Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
431 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 2. C2×D5⋊#168 | C2 | semidirect |
| 3. C2×C5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. #11716734 | C2 | direct (N × H) |
| 7. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 8. C2×C5×D20 | C4 | semidirect |
| 13. D5×D20 | C4 | semidirect |
| 17. D5⋊#168 | C22 | semidirect |
| 19. C5×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 33. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 36. C5×D20 | C2×C4 | semidirect |
| 46. C2×C4⋊AGL(1,𝔽5) | D5 | semidirect |
| 88. C2×D20 | AGL(1,𝔽5) | semidirect |
| 92. C4⋊AGL(1,𝔽5) | C2×D5 | semidirect |
| 101. C2×C52 | #102 | semidirect |
| 105. C5×D5 | #102 | semidirect |
| 149. D20 | C2×AGL(1,𝔽5) | semidirect |
| 160. C52 | C2×#102 | semidirect |
| 221. C2×C5 | #3941 | semidirect |
| 222. C2×C5 | #4007 | semidirect |
| 229. D5 | #3941 | semidirect |
| 255. C5 | C2×#3941 | semidirect |
| 256. C5 | C2×#4007 | semidirect |
| 279. C2 | #11716734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| C2×D5⋊#168 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| #11716734 | 2 |
| C2×#4007 | 5 |
| C2×#3941 | 5 |