Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
412 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 136 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×C3×C5×#168 | C2 | semidirect |
| 3. C3×#87767 | C2 | direct (N × H) |
| 4. C2×#87767 | C3 | direct (N × H) |
| 10. C3×C5×#168 | C22 | semidirect |
| 13. C2×C5×#168 | C2×C3 | semidirect |
| 14. #87767 | C2×C3 | direct (N × H) |
| 16. C2×C3×C5⋊D5 | C8 | semidirect |
| 24. C2×C3×#168 | D5 | semidirect |
| 31. C5×#168 | C22×C3 | semidirect |
| 33. C2×C3×C52 | C2×C8 | semidirect |
| 35. C3×C5⋊D5 | C2×C8 | semidirect |
| 47. C3×#168 | C2×D5 | semidirect |
| 49. C2×C5⋊D5 | C3×C8 | semidirect |
| 58. C2×#168 | C3×D5 | semidirect |
| 60. C3×C52 | C22×C8 | semidirect |
| 73. C2×C52 | C2×C3×C8 | semidirect |
| 75. C5⋊D5 | C2×C3×C8 | semidirect |
| 90. #168 | C2×C3×D5 | semidirect |
| 94. C2×C3×C5 | C8×D5 | semidirect |
| 98. C52 | C22×C3×C8 | semidirect |
| 121. C3×C5 | C2×C8×D5 | semidirect |
| 130. C2×C5 | C3×C8×D5 | semidirect |
| 141. C2×C3 | #87767 | direct (N × H) |
| 144. C5 | C2×C3×C8×D5 | semidirect |
| 151. C3 | C2×#87767 | direct (N × H) |
| 153. C2 | C3×#87767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5⋊D5 | 2 |
| C2×C3×C5×#168 | 2 |
| C3×#87767 | 2 |
| C2×#87767 | 3 |
| C2×C3×C8×D5 | 5 |