Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 2. C2×#3999 | C2 | semidirect |
| 3. #64928 | C2 | semidirect |
| 4. #64922 | C2 | semidirect |
| 5. C2×C5×#41 | C4 | semidirect |
| 8. #4093 | C4 | semidirect |
| 10. #4086 | C4 | semidirect |
| 14. #4072 | C4 | semidirect |
| 21. C2×C5×Q8 | C2×C4 | semidirect |
| 23. C2×C5×D4 | C2×C4 | semidirect |
| 38. C4×Dic5 | C2×C4 | semidirect |
| 39. C4×Dic5 | C2×C4 | semidirect |
| 68. C2×#41 | AGL(1,𝔽5) | semidirect |
| 99. C2×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 107. C2×D4 | C2×AGL(1,𝔽5) | semidirect |
| 149. C5 | #2127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66164 | 2 |
| C2×#3999 | 2 |
| #64928 | 2 |
| #64922 | 2 |
| #2127 | 5 |