Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
207 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 2. C5×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 3. C5×#4003 | C2 | semidirect |
| 5. C2×C52×D4 | C4 | semidirect |
| 10. C5×C4⋊Dic5 | C4 | semidirect |
| 11. #64920 | C5 | direct (N × H) |
| 28. (C2×AGL(1,𝔽5))⋊C4 | C2×C5 | semidirect |
| 29. #4003 | C2×C5 | semidirect |
| 47. C2×C5×D4 | C4×C5 | semidirect |
| 48. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 58. C4⋊Dic5 | C4×C5 | semidirect |
| 98. C52 | #327 | semidirect |
| 129. C2×D4 | C5×AGL(1,𝔽5) | semidirect |
| 165. C5 | C5×#327 | semidirect |
| 166. C5 | #64920 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4084 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| C5×#4003 | 2 |
| #64920 | 5 |
| C5×#327 | 5 |