Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C5×D4 | C2 | semidirect |
| 2. #65811 | C2 | semidirect |
| 3. #65506 | C2 | semidirect |
| 4. #65304 | C2 | semidirect |
| 5. C4×#686 | C2 | semidirect |
| 6. #65296 | C2 | semidirect |
| 7. #65256 | C2 | semidirect |
| 8. #65214 | C2 | semidirect |
| 23. #4020 | C22 | semidirect |
| 25. C4×D20 | C22 | semidirect |
| 26. #4015 | C22 | semidirect |
| 29. #3941 | C22 | semidirect |
| 30. #3939 | C22 | semidirect |
| 31. C4⋊#168 | C22 | semidirect |
| 32. C4×#168 | C22 | semidirect |
| 67. C2×C4×D4 | D5 | semidirect |
| 82. C5×D4 | #41 | semidirect |
| 89. C2×C4×C5 | D8 | semidirect |
| 198. D4 | #709 | semidirect |
| 207. C2×C4 | #686 | semidirect |
| 215. C5 | #3100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D4 | 2 |
| #65811 | 2 |
| #65506 | 2 |
| #65304 | 2 |
| C4×#686 | 2 |
| #65296 | 2 |
| #65256 | 2 |
| #65214 | 2 |
| #3100 | 5 |