Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. C5×C4⋊#168 | C2 | semidirect |
| 4. #11716613 | C2 | semidirect |
| 23. C4×C5⋊D5 | C8 | semidirect |
| 32. C4⋊#168 | D5 | semidirect |
| 38. C4×C52 | C2×C8 | semidirect |
| 43. #1039 | C2×C8 | semidirect |
| 65. C5⋊D5 | C4⋊C8 | semidirect |
| 94. C52 | C2×C4⋊C8 | semidirect |
| 108. C4×C5 | C8×D5 | semidirect |
| 147. C5 | D5×C4⋊C8 | semidirect |
| 156. C4 | #87767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5⋊D5 | 2 |
| C2×#87767 | 2 |
| C5×C4⋊#168 | 2 |
| #11716613 | 2 |
| D5×C4⋊C8 | 5 |