Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q16 | C2 | semidirect |
| 3. Q8×#1039 | C2 | semidirect |
| 5. #11716702 | C2 | semidirect |
| 7. #11716681 | C2 | semidirect |
| 37. C2×C5×Q16 | D5 | semidirect |
| 88. C2×Q16 | C5⋊D5 | semidirect |
| 95. C52 | #464 | semidirect |
| 139. C5 | #65474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| #11717267 | 2 |
| Q8×#1039 | 2 |
| C2×#87811 | 2 |
| #11716702 | 2 |
| #11716688 | 2 |
| #11716681 | 2 |
| #65474 | 5 |