Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
| 4. #11716698 | C2 | semidirect |
| 5. #11716698 | C2 | semidirect |
| 31. C2×C5×C4⋊C4 | D5 | semidirect |
| 81. C2×C4⋊C4 | C5⋊D5 | semidirect |
| 86. C52 | #397 | semidirect |
| 131. C5 | #65282 | 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 |
| #11716698 | 2 |
| #65282 | 5 |