Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. C3×C5×#108 | C2 | semidirect |
| 4. C5×#822 | C2 | semidirect |
| 5. C5×#819 | C2 | semidirect |
| 15. #4893 | C5 | direct (N × H) |
| 20. C5×#108 | D3 | semidirect |
| 32. C3×#108 | C2×C5 | semidirect |
| 33. #822 | C2×C5 | semidirect |
| 34. #819 | C2×C5 | semidirect |
| 71. #108 | C5×D3 | semidirect |
| 98. C3×C5 | #430 | semidirect |
| 120. C5 | #4893 | direct (N × H) |
| 127. C3 | C5×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×M16 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| C3×C5×#108 | 2 |
| C5×#822 | 2 |
| C5×#819 | 2 |
| C5×#430 | 3 |
| #4893 | 5 |