Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. C3×C5×C4⋊Q8 | C2 | semidirect |
| 4. #91091 | C2 | semidirect |
| 5. C4⋊(C3⋊#168) | C2 | semidirect |
| 17. C5×C4⋊Q8 | D3 | semidirect |
| 30. D60 | Q8 | semidirect |
| 33. C3×C4⋊Q8 | D5 | semidirect |
| 78. C4⋊Q8 | D15 | semidirect |
| 117. C3×C5 | #474 | semidirect |
| 147. C5 | #5087 | semidirect |
| 158. C3 | #65376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C4×D60 | 2 |
| #91093 | 2 |
| #91091 | 2 |
| C4⋊(C3⋊#168) | 2 |
| #65376 | 3 |
| #5087 | 5 |