Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
560 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 163 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 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×C4⋊Q8 | C2 |
| prime radical | C2×D60 | C22 |
| hypercenter | C4⋊Q8 | D15 |
| hypocenter | C3×C5 | D4×Q8 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D15 | C2 | semidirect |
| 2. C3×C5×C4⋊Q8 | C2 | semidirect |
| 3. #91835 | C2 | semidirect |
| 4. #91785 | C2 | semidirect |
| 6. #91777 | C2 | semidirect |
| 8. C4×Dic30 | C2 | semidirect |
| 29. C5×C4⋊Q8 | D3 | semidirect |
| 45. D60 | Q8 | semidirect |
| 49. Dic30 | D4 | semidirect |
| 51. C3×C4⋊Q8 | D5 | semidirect |
| 79. C2×D15 | C2×Q8 | semidirect |
| 83. C3×C4×C5 | C2×Q8 | semidirect |
| 120. C4⋊Q8 | D15 | semidirect |
| 151. C4×C5 | D3×Q8 | semidirect |
| 172. C3×C5 | D4×Q8 | semidirect |
| 180. C3×C4 | Q8×D5 | semidirect |
| 206. C5 | #5727 | semidirect |
| 217. C4 | Q8×D15 | semidirect |
| 218. C3 | #66061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D15 | 2 |
| C3×C5×C4⋊Q8 | 2 |
| #91835 | 2 |
| #91785 | 2 |
| #91782 | 2 |
| #91777 | 2 |
| C4×D60 | 2 |
| C4×Dic30 | 2 |
| #66061 | 3 |
| #5727 | 5 |