Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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. C4×C5×Q16 | C2 | semidirect |
| 2. C2×#3960 | C2 | semidirect |
| 4. #64711 | C2 | semidirect |
| 5. C4⋊#672 | C2 | semidirect |
| 22. C5×Q16 | D4 | semidirect |
| 35. C4×Q16 | D5 | semidirect |
| 70. C4×C5 | SD32 | semidirect |
| 78. Q16 | D20 | semidirect |
| 108. C5 | #2207 | semidirect |
| 116. C4 | #3960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Q16 | 2 |
| C2×#3960 | 2 |
| #64984 | 2 |
| #64711 | 2 |
| C4⋊#672 | 2 |
| #2207 | 5 |