Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
115 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 115 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 7. C4⋊#674 | C5 | direct (N × H) |
| 21. C4×C52 | C16 | semidirect |
| 54. C52 | C4⋊C16 | semidirect |
| 64. C4×C5 | C5×C16 | semidirect |
| 65. C4×C5 | #674 | semidirect |
| 90. C5 | C5×C4⋊C16 | semidirect |
| 91. C5 | C4⋊#674 | direct (N × H) |
| 94. C4 | C5×#674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#674 | 2 |
| C4×C5×#168 | 2 |
| C4⋊#674 | 5 |
| C5×C4⋊C16 | 5 |