Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 200 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. C5×Q8×Dic5 | C2 | semidirect |
| 3. #11717018 | C2 | semidirect |
| 4. #11717013 | C2 | semidirect |
| 5. #11716992 | C2 | semidirect |
| 7. #87904 | C4 | semidirect |
| 18. C52×Q8 | C2×C4 | semidirect |
| 21. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 22. C4×C5⋊D5 | C2×C4 | semidirect |
| 29. Q8×Dic5 | D5 | semidirect |
| 67. C5×Q8 | C4×D5 | semidirect |
| 86. C52 | #520 | semidirect |
| 122. Q8 | #6036 | semidirect |
| 131. C5 | #65908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C5×Q8×Dic5 | 2 |
| #11717018 | 2 |
| #11717013 | 2 |
| #11716992 | 2 |
| #65908 | 5 |