Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
472 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
| 3. #11716676 | C2 | semidirect |
| 4. C4×#6029 | C2 | semidirect |
| 24. C5×C4⋊Q8 | D5 | semidirect |
| 59. C4⋊Q8 | C5⋊D5 | semidirect |
| 63. C52 | #486 | semidirect |
| 94. C5 | #65377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| #11717194 | 2 |
| #11716676 | 2 |
| C4×#6029 | 2 |
| #65377 | 5 |