Subgroups — C₁₉⋊C₃×D₂₉⋊C₇ #37529049

Order 23142.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₉⋊C₃×D₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂₉×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₉⋊C₇	—	19	1	no	maximal, Hall
7	C₁₉×D₂₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×C₁₉⋊C₃	—	29	1	no	maximal, Hall
9	C₃×C₂₉⋊C₇	—	19	1	no	Hall
10	C₁₉×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	D₂₉⋊C₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₁₉⋊C₃	—	29	1	no	Hall
13	C₂×C₇×C₁₉	—	29	1	no	Hall
14	C₂₉⋊C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×D₂₉	—	19	1	no	Hall
16	C₇×C₁₉	—	29	1	no	Hall
17	C₂×C₁₉⋊C₃	—	203	1	no	Hall
18	C₃×C₂₉	—	19	1	no	Hall
19	D₂₉	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₁₉⋊C₃	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₇	—	551	1	no	Hall
22	C₂×C₁₉	—	203	1	no	Hall
23	C₂₉	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	—	551	1	no	Hall
25	C₁₉	C₃×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇	—	29	1	no	Hall
27	C₇	—	29	1	no	Sylow
28	C₂×C₃	—	3857	1	no	Hall
29	C₃	—	19	1	no	Sylow
30	C₂	—	203	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₂₉	C₂×C₃×C₇
LCS	G ▷ C₁₉×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊C₃×C₂₉⋊C₇	C₂	semidirect
2. C₁₉×D₂₉⋊C₇	C₃	semidirect
3. C₁₉×C₂₉⋊C₇	C₂×C₃	semidirect
4. C₁₉⋊C₃×D₂₉	C₇	semidirect
5. C₂₉×C₁₉⋊C₃	C₂×C₇	semidirect
7. C₁₉×D₂₉	C₃×C₇	semidirect
10. C₁₉×C₂₉	C₂×C₃×C₇	semidirect
11. D₂₉⋊C₇	C₁₉⋊C₃	direct (N × H)
14. C₂₉⋊C₇	C₂×C₁₉⋊C₃	semidirect
19. D₂₉	C₇×C₁₉⋊C₃	semidirect
20. C₁₉⋊C₃	D₂₉⋊C₇	direct (N × H)
23. C₂₉	C₂×C₇×C₁₉⋊C₃	semidirect
25. C₁₉	C₃×D₂₉⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊C₃×C₂₉⋊C₇	2
C₁₉×D₂₉⋊C₇	3
C₁₉⋊C₃×D₂₉	7
C₃×D₂₉⋊C₇	19
C₂×C₇×C₁₉⋊C₃	29

Subgroups — C19⋊C3×D29⋊C7 #37529049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊C₃×D₂₉⋊C₇ #37529049