Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
219 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 219 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×#3995 | C2 | semidirect |
| 5. C5×#3992 | C2 | semidirect |
| 12. C52×D8 | C4 | semidirect |
| 13. C5×#687 | C4 | semidirect |
| 14. C5×Dic20 | C4 | semidirect |
| 16. #65733 | C5 | direct (N × H) |
| 28. #4131 | C2×C5 | semidirect |
| 32. #4008 | C2×C5 | semidirect |
| 33. #3995 | C2×C5 | semidirect |
| 34. #3992 | C2×C5 | semidirect |
| 54. C5×D8 | C4×C5 | semidirect |
| 55. C5×D8 | AGL(1,𝔽5) | semidirect |
| 62. #687 | C4×C5 | semidirect |
| 63. Dic20 | C4×C5 | semidirect |
| 96. C52 | #444 | semidirect |
| 114. D8 | C5×AGL(1,𝔽5) | semidirect |
| 140. C5 | C5×#444 | semidirect |
| 141. C5 | #65733 | 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×#3995 | 2 |
| C5×#3992 | 2 |
| #65733 | 5 |
| C5×#444 | 5 |