Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊#674 | C2 | semidirect |
| 3. D5⋊(C3⋊C16) | C2 | direct (N × H) |
| 10. C3⋊#674 | C22 | semidirect |
| 34. C2×C3×D5 | C16 | semidirect |
| 56. C2×C3×C5 | C2×C16 | semidirect |
| 58. C3×D5 | C2×C16 | semidirect |
| 68. C2×D5 | C3⋊C16 | semidirect |
| 79. C3×C5 | C22×C16 | semidirect |
| 86. C2×C5 | C2×C3⋊C16 | semidirect |
| 88. D5 | C2×C3⋊C16 | semidirect |
| 98. C2×C3 | D5⋊C16 | semidirect |
| 100. C5 | C22×C3⋊C16 | semidirect |
| 107. C3 | C2×D5⋊C16 | semidirect |
| 109. C2 | D5⋊(C3⋊C16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D5 | 2 |
| C2×C3⋊#674 | 2 |
| D5⋊(C3⋊C16) | 2 |
| C2×D5⋊C16 | 3 |
| C22×C3⋊C16 | 5 |