Subgroups — C₃×D₃₈₅₇ #37529005

Order 23142.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₈₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₉×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₅₅₁	—	7	1	no	maximal, Hall
5	C₃×C₁₉×C₂₉	D₇	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₀₃	—	19	1	no	maximal, Hall
7	D₅₅₁	—	7	1	no	Hall
8	C₃×D₁₃₃	—	29	1	no	maximal, Hall
9	C₃×C₇×C₂₉	D₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×C₂₉	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	D₂₀₃	—	19	1	no	Hall
12	C₃×C₇×C₁₉	D₂₉	1	1	yes	characteristic, complemented, Hall
13	D₁₃₃	—	29	1	no	Hall
14	C₇×C₂₉	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
15	C₃×D₂₉	—	133	1	no	Hall
16	C₇×C₁₉	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₉	—	203	1	no	Hall
18	C₃×C₂₉	D₁₃₃	1	1	yes	characteristic, complemented, Hall
19	D₂₉	—	133	1	no	Hall
20	C₃×C₁₉	D₂₀₃	1	1	yes	characteristic, complemented, Hall
21	C₃×D₇	—	551	1	no	Hall
22	D₁₉	—	203	1	no	Hall
23	C₂₉	C₃×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	D₅₅₁	1	1	yes	characteristic, complemented, Hall
25	C₁₉	C₃×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	551	1	no	Hall
27	C₇	C₃×D₅₅₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3857	1	no	Hall
29	C₃	D₃₈₅₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3857	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₈₅₇
commutator, cosocle, hypocenter	C₇×C₁₉×C₂₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉×C₂₉	C₂
LCS	G ▷ C₇×C₁₉×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₉×C₂₉	C₂	semidirect
2. D₃₈₅₇	C₃	direct (N × H)
3. C₇×C₁₉×C₂₉	C₂×C₃	semidirect
5. C₃×C₁₉×C₂₉	D₇	semidirect
9. C₃×C₇×C₂₉	D₁₉	semidirect
10. C₁₉×C₂₉	C₃×D₇	semidirect
12. C₃×C₇×C₁₉	D₂₉	semidirect
14. C₇×C₂₉	C₃×D₁₉	semidirect
16. C₇×C₁₉	C₃×D₂₉	semidirect
18. C₃×C₂₉	D₁₃₃	semidirect
20. C₃×C₁₉	D₂₀₃	semidirect
23. C₂₉	C₃×D₁₃₃	semidirect
24. C₃×C₇	D₅₅₁	semidirect
25. C₁₉	C₃×D₂₀₃	semidirect
27. C₇	C₃×D₅₅₁	semidirect
29. C₃	D₃₈₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₉×C₂₉	2
D₃₈₅₇	3
C₃×D₅₅₁	7
C₃×D₂₀₃	19
C₃×D₁₃₃	29

Subgroups — C3×D3857 #37529005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₈₅₇ #37529005