Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
484 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting, prime radical | C24×C3×C5 | C22 |
| hypercenter | C24 | D3×D5 |
| hypocenter | C3×C5 | #543 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #91576 | C2 | semidirect |
| 5. #91575 | C2 | semidirect |
| 6. #91574 | C2 | semidirect |
| 12. C2×#1204 | C22 | semidirect |
| 19. Dic3⋊Dic5 | C22 | semidirect |
| 20. #6669 | C22 | semidirect |
| 21. #6668 | C22 | semidirect |
| 30. C23×C3×C5 | Q8 | semidirect |
| 88. C23×C5 | Dic6 | semidirect |
| 111. C23×C3 | Dic10 | semidirect |
| 147. C3×C5 | #543 | semidirect |
| 165. C23 | #1204 | semidirect |
| 181. C5 | #5483 | semidirect |
| 193. C3 | #65817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6719 | 2 |
| C2×C5×#217 | 2 |
| C2×C3×C22⋊Dic5 | 2 |
| #91576 | 2 |
| #91575 | 2 |
| #91574 | 2 |
| #65817 | 3 |
| #5483 | 5 |