Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
223 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C5×#4131 | C2 | semidirect |
| 3. C5×#4008 | C2 | semidirect |
| 4. C5×#3996 | C2 | semidirect |
| 5. C5×C8×AGL(1,𝔽5) | C2 | semidirect |
| 12. C52×D8 | C4 | semidirect |
| 13. C5×#687 | C4 | semidirect |
| 14. C5×Dic20 | C4 | semidirect |
| 16. #65732 | C5 | direct (N × H) |
| 29. #4131 | C2×C5 | semidirect |
| 33. #4008 | C2×C5 | semidirect |
| 34. #3996 | C2×C5 | semidirect |
| 35. C8×AGL(1,𝔽5) | C2×C5 | semidirect |
| 55. C5×D8 | C4×C5 | semidirect |
| 56. C5×D8 | AGL(1,𝔽5) | semidirect |
| 63. #687 | C4×C5 | semidirect |
| 64. Dic20 | C4×C5 | semidirect |
| 99. C52 | #443 | semidirect |
| 117. D8 | C5×AGL(1,𝔽5) | semidirect |
| 144. C5 | C5×#443 | semidirect |
| 145. C5 | #65732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4131 | 2 |
| C5×#4058 | 2 |
| C5×#4008 | 2 |
| C5×#3996 | 2 |
| C5×C8×AGL(1,𝔽5) | 2 |
| #65732 | 5 |
| C5×#443 | 5 |