Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
525 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 525 conjugacy classes of subgroups — too many to draw. Only its 134 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. #72242248 | C2 | semidirect |
| 2. #72242247 | C2 | semidirect |
| 8. #13100161 | C4 | semidirect |
| 9. C5×#64877 | C4 | semidirect |
| 15. #13099743 | C4 | semidirect |
| 32. #11716579 | C2×C4 | semidirect |
| 33. C5×#3928 | C2×C4 | semidirect |
| 63. #64877 | AGL(1,𝔽5) | semidirect |
| 116. #3928 | C2×AGL(1,𝔽5) | semidirect |
| 187. C5⋊D5 | #1398 | semidirect |
| 244. C52 | C2×#1398 | semidirect |
| 318. C5 | #13027533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72242248 | 2 |
| #72242247 | 2 |
| #72242220 | 2 |
| C2×#13099850 | 2 |
| #13027533 | 5 |