Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
272 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 4. #11716674 | C2 | semidirect |
| 5. C5×#3940 | C2 | semidirect |
| 6. #11716616 | C2 | semidirect |
| 7. #11716615 | C2 | semidirect |
| 19. #87768 | C4 | semidirect |
| 32. #6029 | C2×C4 | semidirect |
| 33. C5×#168 | C2×C4 | semidirect |
| 44. #3940 | D5 | semidirect |
| 119. #168 | C4×D5 | semidirect |
| 127. C52 | #428 | semidirect |
| 191. C5 | #65150 | semidirect |
| 192. C5 | #65253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×C4⋊C4 | 2 |
| #11716959 | 2 |
| C2×#87768 | 2 |
| #11716674 | 2 |
| C5×#3940 | 2 |
| #11716616 | 2 |
| #11716615 | 2 |
| #65253 | 5 |
| #65150 | 5 |