Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
468 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 165 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, prime radical, cosocle | C23×C5 | C24 |
| Fitting | C5×#391 | C2 |
| hypercenter | #391 | D5 |
| hypocenter | C5 | #2568 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. C2×C5×Q8 | Q8 | semidirect |
| 125. C2×Q8 | Dic10 | semidirect |
| 175. C5 | #2568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic5 | 2 |
| C2×#4034 | 2 |
| C5×#391 | 2 |
| #65519 | 2 |
| #65266 | 2 |
| #65225 | 2 |
| C4×#683 | 2 |
| #64949 | 2 |
| #64935 | 2 |
| #2568 | 5 |