Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
560 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 174 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. C2×C5×D3×Q8 | C2 | semidirect |
| 2. C2×C3×Q8×D5 | C2 | semidirect |
| 3. Q8×Dic15 | C2 | semidirect |
| 5. #91385 | C2 | semidirect |
| 6. #91369 | C2 | semidirect |
| 7. #91359 | C2 | semidirect |
| 25. C2×Q8×D5 | D3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 43. #1201 | Q8 | direct (N × H) |
| 45. C2×D3×Q8 | D5 | semidirect |
| 69. C2×C5×D3 | C2×Q8 | semidirect |
| 72. C2×C3×D5 | C2×Q8 | semidirect |
| 75. Dic15 | C2×Q8 | semidirect |
| 95. C5×Q8 | #67 | semidirect |
| 120. C3×Q8 | C22⋊D5 | semidirect |
| 136. C2×D5 | D3×Q8 | semidirect |
| 156. C3×C5 | D4×Q8 | semidirect |
| 163. C2×D3 | Q8×D5 | semidirect |
| 178. Q8 | #1201 | direct (N × H) |
| 192. C5 | Q8×#67 | semidirect |
| 205. C3 | Q8×C22⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| C2×C3×Q8×D5 | 2 |
| Q8×Dic15 | 2 |
| C4×#1201 | 2 |
| #91385 | 2 |
| #91369 | 2 |
| #91359 | 2 |
| Q8×C22⋊D5 | 3 |
| Q8×#67 | 5 |