Subgroups — D₇×C₂₉×C₁₉⋊C₃ #37529033

Order 23142.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂₉	D₇×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₂₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉×C₁₉⋊C₃	C₂	semidirect
2. D₇×C₁₉×C₂₉	C₃	semidirect
3. C₇×C₁₉×C₂₉	C₂×C₃	semidirect
5. C₂₉×C₁₉⋊C₃	D₇	direct (N × H)
8. D₇×C₁₉⋊C₃	C₂₉	direct (N × H)
10. C₁₉×C₂₉	C₃×D₇	semidirect
11. D₇×C₂₉	C₁₉⋊C₃	direct (N × H)
12. C₇×C₁₉⋊C₃	C₂×C₂₉	semidirect
13. D₇×C₁₉	C₃×C₂₉	semidirect
14. C₇×C₂₉	C₂×C₁₉⋊C₃	semidirect
16. C₇×C₁₉	C₂×C₃×C₂₉	semidirect
20. C₁₉⋊C₃	D₇×C₂₉	direct (N × H)
23. C₂₉	D₇×C₁₉⋊C₃	direct (N × H)
25. C₁₉	C₃×D₇×C₂₉	semidirect
26. D₇	C₂₉×C₁₉⋊C₃	direct (N × H)
27. C₇	C₂×C₂₉×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₂₉×C₁₉⋊C₃	2
D₇×C₁₉×C₂₉	3
C₂×C₂₉×C₁₉⋊C₃	7
C₃×D₇×C₂₉	19
D₇×C₁₉⋊C₃	29

Subgroups — D7×C29×C19⋊C3 #37529033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₂₉×C₁₉⋊C₃ #37529033