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. C2×C52×SD16 | C2 | semidirect |
| 2. #11717266 | C2 | semidirect |
| 4. C2×C8×C5⋊D5 | C2 | semidirect |
| 5. #11716702 | C2 | semidirect |
| 6. #11716699 | C2 | semidirect |
| 7. #11716684 | C2 | semidirect |
| 36. C52×C8 | D4 | semidirect |
| 38. C2×C5×SD16 | D5 | semidirect |
| 51. C2×C5⋊D5 | SD16 | semidirect |
| 91. C5×C8 | C22⋊D5 | semidirect |
| 93. C2×SD16 | C5⋊D5 | semidirect |
| 100. C52 | #465 | semidirect |
| 147. C8 | C22⋊(C5⋊D5) | semidirect |
| 148. C5 | #65460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| #11717266 | 2 |
| #11717258 | 2 |
| C2×C8×C5⋊D5 | 2 |
| #11716702 | 2 |
| #11716699 | 2 |
| #11716684 | 2 |
| #65460 | 5 |