Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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×Dic20 | C2 | semidirect |
| 4. C3×#4015 | C2 | semidirect |
| 5. C3×C5×#97 | C2 | semidirect |
| 6. #65004 | C3 | direct (N × H) |
| 17. C2×Dic20 | C2×C3 | semidirect |
| 20. #4015 | C2×C3 | semidirect |
| 21. C5×#97 | C2×C3 | semidirect |
| 36. C3×#97 | D5 | semidirect |
| 77. #97 | C3×D5 | semidirect |
| 107. C3×C5 | #497 | semidirect |
| 131. C5 | C3×#497 | semidirect |
| 139. C3 | #65004 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic20 | 2 |
| C2×C3×#677 | 2 |
| C3×#4021 | 2 |
| C3×#4015 | 2 |
| C3×C5×#97 | 2 |
| #65004 | 3 |
| C3×#497 | 5 |