Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
936 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 4. C2×C4⋊#1039 | C2 | semidirect |
| 5. C2×#87806 | C2 | semidirect |
| 6. C52×#95 | C2 | semidirect |
| 7. #11716698 | C2 | semidirect |
| 19. #87808 | C4 | semidirect |
| 38. C2×C4×C52 | C2×C4 | semidirect |
| 47. C2×#1039 | C2×C4 | semidirect |
| 55. C5×#95 | D5 | semidirect |
| 70. C2×C5⋊D5 | C4⋊C4 | semidirect |
| 115. C2×C4×C5 | C4×D5 | semidirect |
| 133. #95 | C5⋊D5 | semidirect |
| 134. C52 | #385 | semidirect |
| 202. C2×C4 | C4×C5⋊D5 | semidirect |
| 204. C5 | #64957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C2×#87808 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×#87806 | 2 |
| C52×#95 | 2 |
| #11716698 | 2 |
| #64957 | 5 |