Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
500 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C5 |
| prime radical | C22×C5×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×C5×Q8 | C2 | semidirect |
| 3. C5×#399 | C2 | semidirect |
| 4. C5×#395 | C2 | semidirect |
| 6. C5×#393 | C2 | semidirect |
| 7. C5×#388 | C2 | semidirect |
| 8. C5×#383 | C2 | semidirect |
| 27. #2632 | C5 | direct (N × H) |
| 52. C2×C4×Q8 | C2×C5 | semidirect |
| 53. #399 | C2×C5 | semidirect |
| 54. #395 | C2×C5 | semidirect |
| 56. #393 | C2×C5 | semidirect |
| 57. #388 | C2×C5 | semidirect |
| 58. #383 | C2×C5 | semidirect |
| 168. C5 | #2632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#124 | 2 |
| C2×C4×C5×Q8 | 2 |
| C5×#399 | 2 |
| C5×#395 | 2 |
| C5×#394 | 2 |
| C5×#393 | 2 |
| C5×#388 | 2 |
| C5×#383 | 2 |
| #2632 | 5 |