Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
246 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 100 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×#3994 | C2 | semidirect |
| 5. C5×#3993 | C2 | semidirect |
| 14. C52×M16 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. C5×#676 | C4 | semidirect |
| 18. #65727 | C5 | direct (N × H) |
| 31. C52×C8 | C2×C4 | semidirect |
| 32. C5×#168 | C2×C4 | semidirect |
| 39. #3994 | C2×C5 | semidirect |
| 40. #3993 | C2×C5 | semidirect |
| 68. C5×M16 | C4×C5 | semidirect |
| 69. C5×M16 | AGL(1,𝔽5) | semidirect |
| 77. #681 | C4×C5 | semidirect |
| 78. #676 | C4×C5 | semidirect |
| 111. C5×C8 | C2×C4×C5 | semidirect |
| 112. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 113. #168 | C2×C4×C5 | semidirect |
| 119. C52 | #428 | semidirect |
| 151. M16 | C5×AGL(1,𝔽5) | semidirect |
| 183. C8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 185. C5 | C5×#428 | semidirect |
| 186. C5 | #65727 | 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×C4⋊AGL(1,𝔽5) | 2 |
| C5×D5×M16 | 2 |
| C5×#3994 | 2 |
| C5×#3993 | 2 |
| #65727 | 5 |
| C5×#428 | 5 |