Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. C2×C5×#689 | C2 | semidirect |
| 4. #11717062 | C2 | direct (N × H) |
| 5. C2×#87776 | C2 | semidirect |
| 19. C5×#689 | C22 | semidirect |
| 21. #87776 | C22 | semidirect |
| 48. C2×#689 | D5 | semidirect |
| 53. C2×C5⋊D5 | Q16 | semidirect |
| 84. #689 | C2×D5 | semidirect |
| 89. C2×C52 | C2×Q16 | semidirect |
| 91. C5⋊D5 | C2×Q16 | semidirect |
| 134. C52 | C22×Q16 | semidirect |
| 171. C2×C5 | D5×Q16 | semidirect |
| 195. C5 | C2×D5×Q16 | semidirect |
| 206. C2 | #11717062 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C2×#87872 | 2 |
| C2×C5×#689 | 2 |
| #11717062 | 2 |
| C2×#87776 | 2 |
| C2×#87767 | 2 |
| C2×D5×Q16 | 5 |