Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
484 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 484 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. C2×D3×#1044 | C2 | semidirect |
| 3. C4×C3⋊#1044 | C2 | semidirect |
| 4. C3×C4⋊#1044 | C2 | semidirect |
| 5. (C2×D3)⋊#1044 | C2 | semidirect |
| 12. C4⋊(C3⋊(C5⋊D5)) | C4 | semidirect |
| 13. C52×D12 | C4 | semidirect |
| 15. #10597116 | C4 | semidirect |
| 20. C4⋊#1044 | D3 | semidirect |
| 22. C2×C3⋊(C5⋊D5) | C2×C4 | semidirect |
| 23. C2×C52×D3 | C2×C4 | semidirect |
| 28. C3⋊#1044 | D4 | semidirect |
| 30. C3×C4×C52 | C2×C4 | semidirect |
| 31. C3×#1039 | C2×C4 | semidirect |
| 62. C5×D12 | AGL(1,𝔽5) | semidirect |
| 75. C4×C52 | C4×D3 | semidirect |
| 76. #1039 | C4×D3 | semidirect |
| 84. C3×C52 | C4×D4 | semidirect |
| 88. C2×C5×D3 | C2×AGL(1,𝔽5) | semidirect |
| 99. C3×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 137. C52 | #893 | semidirect |
| 145. D12 | #1044 | semidirect |
| 161. C4×C5 | D3×AGL(1,𝔽5) | semidirect |
| 170. C3×C5 | D4×AGL(1,𝔽5) | semidirect |
| 175. C2×D3 | C2×#1044 | semidirect |
| 178. C3×C4 | C2×#1044 | semidirect |
| 206. C5 | #91921 | semidirect |
| 216. C4 | D3×#1044 | semidirect |
| 217. C3 | D4×#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#1044 | 2 |
| D12×C5⋊D5 | 2 |
| C4×C3⋊#1044 | 2 |
| C3×C4⋊#1044 | 2 |
| (C2×D3)⋊#1044 | 2 |
| D4×#1044 | 3 |
| #91921 | 5 |