Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 14. C5×Dic12 | C4 | semidirect |
| 15. #4873 | C5 | direct (N × H) |
| 50. C5×Dic3 | Q16 | semidirect |
| 58. Dic12 | C4×C5 | semidirect |
| 100. C3×C5 | C4×Q16 | semidirect |
| 107. Dic3 | C5×Q16 | semidirect |
| 123. C5 | #4873 | direct (N × H) |
| 131. C3 | C4×C5×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic12 | 2 |
| C5×#887 | 2 |
| C3×C5×#107 | 2 |
| C5×C8×Dic3 | 2 |
| C5×#810 | 2 |
| C4×C5×Q16 | 3 |
| #4873 | 5 |