Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
778 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 117 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. #13104653 | C2 | semidirect |
| 5. #13100147 | C2 | semidirect |
| 12. C52×#127 | C4 | semidirect |
| 13. C5×#4086 | C4 | semidirect |
| 16. C5×#4082 | C4 | semidirect |
| 17. C5×#4021 | C4 | semidirect |
| 27. C2×C52×D4 | C2×C4 | semidirect |
| 38. C2×C5×Dic10 | C2×C4 | semidirect |
| 43. C4×#1042 | D4 | semidirect |
| 46. C42×C52 | C2×C4 | semidirect |
| 51. C4×C5×Dic5 | C2×C4 | semidirect |
| 99. C5×#127 | Dic5 | semidirect |
| 100. C5×#127 | AGL(1,𝔽5) | semidirect |
| 107. #4086 | Dic5 | semidirect |
| 110. #4082 | Dic5 | semidirect |
| 114. #4021 | Dic5 | semidirect |
| 157. C2×C5×D4 | C2×Dic5 | semidirect |
| 159. C2×C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 173. C2×Dic10 | C2×Dic5 | semidirect |
| 187. C42×C5 | C2×Dic5 | semidirect |
| 188. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 197. C4×Dic5 | C2×Dic5 | semidirect |
| 278. #127 | #1042 | semidirect |
| 289. C52 | #1911 | semidirect |
| 345. C2×D4 | C2×#1042 | semidirect |
| 361. C42 | C2×#1042 | semidirect |
| 408. C5 | #10602646 | semidirect |
| 409. C5 | #10604615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107788 | 2 |
| C5×#66049 | 2 |
| D5⋊#3965 | 2 |
| #13104653 | 2 |
| #13100147 | 2 |
| #10604615 | 5 |
| #10602646 | 5 |