Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
206 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 6. C5×#704 | C4 | semidirect |
| 11. C52×M16 | C4 | semidirect |
| 12. C5×#681 | C4 | semidirect |
| 15. #64899 | C5 | direct (N × H) |
| 49. #704 | C4×C5 | semidirect |
| 59. C5×M16 | C4×C5 | semidirect |
| 60. C5×M16 | AGL(1,𝔽5) | semidirect |
| 65. #681 | C4×C5 | semidirect |
| 103. C52 | #343 | semidirect |
| 133. M16 | C5×AGL(1,𝔽5) | semidirect |
| 163. C5 | C5×#343 | semidirect |
| 164. C5 | #64899 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C5×D5⋊M16 | 2 |
| C5×D5×M16 | 2 |
| #64899 | 5 |
| C5×#343 | 5 |