Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
718 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 132 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×#66256 | C2 | semidirect |
| 3. C5×#65771 | C2 | semidirect |
| 4. C5×#65769 | C2 | semidirect |
| 5. C5×#64862 | C2 | semidirect |
| 12. C52×#127 | C4 | semidirect |
| 14. C5×#4082 | C4 | semidirect |
| 15. C5×#4082 | C4 | semidirect |
| 18. C5×#4015 | C4 | semidirect |
| 21. #10604618 | C5 | direct (N × H) |
| 44. C5×#700 | D4 | semidirect |
| 52. #66256 | C2×C5 | semidirect |
| 56. #65771 | C2×C5 | semidirect |
| 57. #65769 | C2×C5 | semidirect |
| 60. #64862 | C2×C5 | semidirect |
| 100. C5×#127 | C4×C5 | semidirect |
| 101. C5×#127 | AGL(1,𝔽5) | semidirect |
| 109. #4082 | C4×C5 | semidirect |
| 110. #4082 | C4×C5 | semidirect |
| 113. #4015 | C4×C5 | semidirect |
| 173. #700 | C5×D4 | semidirect |
| 269. #127 | C5×AGL(1,𝔽5) | semidirect |
| 278. C52 | #1884 | semidirect |
| 385. C5 | C5×#1884 | semidirect |
| 386. C5 | #10604618 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#66256 | 2 |
| C5×#66050 | 2 |
| C5×#65771 | 2 |
| C5×#65769 | 2 |
| C5×#64862 | 2 |
| #10604618 | 5 |
| C5×#1884 | 5 |