Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 127 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. C52×C4⋊Q8 | C2 | semidirect |
| 2. C2×#87812 | C2 | semidirect |
| 5. #11716670 | C2 | semidirect |
| 26. C5×C4⋊Q8 | D5 | semidirect |
| 63. C4⋊Q8 | C5⋊D5 | semidirect |
| 66. C52 | #497 | semidirect |
| 96. C5 | #65375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C2×#87812 | 2 |
| C2×#87811 | 2 |
| #11717195 | 2 |
| #11716670 | 2 |
| #65375 | 5 |