Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
241 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 9. C5×C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 11. C5×D5⋊C8 | C4 | semidirect |
| 12. C52×C4⋊C4 | C4 | semidirect |
| 13. C5×C4⋊Dic5 | C4 | semidirect |
| 15. #64874 | C5 | direct (N × H) |
| 60. C4⋊AGL(1,𝔽5) | C4×C5 | semidirect |
| 62. D5⋊C8 | C4×C5 | semidirect |
| 71. C5×C4⋊C4 | C4×C5 | semidirect |
| 72. C5×C4⋊C4 | AGL(1,𝔽5) | semidirect |
| 73. C4⋊Dic5 | C4×C5 | semidirect |
| 118. C52 | #340 | semidirect |
| 161. C4⋊C4 | C5×AGL(1,𝔽5) | semidirect |
| 195. C5 | C5×#340 | semidirect |
| 196. C5 | #64874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C5×D5⋊C8 | 2 |
| C5×D5×C4⋊C4 | 2 |
| #64874 | 5 |
| C5×#340 | 5 |