Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 59 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. C3×C5×#135 | C2 | semidirect |
| 2. #91793 | C2 | semidirect |
| 3. #91113 | C2 | semidirect |
| 4. #91112 | C2 | semidirect |
| 5. #91111 | C2 | semidirect |
| 6. #91110 | C2 | semidirect |
| 7. C2×C3⋊#672 | C2 | semidirect |
| 21. C5×#135 | D3 | semidirect |
| 39. C3×#135 | D5 | semidirect |
| 88. #135 | D15 | semidirect |
| 127. C3×C5 | #508 | semidirect |
| 154. C5 | #5194 | semidirect |
| 162. C3 | #65483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#135 | 2 |
| #91793 | 2 |
| #91113 | 2 |
| #91112 | 2 |
| #91111 | 2 |
| #91110 | 2 |
| C2×C3⋊#672 | 2 |
| #65483 | 3 |
| #5194 | 5 |