Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
403 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 403 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4⋊#1042 | C4 | direct (N × H) |
| 11. C42×C52 | C4 | semidirect |
| 12. C4×C5×Dic5 | C4 | semidirect |
| 13. C4×C5×Dic5 | C4 | semidirect |
| 14. C4×C5×Dic5 | C4 | semidirect |
| 46. C4×C52 | C42 | semidirect |
| 47. C4×C52 | C4⋊C4 | semidirect |
| 49. C5×Dic5 | C42 | semidirect |
| 50. C5×Dic5 | C4⋊C4 | semidirect |
| 65. C42×C5 | Dic5 | semidirect |
| 66. C42×C5 | AGL(1,𝔽5) | semidirect |
| 69. C4×Dic5 | Dic5 | semidirect |
| 70. C4×Dic5 | Dic5 | semidirect |
| 71. C4×Dic5 | Dic5 | semidirect |
| 113. C52 | C4×C4⋊C4 | semidirect |
| 134. C4×C5 | C4×Dic5 | semidirect |
| 135. C4×C5 | C4⋊Dic5 | semidirect |
| 136. C4×C5 | C4×AGL(1,𝔽5) | semidirect |
| 137. C4×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 140. Dic5 | C4×Dic5 | semidirect |
| 141. Dic5 | C4⋊Dic5 | semidirect |
| 151. C42 | #1042 | semidirect |
| 180. C5 | C4×C4⋊Dic5 | semidirect |
| 181. C5 | C4×C4⋊AGL(1,𝔽5) | semidirect |
| 192. C4 | C4×#1042 | semidirect |
| 193. C4 | C4⋊#1042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1042 | 2 |
| C2×C4×#1042 | 2 |
| C42×C5×D5 | 2 |
| #11716849 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 5 |
| C4×C4⋊Dic5 | 5 |