Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
552 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 194 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. C22×#700 | C2 | semidirect |
| 3. C2×#4003 | C2 | semidirect |
| 4. C2×C4⋊#170 | C2 | semidirect |
| 5. C2×C4×#170 | C2 | semidirect |
| 6. #65705 | C2 | direct (N × H) |
| 13. C2×#700 | C22 | semidirect |
| 19. #4003 | C22 | semidirect |
| 20. C4⋊#170 | C22 | semidirect |
| 21. C4×#170 | C22 | semidirect |
| 36. C2×#170 | D4 | semidirect |
| 57. C2×C4×C5 | M16 | semidirect |
| 72. #170 | C2×D4 | semidirect |
| 97. C4×C5 | C2×M16 | semidirect |
| 124. C2×C5 | #436 | semidirect |
| 145. C2×C4 | #700 | semidirect |
| 151. C5 | C2×#436 | semidirect |
| 165. C4 | C2×#700 | semidirect |
| 167. C2 | #65705 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#700 | 2 |
| C2×#4039 | 2 |
| C2×#4003 | 2 |
| C2×C4⋊#170 | 2 |
| C2×C4×#170 | 2 |
| #65705 | 2 |
| C2×#436 | 5 |