Finite Group DatabasebetaFinite Group DatabasebetaOrder 720.
176 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 70 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. C32×C5×D4 | C2 | semidirect |
| 2. C3×#1220 | C2 | semidirect |
| 3. C2×C3×Dic15 | C2 | semidirect |
| 4. C3×C4×D15 | C2 | semidirect |
| 5. C3×Dic30 | C2 | semidirect |
| 6. #6819 | C3 | direct (N × H) |
| 15. C3×C5×D4 | D3 | semidirect |
| 16. C3×C5×D4 | C2×C3 | semidirect |
| 17. #1220 | C2×C3 | semidirect |
| 18. C2×Dic15 | C2×C3 | semidirect |
| 19. C4×D15 | C2×C3 | semidirect |
| 20. Dic30 | C2×C3 | semidirect |
| 29. C32×D4 | D5 | semidirect |
| 48. C32×C5 | #41 | semidirect |
| 49. C5×D4 | C3×D3 | semidirect |
| 70. C3×D4 | C3×D5 | semidirect |
| 71. C3×D4 | D15 | semidirect |
| 88. C3×C5 | #237 | semidirect |
| 89. C3×C5 | C3×#41 | semidirect |
| 105. C32 | #711 | semidirect |
| 108. D4 | C3×D15 | semidirect |
| 119. C5 | C3×#237 | semidirect |
| 126. C3 | C3×#711 | semidirect |
| 127. C3 | #6819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×D4 | 2 |
| C3×#1220 | 2 |
| C2×C3×Dic15 | 2 |
| C3×C4×D15 | 2 |
| C3×Dic30 | 2 |
| #6819 | 3 |
| C3×#711 | 3 |
| C3×#237 | 5 |