Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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. C2×C5×H(5,𝔽2) | C2 | semidirect |
| 2. #66283 | C2 | semidirect |
| 3. #66170 | C2 | semidirect |
| 4. #66169 | C2 | semidirect |
| 5. #66156 | C2 | semidirect |
| 6. #66153 | C2 | semidirect |
| 7. C2×#4078 | C2 | semidirect |
| 9. C5×H(5,𝔽2) | C22 | semidirect |
| 12. C2×C5×#41 | C22 | semidirect |
| 14. C22×C5×D4 | C22 | semidirect |
| 15. #4150 | C22 | semidirect |
| 16. #4149 | C22 | semidirect |
| 20. C2×#709 | C22 | semidirect |
| 21. #4097 | C22 | semidirect |
| 22. #4096 | C22 | semidirect |
| 23. #4095 | C22 | semidirect |
| 24. #4094 | C22 | semidirect |
| 25. #4088 | C22 | semidirect |
| 26. C2×#687 | C22 | semidirect |
| 27. #4078 | C22 | semidirect |
| 28. #4078 | C22 | semidirect |
| 29. C2×#686 | C22 | semidirect |
| 30. C2×#681 | C22 | semidirect |
| 57. #709 | C23 | semidirect |
| 58. C2×D20 | C23 | semidirect |
| 60. C2×Dic10 | C23 | semidirect |
| 61. #689 | C23 | semidirect |
| 62. #688 | C23 | semidirect |
| 63. #687 | C23 | semidirect |
| 64. #686 | C23 | semidirect |
| 66. #681 | C23 | semidirect |
| 67. C2×#168 | C23 | semidirect |
| 69. C2×H(5,𝔽2) | D5 | semidirect |
| 109. H(5,𝔽2) | C2×D5 | semidirect |
| 114. C2×#41 | C2×D5 | semidirect |
| 116. C22×D4 | C2×D5 | semidirect |
| 210. C5 | #3585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×H(5,𝔽2) | 2 |
| #66283 | 2 |
| #66170 | 2 |
| #66169 | 2 |
| #66156 | 2 |
| #66153 | 2 |
| C2×#4078 | 2 |
| #3585 | 5 |