Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4009 | C2 | semidirect |
| 4. C4×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. D5⋊(C4⋊C8) | C2 | semidirect |
| 11. C5×#124 | C4 | semidirect |
| 12. #4093 | C4 | semidirect |
| 13. #4082 | C4 | semidirect |
| 18. #4021 | C4 | semidirect |
| 106. #124 | AGL(1,𝔽5) | semidirect |
| 214. C5 | #1983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#124 | 2 |
| C2×#4009 | 2 |
| C2×#4007 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| D5⋊(C4⋊C8) | 2 |
| #1983 | 5 |