Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×C52×C8 | C4 | semidirect |
| 12. C2×C5×#168 | C4 | semidirect |
| 15. #64894 | C5 | direct (N × H) |
| 46. #704 | C4×C5 | semidirect |
| 58. C2×C5×C8 | C4×C5 | semidirect |
| 59. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 63. C2×#168 | C4×C5 | semidirect |
| 98. C52 | #344 | semidirect |
| 127. C2×C8 | C5×AGL(1,𝔽5) | semidirect |
| 153. C5 | C5×#344 | semidirect |
| 154. C5 | #64894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4130 | 2 |
| C5×D5⋊M16 | 2 |
| C2×C5×#676 | 2 |
| #64894 | 5 |
| C5×#344 | 5 |