Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
116 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 7. C3×C5×Q16 | C4 | semidirect |
| 11. #4564 | C5 | direct (N × H) |
| 27. C5×Q16 | Dic3 | semidirect |
| 39. C3×Q16 | C4×C5 | semidirect |
| 70. Q16 | C5×Dic3 | semidirect |
| 74. C3×C5 | #358 | semidirect |
| 93. C5 | #4564 | direct (N × H) |
| 99. C3 | C5×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q16 | 2 |
| C5×#818 | 2 |
| C2×C5×C3⋊C16 | 2 |
| C5×#358 | 3 |
| #4564 | 5 |