Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 196 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. #5080 | C5 | direct (N × H) |
| 26. C5×C3⋊C8 | Q8 | semidirect |
| 76. C3⋊C8 | C5×Q8 | semidirect |
| 91. C3×C5 | #498 | semidirect |
| 112. C5 | #5080 | direct (N × H) |
| 119. C3 | C5×#498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C5×#869 | 2 |
| C5×#808 | 2 |
| C4×C5×C3⋊C8 | 2 |
| C5×#498 | 3 |
| #5080 | 5 |