Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 2. C5×#869 | C2 | semidirect |
| 4. C5×#808 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 16. #5008 | C5 | direct (N × H) |
| 24. C3×C5×D4 | Q8 | semidirect |
| 34. #869 | C2×C5 | semidirect |
| 36. #808 | C2×C5 | semidirect |
| 37. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 70. C5×D4 | Dic6 | semidirect |
| 89. C3×D4 | C5×Q8 | semidirect |
| 117. C3×C5 | #476 | semidirect |
| 135. D4 | C5×Dic6 | semidirect |
| 147. C5 | #5008 | direct (N × H) |
| 158. C3 | C5×#476 | 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×#869 | 2 |
| C5×#832 | 2 |
| C5×#808 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#476 | 3 |
| #5008 | 5 |