Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2960 conjugacy classes of subgroups; only the 648 normal subgroups are shown.
This group has 2960 conjugacy classes of subgroups — too many to draw. Only its 648 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D52 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C23×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D52 | C2 | semidirect |
| 2. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 3. C22×C5×D20 | C2 | semidirect |
| 4. C22×C4×C5×D5 | C2 | semidirect |
| 5. C22×#6038 | C2 | semidirect |
| 6. C2×D5×D20 | C2 | direct (N × H) |
| 7. C23×C5⋊D5 | C22 | semidirect |
| 9. C23×C5×D5 | C22 | semidirect |
| 11. C22×D52 | C22 | semidirect |
| 12. C22×C4×C52 | C22 | semidirect |
| 13. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 14. C22×C5×Dic5 | C22 | semidirect |
| 15. C2×C5×D20 | C22 | semidirect |
| 16. C2×C4×C5×D5 | C22 | semidirect |
| 17. C2×#6038 | C22 | semidirect |
| 18. D5×D20 | C22 | direct (N × H) |
| 23. C22×C5⋊D5 | C23 | semidirect |
| 25. C22×C5×D5 | D4 | semidirect |
| 27. C22×C5×D5 | C23 | semidirect |
| 29. C2×D52 | C23 | semidirect |
| 30. C2×C4×C52 | C23 | semidirect |
| 31. C4⋊(C5⋊D5) | C23 | semidirect |
| 32. C2×C5×Dic5 | C23 | semidirect |
| 33. C5×D20 | C23 | semidirect |
| 34. C4×C5×D5 | C23 | semidirect |
| 35. #6038 | C23 | semidirect |
| 47. C22×D20 | D5 | direct (N × H) |
| 48. C22×C4×D5 | D5 | semidirect |
| 49. C22×C52 | C2×D4 | semidirect |
| 52. C2×C5⋊D5 | C24 | semidirect |
| 54. C2×C5×D5 | C2×D4 | semidirect |
| 56. C2×C5×D5 | C24 | semidirect |
| 58. C4×C52 | C24 | semidirect |
| 59. C5×Dic5 | C24 | semidirect |
| 70. C23×D5 | C2×D5 | semidirect |
| 75. C22×C4×C5 | C2×D5 | semidirect |
| 76. C22×C4×C5 | C2×D5 | semidirect |
| 78. C22×Dic5 | C2×D5 | semidirect |
| 85. C2×D20 | C2×D5 | direct (N × H) |
| 86. C2×C4×D5 | C2×D5 | semidirect |
| 88. C2×C52 | C22×D4 | semidirect |
| 92. C5×D5 | C22×D4 | semidirect |
| 111. C22×D5 | D20 | direct (N × H) |
| 113. C22×D5 | C22×D5 | semidirect |
| 118. C2×C4×C5 | C22×D5 | semidirect |
| 119. C2×C4×C5 | C22×D5 | semidirect |
| 121. C2×Dic5 | C22×D5 | semidirect |
| 126. D20 | C22×D5 | direct (N × H) |
| 127. C4×D5 | C22×D5 | semidirect |
| 134. C52 | C23×D4 | semidirect |
| 141. C22×C5 | C2×D20 | semidirect |
| 142. C22×C5 | D4×D5 | semidirect |
| 154. C2×D5 | C2×D20 | direct (N × H) |
| 156. C2×D5 | C23×D5 | semidirect |
| 159. C4×C5 | C23×D5 | semidirect |
| 160. C4×C5 | C23×D5 | semidirect |
| 161. Dic5 | C23×D5 | semidirect |
| 173. C22×C4 | D52 | semidirect |
| 178. C2×C5 | C22×D20 | semidirect |
| 179. C2×C5 | C2×D4×D5 | semidirect |
| 186. D5 | C22×D20 | direct (N × H) |
| 201. C2×C4 | C2×D52 | semidirect |
| 203. C5 | C23×D20 | semidirect |
| 204. C5 | C22×D4×D5 | semidirect |
| 212. C22 | D5×D20 | direct (N × H) |
| 215. C4 | C22×D52 | semidirect |
| 219. C2 | C2×D5×D20 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C22×C4⋊(C5⋊D5) | 2 |
| C22×C5×D20 | 2 |
| C22×C4×C5×D5 | 2 |
| C22×#6038 | 2 |
| C2×D5×D20 | 2 |
| C22×D4×D5 | 5 |
| C23×D20 | 5 |