Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
924 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 289 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, prime radical | C2×C5×#127 | C2 |
| socle, cosocle | C23×C5 | C24 |
| hypercenter | C2×#127 | D5 |
| hypocenter | C5 | C4×#127 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Dic5 | C2 | semidirect |
| 3. #65510 | C2 | semidirect |
| 4. #65224 | C2 | semidirect |
| 5. C42×Dic5 | C2 | semidirect |
| 8. C5×#127 | C4 | semidirect |
| 19. C2×C5×D4 | C2×C4 | semidirect |
| 25. C42×C5 | C2×C4 | semidirect |
| 29. C4×Dic5 | D4 | semidirect |
| 50. #127 | Dic5 | direct (N × H) |
| 63. C4×C5 | C4×D4 | semidirect |
| 66. Dic5 | #127 | direct (N × H) |
| 70. C2×D4 | C2×Dic5 | semidirect |
| 80. C42 | C2×Dic5 | semidirect |
| 98. C5 | C4×#127 | semidirect |
| 108. C4 | D4×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#127 | 2 |
| C2×D4×Dic5 | 2 |
| #65510 | 2 |
| #65224 | 2 |
| C42×Dic5 | 2 |
| C4×#127 | 5 |