Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1104 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 318 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×C5×D20 | C2 | semidirect |
| 2. C2×C42×C52 | C2 | semidirect |
| 3. C5×#4020 | C2 | direct (N × H) |
| 7. C2×C5×D20 | C22 | semidirect |
| 8. C42×C52 | C22 | semidirect |
| 10. C2×#4020 | C5 | direct (N × H) |
| 14. C2×C4×C52 | D4 | semidirect |
| 18. C22×D20 | C2×C5 | semidirect |
| 21. C2×C42×C5 | D5 | semidirect |
| 22. C2×C42×C5 | C2×C5 | semidirect |
| 23. #4020 | C2×C5 | direct (N × H) |
| 28. C4×C52 | C2×D4 | semidirect |
| 37. C2×D20 | C22×C5 | semidirect |
| 39. C42×C5 | C2×D5 | semidirect |
| 40. C42×C5 | C22×C5 | semidirect |
| 42. C2×C52 | #127 | semidirect |
| 55. C2×C4×C5 | D20 | semidirect |
| 56. C2×C4×C5 | C5×D4 | semidirect |
| 62. C2×C42 | C5×D5 | semidirect |
| 63. C52 | C2×#127 | semidirect |
| 75. C4×C5 | C2×D20 | semidirect |
| 76. C4×C5 | C2×C5×D4 | semidirect |
| 81. C42 | C2×C5×D5 | semidirect |
| 85. C2×C5 | #4020 | direct (N × H) |
| 86. C2×C5 | C5×#127 | semidirect |
| 94. C2×C4 | C5×D20 | semidirect |
| 97. C5 | C2×#4020 | direct (N × H) |
| 98. C5 | C2×C5×#127 | semidirect |
| 103. C4 | C2×C5×D20 | semidirect |
| 105. C2 | C5×#4020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C2×C42×C52 | 2 |
| C5×#4020 | 2 |
| C2×C5×#127 | 5 |
| C2×#4020 | 5 |