Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
536 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 536 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. C22×C52×C8 | C2 | semidirect |
| 2. #11717250 | C2 | semidirect |
| 3. C2×#87801 | C2 | semidirect |
| 4. #11716688 | C2 | semidirect |
| 5. #11716685 | C2 | semidirect |
| 27. C52×C8 | D4 | semidirect |
| 28. C22×C5×C8 | D5 | semidirect |
| 35. C22×C52 | D8 | semidirect |
| 70. C5×C8 | C22⋊D5 | semidirect |
| 72. C22×C8 | C5⋊D5 | semidirect |
| 76. C52 | #466 | semidirect |
| 79. C22×C5 | D40 | semidirect |
| 113. C8 | C22⋊(C5⋊D5) | semidirect |
| 114. C5 | #65404 | semidirect |
| 120. C22 | #87801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| #11717250 | 2 |
| C2×#87801 | 2 |
| #11716688 | 2 |
| #11716685 | 2 |
| #65404 | 5 |