Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
279 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 66 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×D4×AGL(1,𝔽5) | C2 | semidirect |
| 2. AGL(1,𝔽5)×D20 | C2 | semidirect |
| 4. #11716850 | C2 | semidirect |
| 5. #11716743 | C2 | semidirect |
| 6. #11716734 | C2 | semidirect |
| 7. AGL(1,𝔽5)×#168 | C2 | semidirect |
| 18. #87809 | C4 | semidirect |
| 19. C5×#686 | C4 | semidirect |
| 20. #87771 | C4 | semidirect |
| 21. #87770 | C4 | semidirect |
| 33. C52×D4 | C2×C4 | semidirect |
| 34. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 36. C5×D20 | C2×C4 | semidirect |
| 37. C5×D20 | C2×C4 | semidirect |
| 41. #6029 | C2×C4 | semidirect |
| 42. C5×#168 | C2×C4 | semidirect |
| 44. D4×AGL(1,𝔽5) | D5 | semidirect |
| 69. C5×AGL(1,𝔽5) | D8 | semidirect |
| 96. #686 | AGL(1,𝔽5) | direct (N × H) |
| 125. C5×D4 | C4×D5 | semidirect |
| 126. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 139. D20 | C4×D5 | semidirect |
| 140. D20 | C2×AGL(1,𝔽5) | semidirect |
| 149. #168 | C2×AGL(1,𝔽5) | semidirect |
| 157. C52 | C4×D8 | semidirect |
| 181. AGL(1,𝔽5) | #686 | direct (N × H) |
| 230. D4 | D5×AGL(1,𝔽5) | semidirect |
| 242. C5 | C4×#686 | semidirect |
| 243. C5 | D8×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×D20 | 2 |
| D5×#686 | 2 |
| #11716850 | 2 |
| #11716743 | 2 |
| #11716734 | 2 |
| AGL(1,𝔽5)×#168 | 2 |
| D8×AGL(1,𝔽5) | 5 |
| C4×#686 | 5 |