Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C5×#125 | C2 | semidirect |
| 3. C3×#3942 | C2 | semidirect |
| 5. C3×C4×#168 | C2 | semidirect |
| 6. #65357 | C3 | direct (N × H) |
| 15. C5×#125 | C2×C3 | semidirect |
| 17. #3942 | C2×C3 | semidirect |
| 19. C4×#168 | C2×C3 | semidirect |
| 28. C3×#125 | D5 | semidirect |
| 63. #125 | C3×D5 | semidirect |
| 93. C3×C5 | #488 | semidirect |
| 115. C5 | C3×#488 | semidirect |
| 123. C3 | #65357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#125 | 2 |
| C3×#4021 | 2 |
| C3×#3942 | 2 |
| C3×#3941 | 2 |
| C3×C4×#168 | 2 |
| #65357 | 3 |
| C3×#488 | 5 |