Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 271 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. #11716732 | C2 | semidirect |
| 5. AGL(1,𝔽5)×#168 | C2 | semidirect |
| 7. #87853 | C4 | semidirect |
| 8. #87849 | C4 | semidirect |
| 13. C2×#6029 | C4 | semidirect |
| 14. C2×C5×#168 | C4 | semidirect |
| 15. D5×#168 | C4 | semidirect |
| 16. D5×#168 | C4 | semidirect |
| 75. C2×#168 | AGL(1,𝔽5) | semidirect |
| 119. C52 | #405 | semidirect |
| 178. C5 | #65286 | semidirect |
| 179. C5 | #65718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#681 | 2 |
| C5×#4130 | 2 |
| C2×D5×#168 | 2 |
| #11716732 | 2 |
| AGL(1,𝔽5)×#168 | 2 |
| #65718 | 5 |
| #65286 | 5 |