Subgroups — D₃×C₁₁⋊C₅×C₁₀₉ #49112583

Order 35970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊C₅×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₁⋊C₅×C₁₀₉	—	3	1	no	maximal, Hall
3	D₃×C₁₁×C₁₀₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁⋊C₅×C₁₀₉	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₁×C₁₀₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₁₀₉	—	11	1	no	maximal, Hall
7	C₂×C₁₁×C₁₀₉	—	3	1	no	Hall
8	C₃×C₅×C₁₀₉	—	11	1	no	Hall
9	C₁₁×C₁₀₉	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₁₀₉	—	33	1	no	Hall
11	D₃×C₁₀₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₁₀₉	—	11	1	no	Hall
13	D₃×C₁₁⋊C₅	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₁₀₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₀₉	—	3	1	no	Hall
16	C₃×C₁₁⋊C₅	C₂×C₁₀₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁⋊C₅	—	3	1	no	Hall
18	C₁₀₉	D₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
19	D₃×C₁₁	C₅×C₁₀₉	1	1	yes	characteristic, complemented, Hall
20	C₁₁⋊C₅	D₃×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁	C₂×C₅×C₁₀₉	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	11	1	no	Hall
23	C₂×C₁₁	—	3	1	no	Hall
24	C₃×C₅	—	11	1	no	Hall
25	C₁₁	C₅×D₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	33	1	no	Hall
27	D₃	C₁₁⋊C₅×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
28	C₅	—	11	1	no	Sylow
29	C₃	C₂×C₁₁⋊C₅×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₀₉	D₃×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₀₉	C₂×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₁₀₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₁₁⋊C₅×C₁₀₉	C₂	semidirect
3. D₃×C₁₁×C₁₀₉	C₅	semidirect
4. C₁₁⋊C₅×C₁₀₉	D₃	direct (N × H)
5. C₃×C₁₁×C₁₀₉	C₂×C₅	semidirect
9. C₁₁×C₁₀₉	C₅×D₃	semidirect
11. D₃×C₁₀₉	C₁₁⋊C₅	direct (N × H)
13. D₃×C₁₁⋊C₅	C₁₀₉	direct (N × H)
14. C₃×C₁₀₉	C₂×C₁₁⋊C₅	semidirect
16. C₃×C₁₁⋊C₅	C₂×C₁₀₉	semidirect
18. C₁₀₉	D₃×C₁₁⋊C₅	direct (N × H)
19. D₃×C₁₁	C₅×C₁₀₉	semidirect
20. C₁₁⋊C₅	D₃×C₁₀₉	direct (N × H)
21. C₃×C₁₁	C₂×C₅×C₁₀₉	semidirect
25. C₁₁	C₅×D₃×C₁₀₉	semidirect
27. D₃	C₁₁⋊C₅×C₁₀₉	direct (N × H)
29. C₃	C₂×C₁₁⋊C₅×C₁₀₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₁⋊C₅×C₁₀₉	2
C₂×C₁₁⋊C₅×C₁₀₉	3
D₃×C₁₁×C₁₀₉	5
C₅×D₃×C₁₀₉	11
D₃×C₁₁⋊C₅	109

Subgroups — D3×C11⋊C5×C109 #49112583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₁⋊C₅×C₁₀₉ #49112583