Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
42208 conjugacy classes of subgroups; only the 6107 normal subgroups are shown.
This group has 42208 conjugacy classes of subgroups — too many to draw. Only its 6107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C5⋊D5 |
| commutator, cosocle | C2×C52 | C26 |
| Frattini | C2 | C25×C5⋊D5 |
| Fitting | C23×C52×D4 | C2 |
| socle | C24×C52 | C23 |
| hypercenter | C23×D4 | C5⋊D5 |
| hypocenter | C52 | C24×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C5⋊D5 | C2 | semidirect |
| 2. C23×C52×D4 | C2 | semidirect |
| 3. C23×C22⋊(C5⋊D5) | C2 | semidirect |
| 4. C22×D4×C5⋊D5 | C2 | direct (N × H) |
| 5. C23×C4⋊(C5⋊D5) | C2 | semidirect |
| 6. C23×C4×C5⋊D5 | C2 | semidirect |
| 7. C25×C52 | C22 | semidirect |
| 10. C24×C5⋊D5 | C22 | semidirect |
| 11. C24×C5⋊D5 | C22 | semidirect |
| 12. C22×C52×D4 | C22 | semidirect |
| 13. C23×C4×C52 | C22 | semidirect |
| 14. C22×C22⋊(C5⋊D5) | C22 | semidirect |
| 15. C23×#1039 | C22 | semidirect |
| 16. C2×D4×C5⋊D5 | C22 | direct (N × H) |
| 17. C22×C4⋊(C5⋊D5) | C22 | semidirect |
| 18. C22×C4×C5⋊D5 | C22 | semidirect |
| 22. C24×C52 | C23 | semidirect |
| 25. C23×C5⋊D5 | D4 | direct (N × H) |
| 27. C23×C5⋊D5 | C23 | semidirect |
| 28. C23×C5⋊D5 | C23 | semidirect |
| 29. C2×C52×D4 | C23 | semidirect |
| 30. C22×C4×C52 | C23 | semidirect |
| 31. C2×C22⋊(C5⋊D5) | C23 | semidirect |
| 32. C22×#1039 | C23 | semidirect |
| 33. D4×C5⋊D5 | C23 | direct (N × H) |
| 34. C2×C4⋊(C5⋊D5) | C23 | semidirect |
| 35. C2×C4×C5⋊D5 | C23 | semidirect |
| 37. C23×C5×D4 | D5 | semidirect |
| 43. C23×C52 | C2×D4 | semidirect |
| 45. C23×C52 | C24 | semidirect |
| 48. C22×C5⋊D5 | C2×D4 | direct (N × H) |
| 50. C22×C5⋊D5 | C24 | semidirect |
| 51. C22×C5⋊D5 | C24 | semidirect |
| 52. C52×D4 | C24 | semidirect |
| 53. C2×C4×C52 | C24 | semidirect |
| 54. C22⋊(C5⋊D5) | C24 | semidirect |
| 55. C2×#1039 | C24 | semidirect |
| 56. C4⋊(C5⋊D5) | C24 | semidirect |
| 57. C4×C5⋊D5 | C24 | semidirect |
| 58. C25×C5 | C2×D5 | semidirect |
| 63. C22×C5×D4 | C2×D5 | semidirect |
| 64. C23×C4×C5 | C2×D5 | semidirect |
| 72. C22×C52 | C22×D4 | semidirect |
| 74. C22×C52 | C25 | semidirect |
| 77. C2×C5⋊D5 | C22×D4 | direct (N × H) |
| 79. C2×C5⋊D5 | C25 | semidirect |
| 80. C4×C52 | C25 | semidirect |
| 81. #1039 | C25 | semidirect |
| 84. C24×C5 | C22×D5 | semidirect |
| 91. C2×C5×D4 | C22×D5 | semidirect |
| 92. C22×C4×C5 | C22×D5 | semidirect |
| 102. C23×D4 | C5⋊D5 | direct (N × H) |
| 105. C2×C52 | C23×D4 | semidirect |
| 108. C5⋊D5 | C23×D4 | direct (N × H) |
| 110. C23×C5 | D4×D5 | semidirect |
| 112. C23×C5 | C23×D5 | semidirect |
| 119. C5×D4 | C23×D5 | semidirect |
| 120. C2×C4×C5 | C23×D5 | semidirect |
| 129. C25 | C2×C5⋊D5 | semidirect |
| 133. C22×D4 | C2×C5⋊D5 | direct (N × H) |
| 136. C23×C4 | C2×C5⋊D5 | semidirect |
| 137. C52 | C24×D4 | semidirect |
| 139. C22×C5 | C2×D4×D5 | semidirect |
| 141. C22×C5 | C24×D5 | semidirect |
| 147. C4×C5 | C24×D5 | semidirect |
| 157. C24 | C22×C5⋊D5 | semidirect |
| 161. C2×D4 | C22×C5⋊D5 | direct (N × H) |
| 164. C22×C4 | C22×C5⋊D5 | semidirect |
| 166. C2×C5 | C22×D4×D5 | semidirect |
| 177. C23 | D4×C5⋊D5 | direct (N × H) |
| 179. C23 | C23×C5⋊D5 | semidirect |
| 182. D4 | C23×C5⋊D5 | direct (N × H) |
| 185. C2×C4 | C23×C5⋊D5 | semidirect |
| 186. C5 | C23×D4×D5 | semidirect |
| 193. C22 | C2×D4×C5⋊D5 | direct (N × H) |
| 195. C22 | C24×C5⋊D5 | semidirect |
| 197. C4 | C24×C5⋊D5 | semidirect |
| 201. C2 | C22×D4×C5⋊D5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C5⋊D5 | 2 |
| C23×C52×D4 | 2 |
| C23×C22⋊(C5⋊D5) | 2 |
| C22×D4×C5⋊D5 | 2 |
| C23×C4⋊(C5⋊D5) | 2 |
| C23×C4×C5⋊D5 | 2 |
| C23×D4×D5 | 5 |