Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 192 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 |
|---|---|---|
| 1. D4×#170 | C2 | semidirect |
| 3. D4⋊#170 | C2 | semidirect |
| 4. #64881 | C2 | semidirect |
| 5. #64879 | C2 | semidirect |
| 23. C5×D8 | C8 | semidirect |
| 36. C5×D4 | C2×C8 | semidirect |
| 46. C5×C8 | C2×C8 | semidirect |
| 69. D8 | #170 | semidirect |
| 85. D4 | C2×#170 | semidirect |
| 96. C8 | C2×#170 | semidirect |
| 97. C5 | #1580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#170 | 2 |
| D8×Dic5 | 2 |
| D4⋊#170 | 2 |
| #64881 | 2 |
| #64879 | 2 |
| #1580 | 5 |