Finite Group DatabasebetaFinite Group DatabasebetaOrder 2240.
1324 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 262 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. C24×C5×D7 | C2 | semidirect |
| 2. C2×C5×D4×D7 | C2 | semidirect |
| 3. C5×C7×#120 | C2 | semidirect |
| 4. C5×#6516 | C2 | semidirect |
| 5. C5×#6500 | C2 | semidirect |
| 6. C5×#6445 | C2 | semidirect |
| 7. C5×D7×C22⋊C4 | C2 | semidirect |
| 8. C24×C5×C7 | C22 | semidirect |
| 11. C23×C5×D7 | C22 | semidirect |
| 12. C23×C5×D7 | C22 | semidirect |
| 13. C2×C5×C7×D4 | C22 | semidirect |
| 14. C2×C5×C22⋊D7 | C22 | semidirect |
| 15. C2×C5×C22⋊D7 | C22 | semidirect |
| 17. C2×C5×D28 | C22 | semidirect |
| 18. C2×C4×C5×D7 | C22 | semidirect |
| 19. C5×C7×C22⋊C4 | C22 | semidirect |
| 20. C5×C22⋊Dic7 | C22 | semidirect |
| 21. C5×(C2×D7)⋊C4 | C22 | semidirect |
| 22. D7×#120 | C5 | direct (N × H) |
| 26. C23×C5×C7 | C23 | semidirect |
| 32. C22×C5×D7 | D4 | semidirect |
| 35. C22×C5×D7 | C23 | semidirect |
| 37. C2×C4×C5×C7 | C23 | semidirect |
| 40. C2×C5×Dic7 | C23 | semidirect |
| 43. C24×D7 | C2×C5 | semidirect |
| 44. C2×D4×D7 | C2×C5 | semidirect |
| 45. C7×#120 | C2×C5 | semidirect |
| 46. #6516 | C2×C5 | semidirect |
| 47. #6500 | C2×C5 | semidirect |
| 48. #6445 | C2×C5 | semidirect |
| 49. D7×C22⋊C4 | C2×C5 | semidirect |
| 55. C5×#120 | D7 | direct (N × H) |
| 60. C22×C5×C7 | C2×D4 | semidirect |
| 68. C2×C5×D7 | C2×D4 | semidirect |
| 71. C24×C7 | C22×C5 | semidirect |
| 74. C23×D7 | C22×C5 | semidirect |
| 75. C23×D7 | C22×C5 | semidirect |
| 76. C2×C7×D4 | C22×C5 | semidirect |
| 77. C2×C22⋊D7 | C22×C5 | semidirect |
| 78. C2×C22⋊D7 | C22×C5 | semidirect |
| 80. C2×D28 | C22×C5 | semidirect |
| 81. C2×C4×D7 | C22×C5 | semidirect |
| 82. C7×C22⋊C4 | C22×C5 | semidirect |
| 83. C22⋊Dic7 | C22×C5 | semidirect |
| 84. (C2×D7)⋊C4 | C22×C5 | semidirect |
| 89. C24×C5 | C2×D7 | semidirect |
| 94. C2×C5×D4 | C2×D7 | semidirect |
| 98. C5×C22⋊C4 | C2×D7 | semidirect |
| 104. C5×D7 | #120 | direct (N × H) |
| 108. C23×C7 | C23×C5 | semidirect |
| 114. C22×D7 | C5×D4 | semidirect |
| 117. C22×D7 | C23×C5 | semidirect |
| 119. C2×C4×C7 | C23×C5 | semidirect |
| 122. C2×Dic7 | C23×C5 | semidirect |
| 136. C23×C5 | C22×D7 | semidirect |
| 143. C2×C4×C5 | C22×D7 | semidirect |
| 144. C5×C7 | C2×#120 | semidirect |
| 150. #120 | C5×D7 | direct (N × H) |
| 155. C22×C7 | C2×C5×D4 | semidirect |
| 163. C2×D7 | C2×C5×D4 | semidirect |
| 176. C22×C5 | D4×D7 | semidirect |
| 184. C24 | C2×C5×D7 | semidirect |
| 189. C2×D4 | C2×C5×D7 | semidirect |
| 193. C22⋊C4 | C2×C5×D7 | semidirect |
| 199. D7 | C5×#120 | direct (N × H) |
| 217. C23 | C22×C5×D7 | semidirect |
| 224. C2×C4 | C22×C5×D7 | semidirect |
| 225. C7 | C2×C5×#120 | semidirect |
| 226. C5 | D7×#120 | direct (N × H) |
| 237. C22 | C5×D4×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×D7 | 2 |
| C2×C5×D4×D7 | 2 |
| C5×C7×#120 | 2 |
| C5×#6516 | 2 |
| C5×#6500 | 2 |
| C5×#6445 | 2 |
| C5×D7×C22⋊C4 | 2 |
| D7×#120 | 5 |
| C2×C5×#120 | 7 |