Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
2034 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 2034 conjugacy classes of subgroups — too many to draw. Only its 251 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×#11717365 | C2 | semidirect |
| 3. C42×#1044 | C2 | semidirect |
| 4. #13104700 | C2 | semidirect |
| 5. #13103996 | C2 | semidirect |
| 14. C5×#4020 | C4 | semidirect |
| 15. #11717032 | C4 | semidirect |
| 23. C2×C5×D20 | C2×C4 | semidirect |
| 24. C2×#6037 | C2×C4 | semidirect |
| 28. C4×#1044 | D4 | semidirect |
| 31. C42×C52 | C2×C4 | semidirect |
| 32. C4×#1039 | C2×C4 | semidirect |
| 64. #4020 | AGL(1,𝔽5) | semidirect |
| 75. #1044 | #127 | semidirect |
| 77. C4×C52 | C4×D4 | semidirect |
| 78. #1039 | C4×D4 | semidirect |
| 89. C2×D20 | C2×AGL(1,𝔽5) | semidirect |
| 98. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 143. C52 | C4×#127 | semidirect |
| 159. C4×C5 | D4×AGL(1,𝔽5) | semidirect |
| 177. C42 | D5⋊AGL(1,𝔽5) | semidirect |
| 202. C5 | AGL(1,𝔽5)×#127 | semidirect |
| 213. C4 | #11717365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717365 | 2 |
| #13105099 | 2 |
| C42×#1044 | 2 |
| #13104700 | 2 |
| #13103996 | 2 |
| AGL(1,𝔽5)×#127 | 5 |