Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#4072 | C2 | semidirect |
| 3. C5×#407 | C2 | semidirect |
| 4. #65420 | C2 | semidirect |
| 5. #65410 | C2 | semidirect |
| 6. #65026 | C2 | semidirect |
| 7. #65025 | C2 | semidirect |
| 8. #65024 | C2 | semidirect |
| 22. #4072 | C22 | semidirect |
| 24. C2×C4⋊Dic5 | C22 | semidirect |
| 25. C2×C4⋊Dic5 | C22 | semidirect |
| 27. C5×C22⋊C8 | C22 | semidirect |
| 28. C5×C22⋊C8 | C22 | semidirect |
| 29. #3953 | C22 | semidirect |
| 30. #3953 | C22 | semidirect |
| 31. #3950 | C22 | semidirect |
| 32. #3949 | C22 | semidirect |
| 73. #407 | D5 | semidirect |
| 127. C22⋊C8 | C2×D5 | semidirect |
| 128. C22⋊C8 | C2×D5 | semidirect |
| 221. C5 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4076 | 2 |
| C2×#4072 | 2 |
| C5×#407 | 2 |
| #65420 | 2 |
| #65410 | 2 |
| #65026 | 2 |
| #65025 | 2 |
| #65024 | 2 |
| #3094 | 5 |