Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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×C52×Q16 | C2 | semidirect |
| 4. C5×#3968 | C2 | semidirect |
| 5. C5×#3951 | C2 | semidirect |
| 18. #65481 | C5 | direct (N × H) |
| 33. C2×C5×Q16 | D5 | semidirect |
| 34. C2×C5×Q16 | C2×C5 | semidirect |
| 40. #3968 | C2×C5 | semidirect |
| 41. #3951 | C2×C5 | semidirect |
| 109. C2×Q16 | C5×D5 | semidirect |
| 113. C52 | #473 | semidirect |
| 162. C5 | #65481 | direct (N × H) |
| 163. C5 | C5×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C5×#4088 | 2 |
| C5×#4047 | 2 |
| C5×#3968 | 2 |
| C5×#3951 | 2 |
| C5×#473 | 5 |
| #65481 | 5 |