Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 143 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. C52×C22⋊Q8 | C2 | semidirect |
| 3. C2×#87811 | C2 | semidirect |
| 4. C22⋊#6029 | C2 | semidirect |
| 5. #11716676 | C2 | semidirect |
| 7. C2×C52×Q8 | C22 | semidirect |
| 13. C52×C4⋊C4 | C22 | semidirect |
| 16. C2×#6029 | C22 | semidirect |
| 34. C5×C22⋊Q8 | D5 | semidirect |
| 40. C22×C52 | SD16 | semidirect |
| 51. C2×C5×Q8 | C2×D5 | semidirect |
| 57. C5×C4⋊C4 | C2×D5 | semidirect |
| 84. C22⋊Q8 | C5⋊D5 | semidirect |
| 87. C52 | #450 | semidirect |
| 90. C22×C5 | #688 | semidirect |
| 101. C2×Q8 | C2×C5⋊D5 | semidirect |
| 109. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 131. C5 | #65335 | semidirect |
| 138. C22 | #87811 | 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 |
| C52×C22⋊Q8 | 2 |
| C2×#87811 | 2 |
| C22⋊#6029 | 2 |
| #11716676 | 2 |
| #65335 | 5 |