Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
321 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 17. #87806 | C4 | semidirect |
| 18. C5×#683 | C4 | semidirect |
| 19. #87781 | C4 | semidirect |
| 20. #87780 | C4 | semidirect |
| 105. #683 | AGL(1,𝔽5) | semidirect |
| 174. C52 | #387 | semidirect |
| 269. C5 | #65222 | semidirect |
| 270. C5 | #65711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×#87825 | 2 |
| D5×#683 | 2 |
| #11716849 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| #65711 | 5 |
| #65222 | 5 |