Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
435 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 435 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4⋊Q8 | C2 | semidirect |
| 3. #11716506 | C2 | semidirect |
| 5. #11716450 | C2 | semidirect |
| 7. #11716431 | C2 | semidirect |
| 32. C4×D25 | Q8 | semidirect |
| 47. C4×C25 | C2×Q8 | semidirect |
| 50. Dic25 | C2×Q8 | semidirect |
| 67. D25 | C4⋊Q8 | direct (N × H) |
| 85. C4⋊Q8 | D25 | direct (N × H) |
| 88. C25 | C2×C4⋊Q8 | semidirect |
| 136. C4 | Q8×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D25 | 2 |
| C25×C4⋊Q8 | 2 |
| #11716506 | 2 |
| C4⋊C4×D25 | 2 |
| #11716450 | 2 |
| C42×D25 | 2 |
| #11716431 | 2 |
| D5×C4⋊Q8 | 5 |