Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #91227 | C2 | semidirect |
| 3. #91219 | C2 | semidirect |
| 4. D5⋊(C3⋊C16) | C2 | semidirect |
| 13. C3⋊#674 | C22 | semidirect |
| 77. C3×D5 | M32 | semidirect |
| 105. C3×C5 | C2×M32 | semidirect |
| 117. D5 | #812 | semidirect |
| 133. C5 | C2×#812 | semidirect |
| 142. C3 | D5⋊M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D5 | 2 |
| #91227 | 2 |
| #91219 | 2 |
| D5⋊(C3⋊C16) | 2 |
| D5⋊M32 | 3 |
| C2×#812 | 5 |