Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
598 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 214 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. C5×#4149 | C2 | semidirect |
| 2. C52×#131 | C2 | semidirect |
| 3. C5×#4054 | C2 | semidirect |
| 4. C5×#4050 | C2 | semidirect |
| 5. C2×C5×D40 | C2 | semidirect |
| 9. C5×#709 | C22 | semidirect |
| 10. C2×C5×D20 | C22 | semidirect |
| 11. C52×M16 | C22 | semidirect |
| 12. C2×C52×C8 | C22 | semidirect |
| 13. C5×Dic20 | C22 | semidirect |
| 14. C5×D40 | C22 | semidirect |
| 15. C5×D40 | C22 | semidirect |
| 16. C5×#677 | C22 | semidirect |
| 18. #66086 | C5 | direct (N × H) |
| 31. #4149 | C2×C5 | semidirect |
| 36. C5×#131 | D5 | semidirect |
| 37. C5×#131 | C2×C5 | semidirect |
| 38. #4054 | C2×C5 | semidirect |
| 39. #4050 | C2×C5 | semidirect |
| 40. C2×D40 | C2×C5 | semidirect |
| 56. #709 | C22×C5 | semidirect |
| 57. C2×D20 | C22×C5 | semidirect |
| 63. C5×M16 | C2×D5 | semidirect |
| 64. C5×M16 | C22×C5 | semidirect |
| 66. C2×C5×C8 | C2×D5 | semidirect |
| 67. C2×C5×C8 | C22×C5 | semidirect |
| 68. Dic20 | C22×C5 | semidirect |
| 69. D40 | C22×C5 | semidirect |
| 70. D40 | C22×C5 | semidirect |
| 71. #677 | C22×C5 | semidirect |
| 107. #131 | C5×D5 | semidirect |
| 108. C52 | #576 | semidirect |
| 133. M16 | C2×C5×D5 | semidirect |
| 134. C2×C8 | C2×C5×D5 | semidirect |
| 155. C5 | #66086 | direct (N × H) |
| 156. C5 | C5×#576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4149 | 2 |
| C52×#131 | 2 |
| C5×#4054 | 2 |
| C5×#4050 | 2 |
| C2×C5×D40 | 2 |
| C5×#576 | 5 |
| #66086 | 5 |