Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 80 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×D120 | C2 | semidirect |
| 2. C2×C3×D40 | C2 | semidirect |
| 3. #91458 | C2 | semidirect |
| 4. C2×#6653 | C2 | semidirect |
| 5. C5×C8×Dic3 | C2 | semidirect |
| 19. C2×D40 | D3 | semidirect |
| 31. C3×C5×C8 | D4 | semidirect |
| 32. C5×C3⋊C8 | D4 | semidirect |
| 37. C8×Dic3 | D5 | semidirect |
| 55. C5×Dic3 | D8 | semidirect |
| 75. C5×C8 | #67 | semidirect |
| 94. C3×C8 | D20 | semidirect |
| 95. C3⋊C8 | D20 | semidirect |
| 113. C3×C5 | #493 | semidirect |
| 121. Dic3 | D40 | semidirect |
| 136. C8 | #1202 | semidirect |
| 141. C5 | #5151 | semidirect |
| 150. C3 | #64984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D120 | 2 |
| C2×C3×D40 | 2 |
| #91458 | 2 |
| C2×#6653 | 2 |
| C5×C8×Dic3 | 2 |
| #64984 | 3 |
| #5151 | 5 |