Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
792 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 139 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. C52×H(5,𝔽2) | C2 | semidirect |
| 2. #11717257 | C2 | semidirect |
| 3. #11716701 | C2 | semidirect |
| 4. C23×C5⋊D5 | C22 | semidirect |
| 9. C22⋊#1039 | C22 | semidirect |
| 13. C23×C52 | D4 | semidirect |
| 21. C2×C4×C52 | D4 | semidirect |
| 24. C5×H(5,𝔽2) | D5 | semidirect |
| 50. C23×C5 | C22⋊D5 | semidirect |
| 58. C2×C4×C5 | C22⋊D5 | semidirect |
| 61. H(5,𝔽2) | C5⋊D5 | semidirect |
| 64. C52 | B(4,𝔽2) | semidirect |
| 89. C23 | C22⋊(C5⋊D5) | semidirect |
| 97. C2×C4 | C22⋊(C5⋊D5) | semidirect |
| 98. C5 | #65533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×H(5,𝔽2) | 2 |
| #11717257 | 2 |
| #11716701 | 2 |
| #65533 | 5 |