Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C3×C5 |
| prime radical | C2×C3×C5×D8 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×Q16 | C2 | semidirect |
| 2. C2×C3×C5×SD16 | C2 | semidirect |
| 4. C3×C5×#124 | C2 | semidirect |
| 5. C3×C4×C5×C8 | C2 | semidirect |
| 6. C5×#495 | C3 | direct (N × H) |
| 16. C3×#495 | C5 | direct (N × H) |
| 17. C2×C5×Q16 | C2×C3 | semidirect |
| 18. C2×C5×SD16 | C2×C3 | semidirect |
| 20. C5×#124 | C2×C3 | semidirect |
| 21. C4×C5×C8 | C2×C3 | semidirect |
| 32. C2×C3×Q16 | C2×C5 | semidirect |
| 33. C2×C3×SD16 | C2×C5 | semidirect |
| 35. C3×#124 | C2×C5 | semidirect |
| 36. C3×C4×C8 | C2×C5 | semidirect |
| 46. #495 | C3×C5 | direct (N × H) |
| 73. C2×Q16 | C2×C3×C5 | semidirect |
| 74. C2×SD16 | C2×C3×C5 | semidirect |
| 76. #124 | C2×C3×C5 | semidirect |
| 77. C4×C8 | C2×C3×C5 | semidirect |
| 107. C3×C5 | #495 | direct (N × H) |
| 131. C5 | C3×#495 | direct (N × H) |
| 139. C3 | C5×#495 | 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×Q16 | 2 |
| C2×C3×C5×SD16 | 2 |
| C2×C3×C5×D8 | 2 |
| C3×C5×#124 | 2 |
| C3×C4×C5×C8 | 2 |
| C5×#495 | 3 |
| C3×#495 | 5 |