Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
260 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 2. C2×C5×#1042 | C2 | semidirect |
| 3. C22×C53 | C4 | semidirect |
| 5. C2×C52×D5 | C4 | semidirect |
| 8. C22⋊#1042 | C5 | direct (N × H) |
| 19. C2×#1042 | C2×C5 | semidirect |
| 22. C53 | C22⋊C4 | semidirect |
| 30. C22×C52 | Dic5 | semidirect |
| 31. C22×C52 | C4×C5 | semidirect |
| 32. C22×C52 | AGL(1,𝔽5) | semidirect |
| 38. C2×C5×D5 | Dic5 | semidirect |
| 39. C2×C5×D5 | C4×C5 | semidirect |
| 81. C52 | C22⋊Dic5 | semidirect |
| 82. C52 | C5×C22⋊C4 | semidirect |
| 83. C52 | C22⋊AGL(1,𝔽5) | semidirect |
| 97. C22×C5 | C5×Dic5 | semidirect |
| 98. C22×C5 | C5×AGL(1,𝔽5) | semidirect |
| 99. C22×C5 | #1042 | semidirect |
| 101. C2×D5 | C5×Dic5 | semidirect |
| 135. C5 | C5×C22⋊Dic5 | semidirect |
| 136. C5 | C5×C22⋊AGL(1,𝔽5) | semidirect |
| 137. C5 | C22⋊#1042 | direct (N × H) |
| 141. C22 | C5×#1042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D5 | 2 |
| C2×C5×#1042 | 2 |
| C22⋊#1042 | 5 |
| C5×C22⋊AGL(1,𝔽5) | 5 |
| C5×C22⋊Dic5 | 5 |