Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. C3×C5×2−1+4 | C2 | semidirect |
| 2. #92101 | C2 | semidirect |
| 3. #91840 | C2 | semidirect |
| 4. #91839 | C2 | semidirect |
| 5. #91837 | C2 | semidirect |
| 6. C2×#6718 | C2 | semidirect |
| 7. #91831 | C2 | semidirect |
| 26. C5×2−1+4 | D3 | semidirect |
| 50. C3×2−1+4 | D5 | semidirect |
| 115. 2−1+4 | D15 | semidirect |
| 165. C3×C5 | #578 | semidirect |
| 198. C5 | #5838 | semidirect |
| 206. C3 | #66172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×2−1+4 | 2 |
| #92101 | 2 |
| #91840 | 2 |
| #91839 | 2 |
| #91837 | 2 |
| C2×#6718 | 2 |
| #91831 | 2 |
| #66172 | 3 |
| #5838 | 5 |