Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#87800 | C2 | semidirect |
| 3. C4×#6045 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. #11716688 | C2 | semidirect |
| 28. #6045 | D4 | semidirect |
| 33. C5×C4⋊C8 | D5 | semidirect |
| 40. C4×C52 | SD16 | semidirect |
| 76. C4⋊C8 | C5⋊D5 | semidirect |
| 78. C52 | #460 | semidirect |
| 84. C4×C5 | #677 | semidirect |
| 116. C5 | #65137 | semidirect |
| 124. C4 | #87800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87800 | 2 |
| #11717194 | 2 |
| C4×#6045 | 2 |
| C52×C4⋊C8 | 2 |
| #11716688 | 2 |
| #65137 | 5 |