Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
864 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 864 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 |
|---|---|---|
| 3. C4×C52×Dic3 | C2 | semidirect |
| 4. C3×C4×#1039 | C2 | semidirect |
| 5. Dic3×#1039 | C2 | semidirect |
| 10. C4×C3⋊(C5⋊D5) | C4 | semidirect |
| 13. #10597113 | C4 | direct (N × H) |
| 19. C4×#1039 | D3 | semidirect |
| 23. C3×C4×C52 | C2×C4 | semidirect |
| 24. C3⋊#1039 | C2×C4 | semidirect |
| 25. C52×Dic3 | C2×C4 | semidirect |
| 26. C3×#1039 | C2×C4 | semidirect |
| 29. C4×C5×Dic3 | D5 | semidirect |
| 42. C3⋊(C5⋊D5) | C42 | semidirect |
| 54. C4×C52 | C4×D3 | semidirect |
| 56. #1039 | C4×D3 | semidirect |
| 63. C3×C52 | C2×C42 | semidirect |
| 67. C3×C4×C5 | C4×D5 | semidirect |
| 70. C5×Dic3 | C4×D5 | semidirect |
| 78. C4×Dic3 | C5⋊D5 | semidirect |
| 90. C52 | C42×D3 | semidirect |
| 102. C4×C5 | #1200 | semidirect |
| 110. C3×C5 | C42×D5 | semidirect |
| 115. C3×C4 | C4×C5⋊D5 | semidirect |
| 117. Dic3 | C4×C5⋊D5 | semidirect |
| 131. C5 | C4×#1200 | semidirect |
| 138. C4 | #10597113 | direct (N × H) |
| 139. C3 | C42×C5⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C5⋊D5) | 2 |
| C2×#10597113 | 2 |
| C4×C52×Dic3 | 2 |
| C3×C4×#1039 | 2 |
| Dic3×#1039 | 2 |
| C42×C5⋊D5 | 3 |
| C4×#1200 | 5 |