Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11716853 | C2 | semidirect |
| 5. C2×C52×Q8 | C4 | semidirect |
| 8. C5×#713 | C4 | semidirect |
| 11. C2×C5×D20 | C4 | semidirect |
| 17. C4×#1042 | C22 | semidirect |
| 18. #87849 | C22 | semidirect |
| 66. C2×C5×Q8 | Dic5 | semidirect |
| 67. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 74. #713 | Dic5 | semidirect |
| 77. C2×D20 | Dic5 | semidirect |
| 144. C52 | #421 | semidirect |
| 177. C2×Q8 | #1042 | semidirect |
| 220. C5 | #65525 | semidirect |
| 221. C5 | #65784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| #11717425 | 2 |
| D5⋊#681 | 2 |
| #11716853 | 2 |
| #65784 | 5 |
| #65525 | 5 |