Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11717246 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. #11716609 | C2 | semidirect |
| 9. C5×#709 | C4 | semidirect |
| 11. C2×C5×D20 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 16. C4×#1039 | C22 | semidirect |
| 18. C5×#681 | C22 | semidirect |
| 47. C2×#681 | D5 | semidirect |
| 76. #709 | Dic5 | semidirect |
| 78. C2×D20 | Dic5 | semidirect |
| 80. C2×Dic10 | Dic5 | semidirect |
| 94. #681 | C2×D5 | semidirect |
| 152. C52 | #421 | semidirect |
| 235. C5 | #65428 | semidirect |
| 236. C5 | #65525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| #11717246 | 2 |
| C2×C5×#681 | 2 |
| #11716609 | 2 |
| #65525 | 5 |
| #65428 | 5 |