Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
410 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 75 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. A4×Dic10 | C2 | semidirect |
| 4. C22×Q8×D5 | C3 | semidirect |
| 10. C22×C5×Q8 | C2×C3 | semidirect |
| 16. C22×Dic10 | C2×C3 | semidirect |
| 18. D5×A4 | Q8 | direct (N × H) |
| 23. Q8×A4 | D5 | direct (N × H) |
| 36. Q8×D5 | A4 | direct (N × H) |
| 46. C5×A4 | C2×Q8 | semidirect |
| 57. C22×D5 | C3×Q8 | semidirect |
| 60. C5×Q8 | C2×A4 | semidirect |
| 73. Dic10 | C2×A4 | semidirect |
| 79. C22×Q8 | C3×D5 | semidirect |
| 90. C22×C5 | C2×C3×Q8 | semidirect |
| 122. A4 | Q8×D5 | direct (N × H) |
| 129. D5 | Q8×A4 | direct (N × H) |
| 141. Q8 | D5×A4 | direct (N × H) |
| 153. C5 | C2×Q8×A4 | semidirect |
| 162. C22 | C3×Q8×D5 | 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×D5×A4 | 2 |
| A4×Dic10 | 2 |
| C22×Q8×D5 | 3 |
| C3×Q8×D5 | 4 |
| C2×Q8×A4 | 5 |