Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
742 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 742 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. #13107786 | C2 | semidirect |
| 3. #13104657 | C2 | semidirect |
| 4. #13104655 | 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 |
| 45. D5⋊#168 | D4 | semidirect |
| 98. C5×#127 | Dic5 | semidirect |
| 99. C5×#127 | AGL(1,𝔽5) | semidirect |
| 106. #4086 | Dic5 | semidirect |
| 109. #4082 | Dic5 | semidirect |
| 113. #4021 | Dic5 | semidirect |
| 275. #127 | #1042 | semidirect |
| 284. C52 | #1910 | semidirect |
| 398. C5 | #10602647 | semidirect |
| 399. C5 | #10604619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107786 | 2 |
| C5×#66049 | 2 |
| #13104657 | 2 |
| #13104655 | 2 |
| #13100147 | 2 |
| #10604619 | 5 |
| #10602647 | 5 |