirect |
| 7. C2×#3947 | C2 | semidirect |
| 8. #65009 | C2 | semidirect |
| 9. #65008 | C2 | semidirect |
| 170. C5 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic5 | 2 |
| C5×#408 | 2 |
| #65523 | 2 |
| #65408 | 2 |
| M16×Dic5 | 2 |
| #65391 | 2 |
| C2×#3947 | 2 |
| #65009 | 2 |
| #65008 | 2 |
| #2923 | 5 |