Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
254 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 21. C5×#103 | C4 | semidirect |
| 22. #3967 | C4 | semidirect |
| 23. #3948 | C4 | semidirect |
| 24. #3942 | C4 | semidirect |
| 113. #103 | AGL(1,𝔽5) | semidirect |
| 210. C5 | #1928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×AGL(1,𝔽5))⋊Q8 | 2 |
| C2×#4009 | 2 |
| C2×#3994 | 2 |
| C4⋊C4×AGL(1,𝔽5) | 2 |
| D5×#103 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 2 |
| #64874 | 2 |
| #1928 | 5 |