Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
744 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 195 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×M16 | C2 | semidirect |
| 3. C2×#87804 | C2 | semidirect |
| 4. #11716690 | C2 | direct (N × H) |
| 14. C52×M16 | C22 | semidirect |
| 17. #87804 | C22 | semidirect |
| 38. C2×C5×M16 | D5 | semidirect |
| 62. C5×M16 | C2×D5 | semidirect |
| 70. C2×C52 | #100 | semidirect |
| 92. C2×M16 | C5⋊D5 | semidirect |
| 94. C52 | C2×#100 | semidirect |
| 118. M16 | C2×C5⋊D5 | semidirect |
| 123. C2×C5 | #3955 | semidirect |
| 143. C5 | C2×#3955 | semidirect |
| 159. C2 | #11716690 | 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 |
| C2×C52×M16 | 2 |
| C2×#87804 | 2 |
| #11716690 | 2 |
| C2×#3955 | 5 |