Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 88 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. #91103 | C2 | semidirect |
| 4. C3×#3951 | C2 | semidirect |
| 5. #90993 | C2 | semidirect |
| 20. #3951 | D3 | semidirect |
| 98. C3×C5 | #430 | semidirect |
| 120. C5 | #4893 | semidirect |
| 127. C3 | #65414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×ΓL(1,𝔽25) | 2 |
| D3×#681 | 2 |
| #91103 | 2 |
| C3×#3951 | 2 |
| #90993 | 2 |
| #65414 | 3 |
| #4893 | 5 |