Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 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. C23×C5×Q8 | C2 | semidirect |
| 3. C2×#4092 | C2 | direct (N × H) |
| 5. C22×C4⋊Dic5 | C2 | semidirect |
| 6. C22×#683 | C2 | semidirect |
| 9. C22×C5×Q8 | C22 | semidirect |
| 16. #4092 | C22 | direct (N × H) |
| 18. C2×C4⋊Dic5 | C22 | semidirect |
| 19. C2×#683 | C22 | semidirect |
| 24. C23×D5 | Q8 | semidirect |
| 27. C2×C5×Q8 | C23 | semidirect |
| 39. C4⋊Dic5 | C23 | semidirect |
| 40. #683 | C23 | semidirect |
| 41. C23×Q8 | D5 | semidirect |
| 54. C22×D5 | C2×Q8 | semidirect |
| 68. C22×Q8 | C2×D5 | semidirect |
| 79. C22×C5 | C22⋊Q8 | semidirect |
| 87. C2×D5 | C22×Q8 | semidirect |
| 98. C2×Q8 | C22×D5 | semidirect |
| 112. C2×C5 | C2×C22⋊Q8 | semidirect |
| 136. C5 | C22×C22⋊Q8 | semidirect |
| 141. C22 | #4092 | direct (N × H) |
| 151. C2 | C2×#4092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×Q8 | 2 |
| C23×C4×D5 | 2 |
| C2×#4092 | 2 |
| C22×#685 | 2 |
| C22×C4⋊Dic5 | 2 |
| C22×#683 | 2 |
| C22×C22⋊Q8 | 5 |