Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1704 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1704 conjugacy classes of subgroups — too many to draw. Only its 459 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. C23×C4×C52 | C2 | semidirect |
| 3. C22×C4×C5⋊D5 | C2 | semidirect |
| 4. C2×C22⋊#1039 | C2 | semidirect |
| 5. C4×C22⋊(C5⋊D5) | C2 | direct (N × H) |
| 6. C2×#87808 | C2 | semidirect |
| 7. C2×#87806 | C2 | semidirect |
| 8. C2×C4×#1039 | C2 | semidirect |
| 14. C22×C4×C52 | C22 | semidirect |
| 15. C2×C22⋊(C5⋊D5) | C4 | direct (N × H) |
| 21. C2×C4×C5⋊D5 | C22 | semidirect |
| 22. C22⋊#1039 | C22 | semidirect |
| 23. #87808 | C22 | semidirect |
| 24. #87806 | C22 | semidirect |
| 25. C4×#1039 | C22 | semidirect |
| 29. C23×C52 | C2×C4 | semidirect |
| 34. C22×C5⋊D5 | C2×C4 | semidirect |
| 38. C2×C4×C52 | D4 | semidirect |
| 41. C22⋊(C5⋊D5) | C2×C4 | direct (N × H) |
| 44. C2×#1039 | C2×C4 | semidirect |
| 49. C23×C4×C5 | D5 | semidirect |
| 61. C22×C52 | C22×C4 | semidirect |
| 68. C2×C5⋊D5 | C22×C4 | semidirect |
| 70. C4×C52 | C2×D4 | semidirect |
| 73. #1039 | C22×C4 | semidirect |
| 79. C22×C4×C5 | C2×D5 | semidirect |
| 93. C2×C52 | C4×D4 | semidirect |
| 100. C23×C5 | C4×D5 | semidirect |
| 109. C2×C4×C5 | C22⋊D5 | semidirect |
| 122. C23×C4 | C5⋊D5 | semidirect |
| 128. C52 | C2×C4×D4 | semidirect |
| 133. C22×C5 | C2×C4×D5 | semidirect |
| 142. C4×C5 | C2×C22⋊D5 | semidirect |
| 158. C22×C4 | C2×C5⋊D5 | semidirect |
| 164. C2×C5 | C4×C22⋊D5 | semidirect |
| 175. C23 | C4×C5⋊D5 | semidirect |
| 188. C2×C4 | C22⋊(C5⋊D5) | direct (N × H) |
| 191. C5 | C2×C4×C22⋊D5 | semidirect |
| 200. C22 | C2×C4×C5⋊D5 | semidirect |
| 208. C4 | C2×C22⋊(C5⋊D5) | direct (N × H) |
| 211. C2 | C4×C22⋊(C5⋊D5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C22×C22⋊(C5⋊D5) | 2 |
| C22×C4×C5⋊D5 | 2 |
| C2×C22⋊#1039 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| C2×#87808 | 2 |
| C2×#87806 | 2 |
| C2×C4×#1039 | 2 |
| C2×C4×C22⋊D5 | 5 |