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. #11716732 | C2 | semidirect |
| 5. AGL(1,𝔽5)×#168 | C2 | semidirect |
| 7. C2×#6032 | C4 | semidirect |
| 8. D5⋊#168 | C4 | semidirect |
| 14. #87804 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. #87768 | C4 | semidirect |
| 68. #681 | AGL(1,𝔽5) | semidirect |
| 112. C52 | #405 | semidirect |
| 169. C5 | #65286 | semidirect |
| 170. C5 | #65728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊#168 | 2 |
| C5×#4130 | 2 |
| D5×#681 | 2 |
| #11716732 | 2 |
| AGL(1,𝔽5)×#168 | 2 |
| #65728 | 5 |
| #65286 | 5 |