Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 63 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. C25×C22⋊Q8 | C2 | semidirect |
| 3. C2×#87724 | C2 | semidirect |
| 4. C22⋊#6014 | C2 | semidirect |
| 5. #11716358 | C2 | semidirect |
| 7. C2×Q8×C25 | C22 | semidirect |
| 13. C4⋊C4×C25 | C22 | semidirect |
| 16. C2×#6014 | C22 | semidirect |
| 40. C22×C25 | SD16 | semidirect |
| 84. C22⋊Q8 | D25 | semidirect |
| 87. C25 | #450 | semidirect |
| 101. C2×Q8 | C2×D25 | semidirect |
| 109. C4⋊C4 | C2×D25 | semidirect |
| 138. C22 | #87724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D100 | 2 |
| C25×C22⋊Q8 | 2 |
| C2×#87724 | 2 |
| C22⋊#6014 | 2 |
| #11716358 | 2 |
| #65335 | 5 |