Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
960 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 256 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×C4×C5×D5 | C2 | semidirect |
| 3. C2×C4×#1039 | C2 | semidirect |
| 4. C2×#87781 | C2 | semidirect |
| 5. C2×#87778 | C2 | semidirect |
| 6. C4×#6037 | C2 | direct (N × H) |
| 13. C2×C4×C5×D5 | C22 | semidirect |
| 14. C2×#6037 | C4 | direct (N × H) |
| 16. C4×#1039 | C22 | semidirect |
| 17. #87781 | C22 | semidirect |
| 18. #87778 | C22 | semidirect |
| 23. C22×C5×D5 | C2×C4 | semidirect |
| 25. C2×C4×C52 | D4 | semidirect |
| 28. C2×#1039 | C2×C4 | semidirect |
| 34. #6037 | C2×C4 | direct (N × H) |
| 37. C22×C4×D5 | D5 | semidirect |
| 51. C2×C5×D5 | C22×C4 | semidirect |
| 52. C4×C52 | C2×D4 | semidirect |
| 54. #1039 | C22×C4 | semidirect |
| 71. C2×C4×D5 | C2×D5 | semidirect |
| 78. C2×C52 | C4×D4 | semidirect |
| 91. C22×D5 | C4×D5 | semidirect |
| 98. C2×C4×C5 | C22⋊D5 | semidirect |
| 118. C52 | C2×C4×D4 | semidirect |
| 134. C2×D5 | C2×C4×D5 | semidirect |
| 137. C4×C5 | C2×C22⋊D5 | semidirect |
| 160. C2×C5 | C4×C22⋊D5 | semidirect |
| 178. C2×C4 | #6037 | direct (N × H) |
| 181. C5 | C2×C4×C22⋊D5 | semidirect |
| 193. C4 | C2×#6037 | direct (N × H) |
| 195. C2 | C4×#6037 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C22×#6037 | 2 |
| C2×C4×#1039 | 2 |
| C2×#87781 | 2 |
| C2×#87778 | 2 |
| C4×#6037 | 2 |
| C2×C4×C22⋊D5 | 5 |