Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 29. C3×C5×Q8 | Q8 | semidirect |
| 80. C5×Q8 | Dic6 | semidirect |
| 102. C3×Q8 | Dic10 | semidirect |
| 133. C3×C5 | #475 | semidirect |
| 148. Q8 | #1204 | semidirect |
| 161. C5 | #5020 | semidirect |
| 171. C3 | #65080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×Dic5 | 2 |
| #91468 | 2 |
| #91119 | 2 |
| C5×#835 | 2 |
| #90987 | 2 |
| #90986 | 2 |
| #90982 | 2 |
| #65080 | 3 |
| #5020 | 5 |