Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 275 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. C52×2−1+4 | C2 | semidirect |
| 2. #11717522 | C2 | semidirect |
| 3. #11717270 | C2 | semidirect |
| 4. #11717269 | C2 | semidirect |
| 5. #11717268 | C2 | semidirect |
| 6. #11717262 | C2 | semidirect |
| 7. C2×#87811 | C2 | semidirect |
| 10. C52×#41 | C22 | semidirect |
| 12. C2×C52×Q8 | C22 | semidirect |
| 17. #87812 | C22 | semidirect |
| 18. #87811 | C22 | semidirect |
| 19. #87811 | C22 | semidirect |
| 20. #87810 | C22 | semidirect |
| 21. #87809 | C22 | semidirect |
| 22. #87804 | C22 | semidirect |
| 23. C2×#6029 | C22 | semidirect |
| 42. C5×2−1+4 | D5 | semidirect |
| 59. C5×#41 | C2×D5 | semidirect |
| 61. C2×C5×Q8 | C2×D5 | semidirect |
| 95. 2−1+4 | C5⋊D5 | semidirect |
| 102. C52 | #577 | semidirect |
| 115. #41 | C2×C5⋊D5 | semidirect |
| 117. C2×Q8 | C2×C5⋊D5 | semidirect |
| 148. C5 | #66171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×2−1+4 | 2 |
| #11717522 | 2 |
| #11717270 | 2 |
| #11717269 | 2 |
| #11717268 | 2 |
| #11717262 | 2 |
| C2×#87811 | 2 |
| #66171 | 5 |