Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
492 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 171 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×C3×C5×C4⋊C4 | C2 | semidirect |
| 5. C2×C4⋊Dic15 | C2 | semidirect |
| 6. C2×#6712 | C2 | semidirect |
| 7. C2×C4×Dic15 | C2 | semidirect |
| 8. #91787 | C2 | direct (N × H) |
| 17. C3×C5×C4⋊C4 | C22 | semidirect |
| 21. C4⋊Dic15 | C22 | semidirect |
| 22. #6712 | C22 | semidirect |
| 23. C4×Dic15 | C22 | semidirect |
| 25. C2×C5×C4⋊C4 | D3 | semidirect |
| 50. C2×C3×C4⋊C4 | D5 | semidirect |
| 65. C5×C4⋊C4 | C2×D3 | semidirect |
| 94. C3×C4⋊C4 | C2×D5 | semidirect |
| 121. C2×C4⋊C4 | D15 | semidirect |
| 126. C2×C3×C5 | #126 | semidirect |
| 171. C4⋊C4 | C2×D15 | semidirect |
| 176. C3×C5 | C2×#126 | semidirect |
| 191. C2×C5 | #898 | semidirect |
| 213. C2×C3 | #4044 | semidirect |
| 218. C5 | C2×#898 | semidirect |
| 233. C3 | C2×#4044 | semidirect |
| 235. C2 | #91787 | 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×C4⋊C4 | 2 |
| C2×#6714 | 2 |
| C2×C4⋊Dic15 | 2 |
| C2×#6712 | 2 |
| C2×C4×Dic15 | 2 |
| #91787 | 2 |
| C2×#4044 | 3 |
| C2×#898 | 5 |