Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
359 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 359 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 |
|---|---|---|
| 2. C2×C4×#1042 | C2 | semidirect |
| 3. C2×#87849 | C2 | semidirect |
| 4. #11716853 | C2 | direct (N × H) |
| 6. C2×C52×Q8 | C4 | semidirect |
| 9. C5×#713 | C4 | semidirect |
| 12. C2×C5×D20 | C4 | semidirect |
| 17. C4×#1042 | C22 | semidirect |
| 19. #87849 | C22 | semidirect |
| 27. C52×Q8 | C2×C4 | semidirect |
| 34. C5×D20 | C2×C4 | semidirect |
| 68. C2×C5×Q8 | Dic5 | semidirect |
| 69. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 77. #713 | Dic5 | semidirect |
| 80. C2×D20 | Dic5 | semidirect |
| 94. C2×C52 | #104 | semidirect |
| 109. C5×Q8 | C2×Dic5 | semidirect |
| 110. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 134. D20 | C2×Dic5 | semidirect |
| 147. C52 | C2×#104 | semidirect |
| 180. C2×Q8 | #1042 | semidirect |
| 196. C2×C5 | #3969 | semidirect |
| 197. C2×C5 | #4010 | semidirect |
| 206. Q8 | C2×#1042 | semidirect |
| 224. C5 | C2×#3969 | semidirect |
| 225. C5 | C2×#4010 | semidirect |
| 241. C2 | #11716853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×C4×#1042 | 2 |
| C2×#87849 | 2 |
| #11716853 | 2 |
| C2×#4010 | 5 |
| C2×#3969 | 5 |