Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #532 |
| 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×#6766 | C2 | semidirect |
| 2. C42×D15 | C2 | semidirect |
| 3. C5×#869 | C2 | semidirect |
| 4. C3×#4020 | C2 | semidirect |
| 5. #91465 | C2 | semidirect |
| 6. #91434 | C2 | semidirect |
| 7. #91368 | C2 | semidirect |
| 28. #4020 | D3 | semidirect |
| 37. C4×D15 | D4 | semidirect |
| 50. #869 | D5 | semidirect |
| 71. C3×C4×C5 | #41 | semidirect |
| 134. C4×C5 | #237 | semidirect |
| 150. C3×C5 | #532 | semidirect |
| 157. C3×C4 | #713 | semidirect |
| 183. C5 | #5716 | semidirect |
| 192. C4 | #6766 | semidirect |
| 194. C3 | #66059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6766 | 2 |
| C42×D15 | 2 |
| C5×#869 | 2 |
| C3×#4020 | 2 |
| #91465 | 2 |
| #91434 | 2 |
| #91368 | 2 |
| #66059 | 3 |
| #5716 | 5 |