Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. D5×C4⋊Q8 | C2 | semidirect |
| 3. C5×#477 | C2 | semidirect |
| 4. #65373 | C2 | semidirect |
| 5. #65310 | C2 | semidirect |
| 6. #65179 | C2 | semidirect |
| 7. #65170 | C2 | semidirect |
| 8. #65131 | C2 | semidirect |
| 9. #65126 | C2 | semidirect |
| 11. #65080 | C2 | semidirect |
| 47. #713 | Q8 | semidirect |
| 86. #477 | D5 | semidirect |
| 98. C5×Q8 | C2×Q8 | semidirect |
| 112. D20 | C2×Q8 | semidirect |
| 225. Q8 | Q8×D5 | semidirect |
| 250. C5 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| C4×#713 | 2 |
| C5×#477 | 2 |
| #65373 | 2 |
| #65310 | 2 |
| #65179 | 2 |
| #65170 | 2 |
| #65131 | 2 |
| #65126 | 2 |
| #65092 | 2 |
| #65080 | 2 |
| #3079 | 5 |