Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
400 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 179 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, prime radical, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C4×C5×Q8 | C2 |
| hypercenter | C4×Q8 | D15 |
| hypocenter | C3×C5 | #557 |
| 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 |
|---|---|---|
| 22. C3×C5×Q8 | Q8 | semidirect |
| 59. C5×Q8 | Dic6 | semidirect |
| 74. C3×Q8 | Dic10 | semidirect |
| 96. C3×C5 | #557 | semidirect |
| 107. Q8 | Dic30 | semidirect |
| 116. C5 | #5570 | semidirect |
| 123. C3 | #65904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| Q8×Dic15 | 2 |
| #91779 | 2 |
| #91758 | 2 |
| C4×Dic30 | 2 |
| #65904 | 3 |
| #5570 | 5 |