Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
2346 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 2346 conjugacy classes of subgroups — too many to draw. Only its 262 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 |
|---|---|---|
| 1. C2×D4×#1044 | C2 | semidirect |
| 3. #13104918 | C2 | semidirect |
| 4. #13104826 | C2 | semidirect |
| 5. C42×#1044 | C2 | semidirect |
| 13. C52×#127 | C4 | semidirect |
| 14. #11717260 | C4 | semidirect |
| 15. #11717194 | C4 | semidirect |
| 23. C2×C52×D4 | C2×C4 | semidirect |
| 24. C2×C22⋊(C5⋊D5) | C2×C4 | semidirect |
| 27. C2×C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 32. C4×#1044 | D4 | semidirect |
| 33. C42×C52 | C2×C4 | semidirect |
| 34. C4×#1039 | C2×C4 | semidirect |
| 67. C5×#127 | AGL(1,𝔽5) | semidirect |
| 84. #1044 | #127 | direct (N × H) |
| 85. C4×C52 | C4×D4 | semidirect |
| 86. #1039 | C4×D4 | semidirect |
| 94. C2×C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 110. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 156. #127 | #1044 | direct (N × H) |
| 163. C52 | C4×#127 | semidirect |
| 182. C4×C5 | D4×AGL(1,𝔽5) | semidirect |
| 190. C2×D4 | C2×#1044 | semidirect |
| 201. C42 | C2×#1044 | semidirect |
| 230. C5 | AGL(1,𝔽5)×#127 | semidirect |
| 242. C4 | D4×#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1044 | 2 |
| #127×C5⋊D5 | 2 |
| #13104918 | 2 |
| #13104826 | 2 |
| C42×#1044 | 2 |
| AGL(1,𝔽5)×#127 | 5 |