Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
560 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 560 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 | C3×C42×C5 | C22 |
| prime radical | C2×D60 | C22 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | D4×Q8 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D15⋊Q8 | C2 | semidirect |
| 3. C4×C5×Dic6 | C2 | semidirect |
| 4. C3×#4015 | C2 | semidirect |
| 5. #91469 | C2 | semidirect |
| 6. #91429 | C2 | semidirect |
| 8. #91390 | C2 | semidirect |
| 35. #4015 | D3 | semidirect |
| 41. D60 | Q8 | semidirect |
| 45. C5×Dic6 | D4 | semidirect |
| 57. C4×Dic6 | D5 | semidirect |
| 79. C2×D15 | C2×Q8 | semidirect |
| 82. C3×C4×C5 | C2×Q8 | semidirect |
| 143. Dic6 | D20 | semidirect |
| 152. C4×C5 | D3×Q8 | semidirect |
| 172. C3×C5 | D4×Q8 | semidirect |
| 180. C3×C4 | Q8×D5 | semidirect |
| 206. C5 | #5727 | semidirect |
| 216. C4 | D15⋊Q8 | semidirect |
| 218. C3 | Q8×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D15⋊Q8 | 2 |
| C4×D60 | 2 |
| C4×C5×Dic6 | 2 |
| C3×#4015 | 2 |
| #91469 | 2 |
| #91429 | 2 |
| #91428 | 2 |
| #91390 | 2 |
| Q8×D20 | 3 |
| #5727 | 5 |