Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1962 conjugacy classes of subgroups; only the 423 normal subgroups are shown.
This group has 1962 conjugacy classes of subgroups — too many to draw. Only its 423 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 |
|---|---|---|
| 3. #13104826 | C2 | semidirect |
| 4. #13104700 | C2 | semidirect |
| 5. #13104003 | C2 | semidirect |
| 13. C42×C5×D5 | C4 | semidirect |
| 15. C4×D5×Dic5 | C4 | semidirect |
| 30. C42×C52 | C2×C4 | semidirect |
| 31. C4×#1039 | C2×C4 | semidirect |
| 32. C4×C5×Dic5 | C2×C4 | semidirect |
| 33. Dic52 | C2×C4 | semidirect |
| 52. C4×C5×D5 | C4⋊C4 | semidirect |
| 55. D5×Dic5 | C4⋊C4 | semidirect |
| 69. C42×D5 | AGL(1,𝔽5) | semidirect |
| 79. C4×C52 | C2×C4⋊C4 | semidirect |
| 80. #1039 | C2×C4⋊C4 | semidirect |
| 81. C5×Dic5 | C2×C4⋊C4 | semidirect |
| 102. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 106. C4×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 115. C5×D5 | #384 | semidirect |
| 141. C4×D5 | C4⋊AGL(1,𝔽5) | semidirect |
| 152. C52 | C2×#384 | semidirect |
| 168. C4×C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 171. Dic5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 188. C42 | D5⋊AGL(1,𝔽5) | semidirect |
| 196. D5 | #65688 | semidirect |
| 214. C5 | C2×#65688 | semidirect |
| 225. C4 | D5⋊(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×D5⋊(C4⋊AGL(1,𝔽5)) | 2 |
| C42×D52 | 2 |
| #13104826 | 2 |
| #13104700 | 2 |
| #13104003 | 2 |
| C2×#65688 | 5 |