Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 424 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×#391 | C2 |
| socle, prime radical, cosocle | C23×C5 | C24 |
| hypercenter | #391 | D5 |
| hypocenter | C5 | #2381 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #4090 | C4 | semidirect |
| 187. C5 | #2381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4090 | 2 |
| C5×#391 | 2 |
| #65519 | 2 |
| #65267 | 2 |
| #65222 | 2 |
| #64944 | 2 |
| #64941 | 2 |
| #64940 | 2 |
| #64935 | 2 |
| #2381 | 5 |