Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
312 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 62 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. C5×A4⋊Q8 | C2 | semidirect |
| 9. Q8×S4 | C5 | direct (N × H) |
| 11. C22×C5×Q8 | D3 | semidirect |
| 18. C5×S4 | Q8 | direct (N × H) |
| 22. Q8×A4 | C2×C5 | semidirect |
| 24. A4⋊Q8 | C2×C5 | semidirect |
| 41. C5×A4 | C2×Q8 | semidirect |
| 54. C5×Q8 | S4 | direct (N × H) |
| 65. C22×Q8 | C5×D3 | semidirect |
| 74. S4 | C5×Q8 | direct (N × H) |
| 83. C22×C5 | D3×Q8 | semidirect |
| 105. A4 | C2×C5×Q8 | semidirect |
| 118. Q8 | C5×S4 | direct (N × H) |
| 130. C5 | Q8×S4 | direct (N × H) |
| 136. C22 | C5×D3×Q8 | 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 |
| C5×A4⋊Q8 | 2 |
| C5×D4×Q8 | 3 |
| C5×D3×Q8 | 4 |
| Q8×S4 | 5 |