Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 18. C2×#689 | C4 | semidirect |
| 84. C2×C4×C5 | Q16 | semidirect |
| 205. C2×C4 | #689 | semidirect |
| 214. C5 | #1878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×Q8 | 2 |
| C22×#689 | 2 |
| C2×#3967 | 2 |
| C2×#3942 | 2 |
| #65218 | 2 |
| #64749 | 2 |
| #64744 | 2 |
| #1878 | 5 |