Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
397 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 397 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. C2×C4⋊#1042 | C2 | semidirect |
| 4. C2×C4×#1042 | C2 | semidirect |
| 6. #11716849 | C2 | semidirect |
| 7. #11716849 | C2 | semidirect |
| 19. C52×C22⋊C4 | C4 | semidirect |
| 20. C5×C22⋊Dic5 | C4 | semidirect |
| 21. C5×#685 | C4 | semidirect |
| 22. C5×#685 | C4 | semidirect |
| 115. C5×C22⋊C4 | Dic5 | semidirect |
| 116. C5×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 119. C22⋊Dic5 | Dic5 | semidirect |
| 120. #685 | Dic5 | semidirect |
| 121. #685 | Dic5 | semidirect |
| 202. C52 | #388 | semidirect |
| 272. C22⋊C4 | #1042 | semidirect |
| 326. C5 | #65240 | semidirect |
| 327. C5 | #65700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#1042 | 2 |
| C2×C4⋊#1042 | 2 |
| C2×C4×#1042 | 2 |
| C5×D5×C22⋊C4 | 2 |
| #11716849 | 2 |
| #65700 | 5 |
| #65240 | 5 |