Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
144 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊#16838457 |
| commutator, hypocenter | C5×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C72×C13 | C2×C3 |
| prime radical | C2×C5×#14274262 | C2 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×Dic455 | C3 | semidirect |
| 3. C5×#14274262 | C4 | semidirect |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 15. #14274262 | Dic5 | semidirect |
| 16. Dic455 | ΓL(1,𝔽8) | semidirect |
| 31. C72×C13 | C3×Dic5 | semidirect |
| 38. C5×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 39. C5×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 50. C5×C72 | Dic13⋊C3 | semidirect |
| 69. C7×C13 | Dic5×ΓL(1,𝔽8) | semidirect |
| 70. C7×C13 | ΓL(1,𝔽8)⋊Dic5 | semidirect |
| 77. C5×C13 | #10596873 | semidirect |
| 80. C72 | Dic65⋊C3 | semidirect |
| 86. C5×C7 | #11763958 | semidirect |
| 87. C5×C7 | #11763964 | semidirect |
| 100. C13 | #15668736 | semidirect |
| 104. C7 | #19129698 | semidirect |
| 105. C7 | #19129706 | semidirect |
| 107. C5 | #21439533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#14274262 | 2 |
| C7×Dic455 | 3 |
| #21439533 | 5 |
| #19129706 | 7 |
| #19129698 | 7 |
| #15668736 | 13 |