Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1232 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 286 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. C22×C52×D4 | C2 | semidirect |
| 2. C22×C5×C22⋊D5 | C2 | semidirect |
| 3. C22×C5×D20 | C2 | semidirect |
| 4. C5×#4086 | C2 | direct (N × H) |
| 5. C2×C4×C5×Dic5 | C2 | semidirect |
| 9. C2×C52×D4 | C22 | semidirect |
| 12. C2×C5×C22⋊D5 | C22 | semidirect |
| 15. C2×C5×D20 | C22 | semidirect |
| 16. C4×C5×Dic5 | C22 | semidirect |
| 18. C2×#4086 | C5 | direct (N × H) |
| 27. C2×C4×C52 | D4 | semidirect |
| 30. C2×C5×Dic5 | D4 | semidirect |
| 36. C22×C5×D4 | D5 | semidirect |
| 37. C22×C5×D4 | C2×C5 | semidirect |
| 38. C22×C22⋊D5 | C2×C5 | semidirect |
| 39. C22×D20 | C2×C5 | semidirect |
| 42. #4086 | C2×C5 | direct (N × H) |
| 43. C2×C4×Dic5 | C2×C5 | semidirect |
| 53. C4×C52 | C2×D4 | semidirect |
| 54. C5×Dic5 | C2×D4 | semidirect |
| 68. C2×C5×D4 | C2×D5 | semidirect |
| 69. C2×C5×D4 | C22×C5 | semidirect |
| 75. C2×C22⋊D5 | C22×C5 | semidirect |
| 78. C2×D20 | C22×C5 | semidirect |
| 80. C4×Dic5 | C22×C5 | semidirect |
| 83. C2×C52 | #127 | semidirect |
| 114. C2×C4×C5 | C22⋊D5 | semidirect |
| 115. C2×C4×C5 | C5×D4 | semidirect |
| 119. C2×Dic5 | C5×D4 | semidirect |
| 124. C22×D4 | C5×D5 | semidirect |
| 127. C52 | C2×#127 | semidirect |
| 154. C4×C5 | C2×C22⋊D5 | semidirect |
| 155. C4×C5 | C2×C5×D4 | semidirect |
| 156. Dic5 | C2×C5×D4 | semidirect |
| 164. C2×D4 | C2×C5×D5 | semidirect |
| 175. C2×C5 | #4086 | direct (N × H) |
| 176. C2×C5 | C5×#127 | semidirect |
| 194. C2×C4 | C5×C22⋊D5 | semidirect |
| 197. C5 | C2×#4086 | direct (N × H) |
| 198. C5 | C2×C5×#127 | semidirect |
| 209. C4 | C2×C5×C22⋊D5 | semidirect |
| 212. C2 | C5×#4086 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C22×C5×C22⋊D5 | 2 |
| C22×C5×D20 | 2 |
| C5×#4086 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C5×#127 | 5 |
| C2×#4086 | 5 |