Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
1056 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 203 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×C3⋊(C5⋊D5) | C2 | semidirect |
| 3. C3×C52×C22⋊C4 | C2 | semidirect |
| 4. #11925254 | C2 | semidirect |
| 5. #11925249 | C2 | semidirect |
| 9. C22×C3⋊(C5⋊D5) | C4 | semidirect |
| 12. C2×C3×C4×C52 | C22 | semidirect |
| 13. C2×C3⋊#1039 | C22 | semidirect |
| 18. C52×C22⋊C4 | D3 | semidirect |
| 22. C22×C3×C52 | C2×C4 | semidirect |
| 27. C2×C3⋊(C5⋊D5) | C2×C4 | semidirect |
| 33. C3×C5×C22⋊C4 | D5 | semidirect |
| 41. C2×C4×C52 | C2×D3 | semidirect |
| 49. C3⋊(C5⋊D5) | C22⋊C4 | direct (N × H) |
| 55. C2×C3×C4×C5 | C2×D5 | semidirect |
| 59. C22×C52 | C4×D3 | semidirect |
| 71. C5×C22⋊C4 | D15 | semidirect |
| 74. C3×C52 | C2×C22⋊C4 | semidirect |
| 76. C22×C3×C5 | C4×D5 | semidirect |
| 92. C3×C22⋊C4 | C5⋊D5 | semidirect |
| 100. C2×C4×C5 | C2×D15 | semidirect |
| 109. C52 | D3×C22⋊C4 | semidirect |
| 115. C2×C3×C4 | C2×C5⋊D5 | semidirect |
| 119. C22×C5 | C4×D15 | semidirect |
| 132. C22⋊C4 | C3⋊(C5⋊D5) | direct (N × H) |
| 133. C3×C5 | D5×C22⋊C4 | semidirect |
| 135. C22×C3 | C4×C5⋊D5 | semidirect |
| 156. C2×C4 | C2×C3⋊(C5⋊D5) | semidirect |
| 162. C5 | C22⋊C4×D15 | semidirect |
| 169. C22 | C4×C3⋊(C5⋊D5) | semidirect |
| 173. C3 | C22⋊C4×C5⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊(C5⋊D5) | 2 |
| C2×C4×C3⋊(C5⋊D5) | 2 |
| C3×C52×C22⋊C4 | 2 |
| #11925254 | 2 |
| #11925249 | 2 |
| C22⋊C4×C5⋊D5 | 3 |
| C22⋊C4×D15 | 5 |