Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
156 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 7. C5×#1039 | C4 | semidirect |
| 8. C52×Dic5 | C4 | semidirect |
| 10. #87825 | C5 | direct (N × H) |
| 25. C53 | C4⋊C4 | semidirect |
| 37. #1039 | C4×C5 | semidirect |
| 43. C5×Dic5 | C4×C5 | semidirect |
| 44. C5×Dic5 | AGL(1,𝔽5) | semidirect |
| 77. C52 | #683 | semidirect |
| 78. C52 | C5×C4⋊C4 | semidirect |
| 79. C52 | C4⋊AGL(1,𝔽5) | semidirect |
| 98. Dic5 | C5×AGL(1,𝔽5) | semidirect |
| 122. C5 | C5×#683 | semidirect |
| 123. C5 | #87825 | direct (N × H) |
| 124. C5 | C5×C4⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#1042 | 2 |
| C2×C52×AGL(1,𝔽5) | 2 |
| C5×D5×Dic5 | 2 |
| C5×C4⋊AGL(1,𝔽5) | 5 |
| #87825 | 5 |
| C5×#683 | 5 |