Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
898 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 103 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×#11716886 | C2 | semidirect |
| 3. C2×#11716860 | C2 | semidirect |
| 4. #13103991 | C2 | semidirect |
| 5. C2×#11716766 | C2 | semidirect |
| 12. C2×C5×D40 | C4 | semidirect |
| 13. C2×#87770 | C4 | semidirect |
| 71. C52×C8 | C22⋊C4 | semidirect |
| 72. #6029 | C22⋊C4 | semidirect |
| 84. C2×D40 | AGL(1,𝔽5) | semidirect |
| 196. C5×C8 | C22⋊AGL(1,𝔽5) | semidirect |
| 212. C52 | #1972 | semidirect |
| 296. C8 | #87831 | semidirect |
| 298. C5 | #10604803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716915 | 2 |
| C2×#11716886 | 2 |
| C2×#11716860 | 2 |
| #13103991 | 2 |
| C2×#11716766 | 2 |
| #10604803 | 5 |