Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | C2×D4 |
| commutator | C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C4 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×C4⋊C4 |
| prime radical | C23×C3×C5 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×C5×#108 | C2 | semidirect |
| 4. C5×#430 | C3 | direct (N × H) |
| 11. C3×#430 | C5 | direct (N × H) |
| 14. C5×#108 | C2×C3 | semidirect |
| 24. C3×#108 | C2×C5 | semidirect |
| 31. #430 | C3×C5 | direct (N × H) |
| 53. #108 | C2×C3×C5 | semidirect |
| 76. C3×C5 | #430 | direct (N × H) |
| 96. C5 | C3×#430 | direct (N × H) |
| 103. C3 | C5×#430 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×M16 | 2 |
| C3×C5×#108 | 2 |
| C5×#430 | 3 |
| C3×#430 | 5 |