Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
444 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 152 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. #91759 | C2 | semidirect |
| 2. C5×#870 | C2 | semidirect |
| 4. #91468 | C2 | semidirect |
| 7. #91323 | C2 | semidirect |
| 38. C3×C4×D5 | Q8 | semidirect |
| 44. #870 | D5 | semidirect |
| 91. C4×D5 | Dic6 | semidirect |
| 135. C3×C5 | #533 | semidirect |
| 161. C5 | #5470 | semidirect |
| 171. C3 | #66022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91759 | 2 |
| C5×#870 | 2 |
| C3×C42×D5 | 2 |
| #91468 | 2 |
| #91358 | 2 |
| #91349 | 2 |
| #91323 | 2 |
| #66022 | 3 |
| #5470 | 5 |