Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 52. C3×C4×C5 | Q16 | semidirect |
| 100. C4×C5 | #216 | semidirect |
| 116. C3×C5 | #462 | semidirect |
| 120. C3×C4 | Dic20 | semidirect |
| 142. C5 | #5090 | semidirect |
| 148. C4 | #6662 | semidirect |
| 151. C3 | #65138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic30 | 2 |
| C3×#4015 | 2 |
| C2×#6662 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| #90971 | 2 |
| #65138 | 3 |
| #5090 | 5 |