Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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×#4010 | C2 | semidirect |
| 3. C2×#4008 | C2 | semidirect |
| 4. C4×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. C4×#700 | C2 | semidirect |
| 11. C5×#124 | C4 | semidirect |
| 12. #4090 | C4 | semidirect |
| 13. #4086 | C4 | semidirect |
| 18. #4021 | C4 | semidirect |
| 49. #700 | D4 | semidirect |
| 102. #124 | AGL(1,𝔽5) | semidirect |
| 133. Dic5 | #104 | semidirect |
| 207. C5 | #1980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66002 | 2 |
| C2×#4010 | 2 |
| C2×#4008 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| C4×#700 | 2 |
| #1980 | 5 |