Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
315 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×C22⋊#1035 | C2 | semidirect |
| 3. #11716421 | C2 | direct (N × H) |
| 4. C23×D25 | C4 | semidirect |
| 7. C22×C4×C25 | C4 | semidirect |
| 10. C2×D100 | C4 | semidirect |
| 13. C22⋊#1035 | C22 | semidirect |
| 21. C22×D25 | C2×C4 | semidirect |
| 29. C2×C4×C25 | C2×C4 | semidirect |
| 64. C2×C25 | #99 | semidirect |
| 89. C25 | C2×#99 | semidirect |
| 113. C22×C4 | #1035 | semidirect |
| 139. C2×C4 | C2×#1035 | semidirect |
| 162. C2 | #11716421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D100 | 2 |
| C2×C22⋊#1035 | 2 |
| #11716421 | 2 |
| C2×#3999 | 5 |