Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D15 |
| commutator, hypocenter | C3×C5 | C22×C16 |
| Frattini | C8 | C22×D15 |
| Fitting | C2×C3×C5×C16 | C2 |
| socle | C22×C3×C5 | C2×C8 |
| prime radical | C22×D15 | C8 |
| cosocle | C3×C5×C8 | C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C5×C16 | C2 | semidirect |
| 3. C2×C3⋊#672 | C2 | semidirect |
| 4. C16×D15 | C2 | direct (N × H) |
| 11. C3×C5×C16 | C22 | semidirect |
| 12. C3⋊#672 | C22 | semidirect |
| 15. C2×C5×C16 | D3 | semidirect |
| 27. C2×C3×C16 | D5 | semidirect |
| 35. C5×C16 | C2×D3 | semidirect |
| 39. C2×D15 | C16 | direct (N × H) |
| 49. C3×C16 | C2×D5 | semidirect |
| 62. C2×C16 | D15 | direct (N × H) |
| 63. C2×C3×C5 | C2×C16 | semidirect |
| 65. D15 | C2×C16 | direct (N × H) |
| 86. C16 | C2×D15 | direct (N × H) |
| 87. C3×C5 | C22×C16 | semidirect |
| 94. C2×C5 | D3×C16 | semidirect |
| 105. C2×C3 | D5×C16 | semidirect |
| 108. C5 | C2×D3×C16 | semidirect |
| 115. C3 | C2×D5×C16 | semidirect |
| 117. C2 | C16×D15 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D15 | 2 |
| C2×C3×C5×C16 | 2 |
| C2×C3⋊#672 | 2 |
| C16×D15 | 2 |
| C2×D5×C16 | 3 |
| C2×D3×C16 | 5 |