Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
942 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 121 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. #13107788 | C2 | semidirect |
| 3. D5⋊#3965 | C2 | semidirect |
| 4. #13104657 | C2 | semidirect |
| 5. #13100146 | C2 | semidirect |
| 13. C52×#127 | C4 | semidirect |
| 15. C5×#4086 | C4 | semidirect |
| 16. C5×#4086 | C4 | semidirect |
| 17. C5×#4020 | C4 | semidirect |
| 28. C2×C52×D4 | C2×C4 | semidirect |
| 40. C2×C5×D20 | C2×C4 | semidirect |
| 46. C4⋊#1042 | D4 | semidirect |
| 50. C42×C52 | C2×C4 | semidirect |
| 52. C4×C5×Dic5 | C2×C4 | semidirect |
| 109. C5×#127 | Dic5 | semidirect |
| 110. C5×#127 | AGL(1,𝔽5) | semidirect |
| 114. #4086 | Dic5 | semidirect |
| 115. #4086 | Dic5 | semidirect |
| 119. #4020 | Dic5 | semidirect |
| 170. C2×C5×D4 | C2×Dic5 | semidirect |
| 172. C2×C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 187. C2×D20 | C2×Dic5 | semidirect |
| 200. C42×C5 | C2×Dic5 | semidirect |
| 201. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 207. C4×Dic5 | C2×Dic5 | semidirect |
| 301. #127 | #1042 | semidirect |
| 308. C52 | #1887 | semidirect |
| 374. C2×D4 | C2×#1042 | semidirect |
| 387. C42 | C2×#1042 | semidirect |
| 440. C5 | #10602556 | semidirect |
| 441. C5 | #10604614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107788 | 2 |
| C5×D5×#127 | 2 |
| D5⋊#3965 | 2 |
| #13104657 | 2 |
| #13100146 | 2 |
| #10604614 | 5 |
| #10602556 | 5 |