Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. C52×#125 | C2 | semidirect |
| 5. #11716675 | C2 | semidirect |
| 6. #11716674 | C2 | semidirect |
| 7. C4⋊#6029 | C2 | semidirect |
| 32. C5×#125 | D5 | semidirect |
| 78. #125 | C5⋊D5 | semidirect |
| 85. C52 | #478 | semidirect |
| 124. C5 | #65355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#125 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| #11716676 | 2 |
| #11716675 | 2 |
| #11716674 | 2 |
| C4⋊#6029 | 2 |
| #65355 | 5 |