Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1320 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1320 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. C22×C52×Q8 | C2 | semidirect |
| 3. #11717267 | C2 | direct (N × H) |
| 4. C2×#87808 | C2 | semidirect |
| 5. C2×C4×#1039 | C2 | semidirect |
| 8. C2×C52×Q8 | C22 | semidirect |
| 14. #87808 | C22 | semidirect |
| 15. C4×#1039 | C22 | semidirect |
| 29. C22×C5×Q8 | D5 | semidirect |
| 45. C2×C5×Q8 | C2×D5 | semidirect |
| 54. C2×C52 | #124 | semidirect |
| 70. C22×Q8 | C5⋊D5 | semidirect |
| 75. C52 | C2×#124 | semidirect |
| 87. C2×Q8 | C2×C5⋊D5 | semidirect |
| 95. C2×C5 | #4093 | semidirect |
| 111. C5 | C2×#4093 | semidirect |
| 122. C2 | #11717267 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C22×C4⋊(C5⋊D5) | 2 |
| #11717267 | 2 |
| C2×#87808 | 2 |
| C2×C4×#1039 | 2 |
| C2×#4093 | 5 |