Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C2×Dic60 | C2 | semidirect |
| 3. C2×C3×C5×C16 | C2 | semidirect |
| 4. #91084 | C2 | direct (N × H) |
| 10. Dic60 | C22 | semidirect |
| 13. C3×C5×C16 | C22 | semidirect |
| 17. C2×C5×C16 | D3 | semidirect |
| 30. C2×C3×C16 | D5 | semidirect |
| 39. C5×C16 | C2×D3 | semidirect |
| 54. C3×C16 | C2×D5 | semidirect |
| 67. C2×C16 | D15 | semidirect |
| 68. C2×C3×C5 | SD32 | semidirect |
| 93. C16 | C2×D15 | semidirect |
| 94. C3×C5 | C2×SD32 | semidirect |
| 101. C2×C5 | #800 | semidirect |
| 113. C2×C3 | #3932 | semidirect |
| 116. C5 | C2×#800 | semidirect |
| 123. C3 | C2×#3932 | semidirect |
| 125. C2 | #91084 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic60 | 2 |
| C2×D120 | 2 |
| C2×C3×C5×C16 | 2 |
| #91084 | 2 |
| C2×#3932 | 3 |
| C2×#800 | 5 |