Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
407 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11717425 | C2 | semidirect |
| 3. D5⋊#681 | C2 | semidirect |
| 4. #11716850 | C2 | semidirect |
| 6. C2×C52×D4 | C4 | semidirect |
| 10. C5×D4×D5 | C4 | semidirect |
| 12. C2×C5×D20 | C4 | semidirect |
| 16. C4⋊#1042 | C22 | semidirect |
| 19. D5⋊#168 | C22 | semidirect |
| 74. C2×C5×D4 | Dic5 | semidirect |
| 75. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 80. D4×D5 | Dic5 | semidirect |
| 82. C2×D20 | Dic5 | semidirect |
| 151. C52 | #418 | semidirect |
| 194. C2×D4 | #1042 | semidirect |
| 238. C5 | #65504 | semidirect |
| 239. C5 | #65767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| #11717425 | 2 |
| D5⋊#681 | 2 |
| #11716850 | 2 |
| #65767 | 5 |
| #65504 | 5 |