Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
1056 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 2. C2×C4×C52×D3 | C2 | semidirect |
| 3. C2×D3×#1039 | C2 | semidirect |
| 4. #11925249 | C2 | semidirect |
| 5. C3×#87808 | C2 | semidirect |
| 6. #11925120 | C2 | semidirect |
| 7. #11925118 | C2 | semidirect |
| 14. C2×D3×C5⋊D5 | C4 | semidirect |
| 15. C2×C3×C4×C52 | C22 | semidirect |
| 16. C2×C3⋊#1039 | C22 | semidirect |
| 17. C2×C52×Dic3 | C22 | semidirect |
| 19. C2×C3×#1039 | C22 | semidirect |
| 28. #87808 | D3 | direct (N × H) |
| 32. C2×C3⋊(C5⋊D5) | C2×C4 | semidirect |
| 38. C2×C3×C5⋊D5 | C2×C4 | semidirect |
| 45. C2×C4×C5×D3 | D5 | semidirect |
| 59. C2×C4×C52 | C2×D3 | semidirect |
| 62. C2×#1039 | C2×D3 | semidirect |
| 68. C52×D3 | C22⋊C4 | semidirect |
| 76. C2×C3×C4×C5 | C2×D5 | semidirect |
| 78. C2×C5×Dic3 | C2×D5 | semidirect |
| 92. C2×C5⋊D5 | C4×D3 | semidirect |
| 105. C3×C52 | C2×C22⋊C4 | semidirect |
| 129. C2×C4×D3 | C5⋊D5 | semidirect |
| 142. C2×C4×C5 | D3×D5 | semidirect |
| 152. C5×D3 | #685 | semidirect |
| 153. C52 | D3×C22⋊C4 | semidirect |
| 161. C2×C3×C4 | C2×C5⋊D5 | semidirect |
| 163. C2×Dic3 | C2×C5⋊D5 | semidirect |
| 188. C3×C5 | C2×#685 | semidirect |
| 221. C2×C4 | D3×C5⋊D5 | semidirect |
| 227. D3 | #87808 | direct (N × H) |
| 228. C5 | D3×#685 | semidirect |
| 244. C3 | C2×#87808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C5⋊D5 | 2 |
| C2×C4×C52×D3 | 2 |
| C2×D3×#1039 | 2 |
| #11925249 | 2 |
| C3×#87808 | 2 |
| #11925120 | 2 |
| #11925118 | 2 |
| C2×#87808 | 3 |
| D3×#685 | 5 |