Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
520 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 2. (C2×AGL(1,𝔽5))⋊Q8 | C2 | semidirect |
| 4. #65700 | C2 | semidirect |
| 5. #65699 | C2 | semidirect |
| 6. #65689 | C2 | semidirect |
| 16. C5×#124 | C4 | semidirect |
| 17. #4093 | C4 | semidirect |
| 18. #4082 | C4 | semidirect |
| 19. #4031 | C4 | semidirect |
| 21. #4021 | C4 | semidirect |
| 32. C2×C5×Q8 | C2×C4 | semidirect |
| 43. C2×Dic10 | C2×C4 | semidirect |
| 44. C2×Dic10 | C2×C4 | semidirect |
| 51. C5×C22⋊C4 | C2×C4 | semidirect |
| 52. C42×C5 | C2×C4 | semidirect |
| 53. C22⋊Dic5 | C2×C4 | semidirect |
| 54. #685 | C2×C4 | semidirect |
| 55. #685 | C2×C4 | semidirect |
| 56. C4×Dic5 | C2×C4 | semidirect |
| 57. C4×Dic5 | C2×C4 | semidirect |
| 103. #124 | AGL(1,𝔽5) | semidirect |
| 140. C2×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 161. C22⋊C4 | C2×AGL(1,𝔽5) | semidirect |
| 165. C42 | C2×AGL(1,𝔽5) | semidirect |
| 205. C5 | #2379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#124 | 2 |
| (C2×AGL(1,𝔽5))⋊Q8 | 2 |
| #65779 | 2 |
| #65700 | 2 |
| #65699 | 2 |
| #65689 | 2 |
| #2379 | 5 |