Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 155 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×#41 | C2 | semidirect |
| 2. C2×#87811 | C2 | semidirect |
| 3. C2×#87809 | C2 | semidirect |
| 4. #11717250 | C2 | semidirect |
| 5. #11716702 | C2 | semidirect |
| 6. #11716699 | C2 | semidirect |
| 7. C22⋊#6029 | C2 | semidirect |
| 28. C52×Q8 | D4 | semidirect |
| 31. C52×D4 | D4 | semidirect |
| 44. C2×C5×#41 | D5 | semidirect |
| 92. C5×Q8 | C22⋊D5 | semidirect |
| 95. C5×D4 | C22⋊D5 | semidirect |
| 108. C2×#41 | C5⋊D5 | semidirect |
| 115. C52 | #449 | semidirect |
| 156. Q8 | C22⋊(C5⋊D5) | semidirect |
| 162. D4 | C22⋊(C5⋊D5) | semidirect |
| 172. C5 | #65527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C2×#87811 | 2 |
| C2×#87809 | 2 |
| #11717250 | 2 |
| #11716702 | 2 |
| #11716699 | 2 |
| C22⋊#6029 | 2 |
| #65527 | 5 |