Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 1. C2×#87871 | C2 | semidirect |
| 2. C2×C8×C5⋊D5 | C2 | semidirect |
| 3. C2×C5×Dic20 | C2 | semidirect |
| 4. C2×C5×D40 | C2 | semidirect |
| 5. C2×#87772 | C2 | semidirect |
| 6. #11716928 | C2 | direct (N × H) |
| 13. #87871 | C22 | semidirect |
| 16. C8×C5⋊D5 | C22 | semidirect |
| 17. C5×Dic20 | C22 | semidirect |
| 18. C5×D40 | C22 | semidirect |
| 19. #87772 | C22 | semidirect |
| 45. C2×Dic20 | D5 | semidirect |
| 46. C2×D40 | D5 | semidirect |
| 84. Dic20 | C2×D5 | semidirect |
| 85. D40 | C2×D5 | semidirect |
| 90. C2×C52 | #135 | semidirect |
| 137. C52 | C2×#135 | semidirect |
| 178. C2×C5 | #4058 | semidirect |
| 179. C2×C5 | #4065 | semidirect |
| 202. C5 | C2×#4058 | semidirect |
| 203. C5 | C2×#4065 | semidirect |
| 215. C2 | #11716928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| C2×C8×C5⋊D5 | 2 |
| C2×C5×Dic20 | 2 |
| C2×C5×D40 | 2 |
| C2×#87772 | 2 |
| #11716928 | 2 |
| C2×#4065 | 5 |
| C2×#4058 | 5 |