Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
624 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 230 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×#713 | C2 | semidirect |
| 2. C3×C4×C5×Q8 | C2 | semidirect |
| 3. C3×#4041 | C2 | semidirect |
| 4. C3×#4020 | C2 | semidirect |
| 5. C3×C4×D20 | C2 | semidirect |
| 6. #65911 | C3 | direct (N × H) |
| 18. C2×#713 | C2×C3 | semidirect |
| 19. C4×C5×Q8 | C2×C3 | semidirect |
| 20. #4041 | C2×C3 | semidirect |
| 21. #4020 | C2×C3 | semidirect |
| 22. C4×D20 | C2×C3 | semidirect |
| 24. C3×C5×Q8 | D4 | semidirect |
| 36. C3×C4×Q8 | D5 | semidirect |
| 55. C3×C4×C5 | #41 | semidirect |
| 68. C5×Q8 | C3×D4 | semidirect |
| 80. C4×Q8 | C3×D5 | semidirect |
| 87. C3×Q8 | D20 | semidirect |
| 102. C4×C5 | C3×#41 | semidirect |
| 114. C3×C5 | #550 | semidirect |
| 122. C3×C4 | #713 | semidirect |
| 128. Q8 | C3×D20 | semidirect |
| 141. C5 | C3×#550 | semidirect |
| 149. C4 | C3×#713 | semidirect |
| 150. C3 | #65911 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| C3×C4×C5×Q8 | 2 |
| C3×#4041 | 2 |
| C3×#4020 | 2 |
| C3×C4×D20 | 2 |
| #65911 | 3 |
| C3×#550 | 5 |