Subgroups — C₁₁×C₂₉⋊(D₁₉⋊C₃) #49138317

Order 36366.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₉×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₅₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₉×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₉⋊(D₁₉⋊C₃)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×D₂₉	—	19	1	no	maximal, Hall
6	C₂₉×C₁₉⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₁×D₁₉⋊C₃	—	29	1	no	maximal, Hall
8	D₅₅₁	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₁×C₂₉	—	19	1	no	Hall
10	C₁₁×D₂₉	—	19	1	no	Hall
11	C₁₁×C₁₉⋊C₃	D₂₉	1	1	yes	characteristic, complemented, Hall
12	C₁₉×C₂₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₁₉	—	29	1	no	Hall
14	C₁₁×C₂₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₉	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
16	C₃×D₂₉	—	19	1	no	Hall
17	D₁₉⋊C₃	—	29	1	no	Hall
18	C₃×C₂₉	—	19	1	no	Hall
19	C₂×C₃×C₁₁	—	551	1	no	Hall
20	D₂₉	—	19	1	no	Hall
21	C₁₉⋊C₃	C₁₁×D₂₉	1	1	yes	characteristic, complemented, Hall
22	D₁₉	—	29	1	no	Hall
23	C₃×C₁₁	—	19	1	no	Hall
24	C₂₉	C₁₁×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₁	—	551	1	no	Hall
26	C₁₉	C₃×C₁₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₂₉⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	551	1	no	Hall
29	C₃	—	19	1	no	Sylow
30	C₂	—	551	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₂₉⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₁₉×C₂₉	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₂₉	C₂×C₃
LCS	G ▷ C₁₉×C₂₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₉×C₁₉⋊C₃	C₂	semidirect
2. C₁₁×D₅₅₁	C₃	semidirect
3. C₁₁×C₁₉×C₂₉	C₂×C₃	semidirect
4. C₂₉⋊(D₁₉⋊C₃)	C₁₁	direct (N × H)
6. C₂₉×C₁₉⋊C₃	C₂×C₁₁	semidirect
8. D₅₅₁	C₃×C₁₁	semidirect
11. C₁₁×C₁₉⋊C₃	D₂₉	semidirect
12. C₁₉×C₂₉	C₂×C₃×C₁₁	semidirect
14. C₁₁×C₂₉	D₁₉⋊C₃	semidirect
15. C₁₁×C₁₉	C₃×D₂₉	semidirect
21. C₁₉⋊C₃	C₁₁×D₂₉	semidirect
24. C₂₉	C₁₁×D₁₉⋊C₃	semidirect
26. C₁₉	C₃×C₁₁×D₂₉	semidirect
27. C₁₁	C₂₉⋊(D₁₉⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₂₉×C₁₉⋊C₃	2
C₁₁×D₅₅₁	3
C₂₉⋊(D₁₉⋊C₃)	11
C₃×C₁₁×D₂₉	19
C₁₁×D₁₉⋊C₃	29

Subgroups — C11×C29⋊(D19⋊C3) #49138317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₂₉⋊(D₁₉⋊C₃) #49138317