Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 76 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×C5×Q8×D5 | C2 | semidirect |
| 2. C2×#87811 | C2 | semidirect |
| 4. C2×#87774 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 28. C52×Q8 | D4 | semidirect |
| 41. C5×Dic10 | D4 | semidirect |
| 46. C2×Q8×D5 | D5 | semidirect |
| 56. #3967 | D5 | semidirect |
| 66. C2×C5×D5 | SD16 | semidirect |
| 125. C5×Q8 | D20 | semidirect |
| 126. C5×Q8 | C22⋊D5 | semidirect |
| 155. Dic10 | C22⋊D5 | semidirect |
| 168. C52 | #448 | semidirect |
| 186. C2×D5 | #688 | semidirect |
| 237. Q8 | #6038 | semidirect |
| 252. C5 | #65095 | semidirect |
| 253. C5 | #65516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×#87811 | 2 |
| #11717027 | 2 |
| C2×#87774 | 2 |
| C5×#3967 | 2 |
| #11716606 | 2 |
| #11716597 | 2 |
| #65516 | 5 |
| #65095 | 5 |