Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1144 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 291 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. C2×#87808 | C2 | semidirect |
| 5. #11716698 | C2 | semidirect |
| 13. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 29. C22×C5⋊D5 | C2×C4 | semidirect |
| 33. C2×C4×C52 | D4 | semidirect |
| 40. C2×#1039 | C2×C4 | semidirect |
| 41. C23×C4×C5 | D5 | semidirect |
| 50. C22×C52 | C22⋊C4 | semidirect |
| 98. C2×C4×C5 | C22⋊D5 | semidirect |
| 107. C23×C4 | C5⋊D5 | semidirect |
| 111. C52 | #386 | semidirect |
| 116. C22×C5 | #685 | semidirect |
| 170. C2×C4 | C22⋊(C5⋊D5) | semidirect |
| 171. C5 | #65502 | semidirect |
| 181. C22 | #87808 | semidirect |
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 |
| C2×#87808 | 2 |
| #11716698 | 2 |
| #65502 | 5 |