Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 204 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 |
|---|---|---|
| 2. C5×#870 | C2 | semidirect |
| 5. C5×#808 | C2 | semidirect |
| 6. C5×#807 | C2 | semidirect |
| 7. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 20. #5009 | C5 | direct (N × H) |
| 41. #870 | C2×C5 | semidirect |
| 44. #808 | C2×C5 | semidirect |
| 45. #807 | C2×C5 | semidirect |
| 46. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 138. C3×C5 | #478 | semidirect |
| 170. C5 | #5009 | direct (N × H) |
| 182. C3 | C5×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| C5×#870 | 2 |
| C5×#832 | 2 |
| C5×#808 | 2 |
| C5×#807 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#478 | 3 |
| #5009 | 5 |