Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C52×SD16 | C2 | semidirect |
| 3. #11717266 | C2 | semidirect |
| 4. C2×#87811 | C2 | semidirect |
| 5. #11716699 | C2 | semidirect |
| 6. #11716688 | C2 | semidirect |
| 7. #11716687 | C2 | semidirect |
| 9. C2×C52×Q8 | C22 | semidirect |
| 17. C2×C52×C8 | C22 | semidirect |
| 20. C4⋊#1039 | C22 | semidirect |
| 22. C2×#6029 | C22 | semidirect |
| 46. C2×C5×SD16 | D5 | semidirect |
| 62. C2×C5⋊D5 | SD16 | semidirect |
| 69. C2×C5×Q8 | C2×D5 | semidirect |
| 77. C2×C5×C8 | C2×D5 | semidirect |
| 113. C2×SD16 | C5⋊D5 | semidirect |
| 118. C52 | #450 | semidirect |
| 136. C2×Q8 | C2×C5⋊D5 | semidirect |
| 146. C2×C8 | C2×C5⋊D5 | semidirect |
| 177. C5 | #65458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C5⋊D5 | 2 |
| C2×C52×SD16 | 2 |
| #11717266 | 2 |
| C2×#87811 | 2 |
| #11716699 | 2 |
| #11716688 | 2 |
| #11716687 | 2 |
| #65458 | 5 |