Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 163 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. C22×C52×C8 | C2 | semidirect |
| 3. C2×#87799 | C2 | semidirect |
| 4. C22⋊#6029 | C2 | semidirect |
| 5. #11716687 | C2 | semidirect |
| 6. #11716682 | C2 | semidirect |
| 7. #11716681 | C2 | semidirect |
| 35. C52×C8 | D4 | semidirect |
| 38. C22×C5×C8 | D5 | semidirect |
| 47. C22×C52 | M16 | semidirect |
| 90. C5×C8 | C22⋊D5 | semidirect |
| 94. C22×C8 | C5⋊D5 | semidirect |
| 100. C52 | #435 | semidirect |
| 103. C22×C5 | #676 | semidirect |
| 147. C8 | C22⋊(C5⋊D5) | semidirect |
| 148. C5 | #65400 | semidirect |
| 154. C22 | #87799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| C2×#87799 | 2 |
| C22⋊#6029 | 2 |
| #11716687 | 2 |
| #11716682 | 2 |
| #11716681 | 2 |
| #65400 | 5 |