Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×C5×Q16 | C2 | semidirect |
| 3. C5×#944 | C2 | semidirect |
| 4. C2×C5×#216 | C2 | semidirect |
| 7. C5×#815 | C2 | semidirect |
| 22. #5190 | C5 | direct (N × H) |
| 24. C2×C5×Q16 | D3 | semidirect |
| 46. C2×C3×Q16 | C2×C5 | semidirect |
| 48. #944 | C2×C5 | semidirect |
| 49. C2×#216 | C2×C5 | semidirect |
| 52. #815 | C2×C5 | semidirect |
| 106. C2×Q16 | C5×D3 | semidirect |
| 153. C3×C5 | #497 | semidirect |
| 185. C5 | #5190 | direct (N × H) |
| 195. C3 | C5×#497 | 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×#947 | 2 |
| C5×#944 | 2 |
| C2×C5×#216 | 2 |
| C2×C5×#215 | 2 |
| C2×C5×#204 | 2 |
| C5×#815 | 2 |
| C5×#497 | 3 |
| #5190 | 5 |