Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×D5×C4⋊C4 | C2 | semidirect |
| 3. C2×C5×#102 | C2 | semidirect |
| 4. C2×#3964 | C2 | semidirect |
| 5. C2×#3952 | C2 | semidirect |
| 6. #64771 | C2 | semidirect |
| 7. #64749 | C2 | semidirect |
| 16. #4084 | C4 | semidirect |
| 34. C2×C5×D4 | C2×C4 | semidirect |
| 56. C5×C4⋊C4 | D4 | semidirect |
| 60. C4⋊Dic5 | C2×C4 | semidirect |
| 61. C4⋊Dic5 | D4 | semidirect |
| 69. C2×#102 | D5 | semidirect |
| 156. C2×D5 | #102 | semidirect |
| 175. C2×D4 | C4×D5 | semidirect |
| 202. C4⋊C4 | C22⋊D5 | semidirect |
| 258. C5 | #1874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4084 | 2 |
| C2×D5×C4⋊C4 | 2 |
| C2×C5×#102 | 2 |
| C2×#3964 | 2 |
| C2×#3952 | 2 |
| #64771 | 2 |
| #64749 | 2 |
| #1874 | 5 |