Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
624 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 160 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. C2×C5×#683 | C2 | semidirect |
| 3. C2×C4×C5×Dic5 | C2 | semidirect |
| 4. C2×#87781 | C2 | semidirect |
| 5. C2×#87780 | C2 | semidirect |
| 8. #11716987 | C2 | direct (N × H) |
| 17. C5×#683 | C22 | semidirect |
| 18. C4×C5×Dic5 | C22 | semidirect |
| 19. #87781 | C22 | semidirect |
| 20. #87780 | C22 | semidirect |
| 55. C2×#683 | D5 | semidirect |
| 56. C2×C4×Dic5 | D5 | semidirect |
| 103. #683 | C2×D5 | semidirect |
| 104. C4×Dic5 | C2×D5 | semidirect |
| 106. C2×C52 | #126 | semidirect |
| 162. C52 | C2×#126 | semidirect |
| 219. C2×C5 | #4022 | semidirect |
| 220. C2×C5 | #4044 | semidirect |
| 248. C5 | C2×#4022 | semidirect |
| 249. C5 | C2×#4044 | semidirect |
| 265. C2 | #11716987 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87808 | 2 |
| C2×C5×#683 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87781 | 2 |
| C2×#87780 | 2 |
| C2×#87779 | 2 |
| #11716987 | 2 |
| C2×#4044 | 5 |
| C2×#4022 | 5 |