Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
312 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 49 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. C5×Q8×A4 | C2 | semidirect |
| 3. #91948 | C2 | semidirect |
| 10. C22×C5×Q8 | D3 | semidirect |
| 18. C5⋊S4 | Q8 | direct (N × H) |
| 22. Q8×A4 | D5 | semidirect |
| 41. C5×A4 | C2×Q8 | semidirect |
| 52. C5×Q8 | S4 | semidirect |
| 65. C22×Q8 | D15 | semidirect |
| 80. C22×C5 | D3×Q8 | semidirect |
| 105. A4 | Q8×D5 | semidirect |
| 118. Q8 | C5⋊S4 | direct (N × H) |
| 130. C5 | Q8×S4 | semidirect |
| 136. C22 | Q8×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×A4 | 2 |
| C4×C5⋊S4 | 2 |
| #91948 | 2 |
| Q8×C22⋊D5 | 3 |
| Q8×D15 | 4 |
| Q8×S4 | 5 |