Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 102 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. #11716733 | C2 | semidirect |
| 5. #11716731 | C2 | semidirect |
| 10. C2×C5×#170 | C4 | semidirect |
| 11. C5×D5⋊C8 | C4 | semidirect |
| 14. #87804 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. #87768 | C4 | semidirect |
| 54. C2×#170 | Dic5 | semidirect |
| 57. D5⋊C8 | Dic5 | semidirect |
| 72. #681 | AGL(1,𝔽5) | semidirect |
| 112. C52 | #405 | semidirect |
| 169. C5 | #65390 | semidirect |
| 170. C5 | #65728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717425 | 2 |
| C2×C5×D5⋊C8 | 2 |
| D5×#681 | 2 |
| #11716733 | 2 |
| #11716731 | 2 |
| #65728 | 5 |
| #65390 | 5 |