Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
912 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 2. C5×#4072 | C2 | semidirect |
| 3. #11717092 | C2 | semidirect |
| 4. #11717013 | C2 | semidirect |
| 7. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 9. C2×#6036 | C22 | semidirect |
| 11. C5×C4⋊Dic5 | C22 | semidirect |
| 12. C4×C5×Dic5 | C22 | semidirect |
| 13. #87779 | C22 | semidirect |
| 17. C22×C5⋊D5 | C2×C4 | semidirect |
| 19. C2×C4×C52 | C2×C4 | semidirect |
| 21. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 27. #4072 | D5 | semidirect |
| 54. C4⋊Dic5 | C2×D5 | semidirect |
| 55. C4×Dic5 | C2×D5 | semidirect |
| 72. C2×C4×C5 | C4×D5 | semidirect |
| 84. C52 | #518 | semidirect |
| 126. C2×C4 | #6036 | semidirect |
| 129. C5 | #65855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C5×#4072 | 2 |
| #11717092 | 2 |
| #11717013 | 2 |
| #65855 | 5 |