Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 251 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⋊#1039 | C2 | semidirect |
| 3. C2×#87804 | C2 | semidirect |
| 4. #11716702 | C2 | semidirect |
| 5. #11716699 | C2 | semidirect |
| 7. C52×#41 | C4 | semidirect |
| 22. C52×Q8 | C2×C4 | semidirect |
| 25. C52×D4 | C2×C4 | semidirect |
| 53. C5×#41 | Dic5 | semidirect |
| 73. C5×Q8 | C2×Dic5 | semidirect |
| 76. C5×D4 | C2×Dic5 | semidirect |
| 91. C52 | #417 | semidirect |
| 105. #41 | #1039 | semidirect |
| 124. Q8 | C2×#1039 | semidirect |
| 127. D4 | C2×#1039 | semidirect |
| 137. C5 | #65521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×#87804 | 2 |
| #11716702 | 2 |
| #11716699 | 2 |
| #65521 | 5 |