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 |
|---|---|---|
| 2. C22×#6045 | C2 | semidirect |
| 3. C2×C42×C52 | C2 | semidirect |
| 4. C2×#87808 | C2 | semidirect |
| 5. #11717195 | C2 | direct (N × H) |
| 13. C2×#6045 | C22 | semidirect |
| 14. C42×C52 | C22 | semidirect |
| 15. #87808 | C22 | semidirect |
| 31. C2×C42×C5 | D5 | semidirect |
| 51. C42×C5 | C2×D5 | semidirect |
| 54. C2×C52 | #124 | semidirect |
| 74. C2×C42 | C5⋊D5 | semidirect |
| 75. C52 | C2×#124 | semidirect |
| 94. C42 | C2×C5⋊D5 | semidirect |
| 95. C2×C5 | #4021 | semidirect |
| 111. C5 | C2×#4021 | semidirect |
| 122. C2 | #11717195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C22×#6045 | 2 |
| C2×C42×C52 | 2 |
| C2×#87808 | 2 |
| #11717195 | 2 |
| C2×#4021 | 5 |