Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
380 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. C2×#6710 | C2 | semidirect |
| 3. C5×#926 | C2 | semidirect |
| 4. #90964 | C2 | semidirect |
| 10. C2×C3×D20 | C4 | semidirect |
| 13. C2×C3⋊#168 | C22 | semidirect |
| 15. C5×C4⋊Dic3 | C22 | semidirect |
| 36. #926 | D5 | semidirect |
| 43. C2×D20 | Dic3 | semidirect |
| 68. C4⋊Dic3 | C2×D5 | semidirect |
| 127. C3×C5 | #418 | semidirect |
| 159. C5 | #5215 | semidirect |
| 170. C3 | #65290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D20 | 2 |
| C2×#6710 | 2 |
| C5×#926 | 2 |
| #90964 | 2 |
| #65290 | 3 |
| #5215 | 5 |