Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
316 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 86 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×C4⋊Q8 | C2 | semidirect |
| 2. C2×C5×#689 | C2 | semidirect |
| 5. C5×#3935 | C2 | semidirect |
| 16. #65375 | C5 | direct (N × H) |
| 30. C5×C4⋊Q8 | D5 | semidirect |
| 31. C5×C4⋊Q8 | C2×C5 | semidirect |
| 33. C2×#689 | C2×C5 | semidirect |
| 37. #3935 | C2×C5 | semidirect |
| 97. C4⋊Q8 | C5×D5 | semidirect |
| 100. C52 | #497 | semidirect |
| 147. C5 | #65375 | direct (N × H) |
| 148. C5 | C5×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#688 | 2 |
| C5×#4021 | 2 |
| C5×#3935 | 2 |
| C5×#497 | 5 |
| #65375 | 5 |