Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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×C4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×#4008 | C2 | semidirect |
| 4. #65756 | C2 | semidirect |
| 5. #64875 | C2 | semidirect |
| 13. C5×#121 | C4 | semidirect |
| 14. #4084 | C4 | semidirect |
| 17. #4070 | C4 | semidirect |
| 18. #4043 | C4 | semidirect |
| 32. C2×C5×D4 | C2×C4 | semidirect |
| 46. C2×Dic10 | C2×C4 | semidirect |
| 50. C4×AGL(1,𝔽5) | D4 | semidirect |
| 53. C5×C4⋊C4 | C2×C4 | semidirect |
| 60. C4⋊Dic5 | C2×C4 | semidirect |
| 111. #121 | AGL(1,𝔽5) | semidirect |
| 127. C22×C5 | #104 | semidirect |
| 135. C2×D5 | #104 | semidirect |
| 153. C2×D4 | C2×AGL(1,𝔽5) | semidirect |
| 173. C4⋊C4 | C2×AGL(1,𝔽5) | semidirect |
| 226. C5 | #1896 | semidirect |
| 241. C22 | #4008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×AGL(1,𝔽5) | 2 |
| #65940 | 2 |
| C2×#4008 | 2 |
| #65756 | 2 |
| #64875 | 2 |
| #1896 | 5 |