Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
744 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 207 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. C2×C52×C4⋊C4 | C2 | semidirect |
| 5. C2×C4⋊#1039 | C2 | semidirect |
| 6. C2×#87806 | C2 | semidirect |
| 7. #11716698 | C2 | semidirect |
| 48. C2×C5×C4⋊C4 | D5 | semidirect |
| 125. C2×C4⋊C4 | C5⋊D5 | semidirect |
| 130. C52 | #396 | semidirect |
| 198. C5 | #65283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×C4⋊C4 | 2 |
| C2×#87808 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×#87806 | 2 |
| #11716698 | 2 |
| #65283 | 5 |