Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 17. #5090 | C5 | direct (N × H) |
| 53. C3×C4×C5 | Q16 | semidirect |
| 103. C4×C5 | #216 | semidirect |
| 116. C3×C5 | #462 | semidirect |
| 120. C3×C4 | C5×Q16 | semidirect |
| 142. C5 | #5090 | direct (N × H) |
| 148. C4 | C5×#216 | semidirect |
| 151. C3 | C5×#462 | 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 |
| C2×C5×#216 | 2 |
| C4×C5×Dic6 | 2 |
| C5×#835 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#462 | 3 |
| #5090 | 5 |