Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
307 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 4. #11716752 | C2 | semidirect |
| 8. D5⋊#168 | C4 | semidirect |
| 10. C5×D5⋊C8 | C4 | semidirect |
| 24. #6032 | C2×C4 | semidirect |
| 25. C5×#170 | C2×C4 | semidirect |
| 49. D5⋊C8 | Dic5 | semidirect |
| 64. C5×D5 | #97 | semidirect |
| 84. #170 | C2×Dic5 | semidirect |
| 91. C52 | C2×#97 | semidirect |
| 127. D5 | #3947 | semidirect |
| 139. C5 | C2×#3947 | semidirect |
| 140. C5 | #65676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊#168 | 2 |
| C2×C5×D5⋊C8 | 2 |
| C4×D5×Dic5 | 2 |
| #11716752 | 2 |
| #65676 | 5 |
| C2×#3947 | 5 |