Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 82 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×D40 | C2 | semidirect |
| 2. C2×C3×#676 | C2 | semidirect |
| 3. C3×#4041 | C2 | semidirect |
| 4. C3×C5×#106 | C2 | semidirect |
| 5. C3×#3941 | C2 | semidirect |
| 6. #65154 | C3 | direct (N × H) |
| 17. C2×D40 | C2×C3 | semidirect |
| 18. C2×#676 | C2×C3 | semidirect |
| 19. #4041 | C2×C3 | semidirect |
| 20. C5×#106 | C2×C3 | semidirect |
| 21. #3941 | C2×C3 | semidirect |
| 32. C3×C5×C8 | D4 | semidirect |
| 37. C3×#106 | D5 | semidirect |
| 78. C5×C8 | C3×D4 | semidirect |
| 83. #106 | C3×D5 | semidirect |
| 100. C3×C8 | D20 | semidirect |
| 120. C3×C5 | #469 | semidirect |
| 146. C8 | C3×D20 | semidirect |
| 151. C5 | C3×#469 | semidirect |
| 162. C3 | #65154 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D40 | 2 |
| C2×C3×#676 | 2 |
| C3×#4041 | 2 |
| C3×C5×#106 | 2 |
| C3×#3941 | 2 |
| #65154 | 3 |
| C3×#469 | 5 |