Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 4. C5×#3992 | C2 | semidirect |
| 5. C5×C8×AGL(1,𝔽5) | C2 | semidirect |
| 8. C2×C5×#170 | C4 | semidirect |
| 11. C5×D5⋊C8 | C4 | semidirect |
| 14. C52×M16 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. C5×#676 | C4 | semidirect |
| 18. #65728 | C5 | direct (N × H) |
| 38. #3992 | C2×C5 | semidirect |
| 39. C8×AGL(1,𝔽5) | C2×C5 | semidirect |
| 54. C2×#170 | C4×C5 | semidirect |
| 57. D5⋊C8 | C4×C5 | semidirect |
| 63. C5×M16 | C4×C5 | semidirect |
| 64. C5×M16 | AGL(1,𝔽5) | semidirect |
| 73. #681 | C4×C5 | semidirect |
| 74. #676 | C4×C5 | semidirect |
| 112. C52 | #405 | semidirect |
| 137. M16 | C5×AGL(1,𝔽5) | semidirect |
| 169. C5 | C5×#405 | semidirect |
| 170. C5 | #65728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4130 | 2 |
| C2×C5×D5⋊C8 | 2 |
| C5×D5×M16 | 2 |
| C5×#3992 | 2 |
| C5×C8×AGL(1,𝔽5) | 2 |
| #65728 | 5 |
| C5×#405 | 5 |