Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
343 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #11716852 | C2 | direct (N × H) |
| 6. C2×C52×Q8 | C4 | semidirect |
| 9. C5×Q8×D5 | C4 | semidirect |
| 14. C2×C5×Dic10 | C4 | semidirect |
| 26. C52×Q8 | C2×C4 | semidirect |
| 40. C5×Dic10 | C2×C4 | semidirect |
| 70. C2×C5×Q8 | Dic5 | semidirect |
| 71. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 77. Q8×D5 | Dic5 | semidirect |
| 82. C2×Dic10 | Dic5 | semidirect |
| 94. C2×C52 | #103 | semidirect |
| 96. C5×D5 | #103 | semidirect |
| 111. C5×Q8 | C2×Dic5 | semidirect |
| 112. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 140. Dic10 | C2×Dic5 | semidirect |
| 147. C52 | C2×#103 | semidirect |
| 182. C2×Q8 | #1042 | semidirect |
| 196. C2×C5 | #3967 | semidirect |
| 197. C2×C5 | #4009 | semidirect |
| 200. D5 | #3967 | semidirect |
| 209. Q8 | C2×#1042 | semidirect |
| 224. C5 | C2×#3967 | semidirect |
| 225. C5 | C2×#4009 | semidirect |
| 241. C2 | #11716852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C4⋊#1042 | 2 |
| C2×D5⋊#168 | 2 |
| #11716852 | 2 |
| C2×#4009 | 5 |
| C2×#3967 | 5 |