Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
908 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 223 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×#395 | C2 |
| prime radical | C23×D5 | C23 |
| hypercenter | #395 | D5 |
| hypocenter | C5 | C2×#395 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#395 | C2 | semidirect |
| 4. #65518 | C2 | semidirect |
| 5. #65268 | C2 | semidirect |
| 7. #64945 | C2 | semidirect |
| 37. C2×C4×D5 | Q8 | semidirect |
| 49. #395 | D5 | direct (N × H) |
| 61. C2×C4×C5 | C2×Q8 | semidirect |
| 67. C2×Dic5 | C2×Q8 | semidirect |
| 122. D5 | #395 | direct (N × H) |
| 143. C2×C4 | Q8×D5 | semidirect |
| 144. C5 | C2×#395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D5 | 2 |
| C2×D5×C4⋊C4 | 2 |
| C5×#395 | 2 |
| #65518 | 2 |
| #65268 | 2 |
| D5×#95 | 2 |
| #64945 | 2 |
| C2×#395 | 5 |