Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1368 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 355 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. C23×C4×C52 | C2 | semidirect |
| 3. C2×C22⋊#1039 | C2 | semidirect |
| 4. #11717249 | C2 | direct (N × H) |
| 5. C2×#87808 | C2 | semidirect |
| 6. C2×#87806 | C2 | semidirect |
| 11. C22×C4×C52 | C22 | semidirect |
| 16. C22⋊#1039 | C22 | semidirect |
| 17. #87808 | C22 | semidirect |
| 18. #87806 | C22 | semidirect |
| 35. C23×C4×C5 | D5 | semidirect |
| 57. C22×C4×C5 | C2×D5 | semidirect |
| 67. C2×C52 | #123 | semidirect |
| 87. C23×C4 | C5⋊D5 | semidirect |
| 92. C52 | C2×#123 | semidirect |
| 113. C22×C4 | C2×C5⋊D5 | semidirect |
| 118. C2×C5 | #4075 | semidirect |
| 137. C5 | C2×#4075 | semidirect |
| 152. C2 | #11717249 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C22×C22⋊(C5⋊D5) | 2 |
| C2×C22⋊#1039 | 2 |
| #11717249 | 2 |
| C2×#87808 | 2 |
| C2×#87806 | 2 |
| C2×#4075 | 5 |