Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
772 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 216 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×C3×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C3×C5×#709 | C2 | semidirect |
| 3. C3×#87886 | C2 | semidirect |
| 4. C3×D5×D20 | C2 | semidirect |
| 5. C3×#87874 | C2 | semidirect |
| 6. #11717473 | C3 | direct (N × H) |
| 7. C22×C3×C5⋊D5 | C22 | semidirect |
| 8. C2×C3×D52 | C22 | semidirect |
| 9. C2×C3×C4×C52 | C22 | semidirect |
| 10. C3×C4⋊(C5⋊D5) | C22 | semidirect |
| 11. C3×C5×C22⋊D5 | C22 | semidirect |
| 12. C3×C5×D20 | C22 | semidirect |
| 13. C3×C4×C5×D5 | C22 | semidirect |
| 14. C3×C5×Dic10 | C22 | semidirect |
| 15. C3×#6038 | C22 | semidirect |
| 16. C3×#6036 | C22 | semidirect |
| 18. C2×C4⋊(C5⋊D5) | C2×C3 | semidirect |
| 19. C5×#709 | C2×C3 | semidirect |
| 20. #87886 | C2×C3 | semidirect |
| 21. D5×D20 | C2×C3 | semidirect |
| 22. #87874 | C2×C3 | semidirect |
| 35. C3×#709 | D5 | semidirect |
| 39. C22×C5⋊D5 | C22×C3 | semidirect |
| 40. C2×D52 | C22×C3 | semidirect |
| 41. C2×C4×C52 | C22×C3 | semidirect |
| 42. C4⋊(C5⋊D5) | C22×C3 | semidirect |
| 43. C5×C22⋊D5 | C22×C3 | semidirect |
| 44. C5×D20 | C22×C3 | semidirect |
| 45. C4×C5×D5 | C22×C3 | semidirect |
| 46. C5×Dic10 | C22×C3 | semidirect |
| 47. #6038 | C22×C3 | semidirect |
| 48. #6036 | C22×C3 | semidirect |
| 62. C2×C3×C4×C5 | C2×D5 | semidirect |
| 64. C3×C22⋊D5 | C2×D5 | semidirect |
| 69. C3×D20 | C2×D5 | semidirect |
| 71. C3×C4×D5 | C2×D5 | semidirect |
| 72. C3×Dic10 | C2×D5 | semidirect |
| 86. #709 | C3×D5 | semidirect |
| 90. C3×C52 | H(5,𝔽2) | semidirect |
| 123. C2×C4×C5 | C2×C3×D5 | semidirect |
| 125. C22⋊D5 | C2×C3×D5 | semidirect |
| 130. D20 | C2×C3×D5 | semidirect |
| 132. C4×D5 | C2×C3×D5 | semidirect |
| 133. Dic10 | C2×C3×D5 | semidirect |
| 144. C52 | C3×H(5,𝔽2) | semidirect |
| 154. C2×C3×C4 | D52 | semidirect |
| 176. C3×C5 | #4149 | semidirect |
| 202. C2×C4 | C3×D52 | semidirect |
| 208. C5 | C3×#4149 | semidirect |
| 216. C3 | #11717473 | 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 |
| C3×C5×#709 | 2 |
| C3×#87886 | 2 |
| C3×D5×D20 | 2 |
| C3×#87874 | 2 |
| #11717473 | 3 |
| C3×#4149 | 5 |