Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 672 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. #11717269 | C2 | semidirect |
| 3. #11717260 | C2 | semidirect |
| 4. #11716704 | C2 | semidirect |
| 5. #11716700 | C2 | semidirect |
| 12. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 15. C4×#1039 | C22 | semidirect |
| 16. #87804 | C22 | semidirect |
| 21. C52×Q8 | D4 | semidirect |
| 25. C52×D4 | D4 | semidirect |
| 33. C5×H(5,𝔽2) | D5 | semidirect |
| 68. C5×Q8 | C22⋊D5 | semidirect |
| 72. C5×D4 | C22⋊D5 | semidirect |
| 80. H(5,𝔽2) | C5⋊D5 | semidirect |
| 85. C52 | #453 | semidirect |
| 115. Q8 | C22⋊(C5⋊D5) | semidirect |
| 121. D4 | C22⋊(C5⋊D5) | semidirect |
| 127. C5 | #65530 | 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 |
| #11717269 | 2 |
| #11717260 | 2 |
| #11716704 | 2 |
| #11716700 | 2 |
| #65530 | 5 |