Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
368 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 54 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. D5⋊#99 | C2 | semidirect |
| 3. #64922 | C2 | semidirect |
| 4. #64853 | C2 | semidirect |
| 6. C2×D4×D5 | C4 | semidirect |
| 9. C5×#127 | C4 | semidirect |
| 11. #4086 | C4 | semidirect |
| 14. C42×D5 | C4 | semidirect |
| 16. #3999 | C22 | semidirect |
| 23. C2×C5×D4 | C2×C4 | semidirect |
| 34. C2×D20 | C2×C4 | semidirect |
| 40. C42×C5 | C2×C4 | semidirect |
| 42. C4×Dic5 | C2×C4 | semidirect |
| 84. #127 | AGL(1,𝔽5) | semidirect |
| 126. C2×D4 | C2×AGL(1,𝔽5) | semidirect |
| 134. C42 | C2×AGL(1,𝔽5) | semidirect |
| 142. D5 | #353 | semidirect |
| 173. C5 | C2×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#127 | 2 |
| D5⋊#99 | 2 |
| #64922 | 2 |
| #64853 | 2 |
| C2×#353 | 5 |