Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×C5×C4⋊Q8 | C2 | semidirect |
| 4. C2×#3967 | C2 | semidirect |
| 5. #65372 | C2 | direct (N × H) |
| 6. C2×C4⋊#168 | C2 | semidirect |
| 11. C5×C4⋊Q8 | C22 | semidirect |
| 22. #3967 | C22 | semidirect |
| 23. C4⋊#168 | C22 | semidirect |
| 52. C2×C4⋊Q8 | D5 | semidirect |
| 68. C2×C4×C5 | SD16 | semidirect |
| 89. C4⋊Q8 | C2×D5 | semidirect |
| 110. C4×C5 | C2×SD16 | semidirect |
| 140. C2×C5 | #461 | semidirect |
| 162. C2×C4 | #688 | semidirect |
| 170. C5 | C2×#461 | semidirect |
| 183. C4 | C2×#688 | semidirect |
| 187. C2 | #65372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊Q8 | 2 |
| C22×#688 | 2 |
| C2×C4×D20 | 2 |
| C2×#3967 | 2 |
| #65372 | 2 |
| C2×C4⋊#168 | 2 |
| C2×#461 | 5 |