Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
424 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 174 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, prime radical, cosocle | C22×C3×C5 | C24 |
| Fitting | C2×C3×C5×Q8 | C22 |
| hypercenter | C2×Q8 | D3×D5 |
| hypocenter | C3×C5 | Q82 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. C3×C5×Q8 | Q8 | semidirect |
| 38. #1204 | Q8 | direct (N × H) |
| 79. C5×Q8 | Dic6 | semidirect |
| 99. C3×Q8 | Dic10 | semidirect |
| 129. C3×C5 | Q82 | semidirect |
| 143. Q8 | #1204 | direct (N × H) |
| 154. C5 | Q8×Dic6 | semidirect |
| 163. C3 | Q8×Dic10 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic15 | 2 |
| C5×Q8×Dic3 | 2 |
| C3×Q8×Dic5 | 2 |
| #91470 | 2 |
| #91469 | 2 |
| #91468 | 2 |
| C4×#1204 | 2 |
| Q8×Dic10 | 3 |
| Q8×Dic6 | 5 |