Subgroups — C₇×C₁₉×D₈₇ #37529007

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	C₇×C₁₉×D₂₉	—	3	1	no	maximal, Hall
3	C₇×C₁₉×C₂₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₉×D₈₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×D₈₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₉×D₂₉	—	3	1	no	Hall
8	D₃×C₇×C₁₉	—	29	1	no	maximal, Hall
9	C₃×C₇×C₂₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₂₉	—	3	1	no	Hall
12	C₃×C₇×C₁₉	D₂₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₉	—	87	1	no	Hall
14	C₇×C₂₉	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
15	D₈₇	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₁₉	D₈₇	1	1	yes	characteristic, direct product factor, Hall
17	D₃×C₁₉	—	29	1	no	Hall
18	C₃×C₂₉	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
19	D₂₉	—	3	1	no	Hall
20	C₃×C₁₉	C₇×D₂₉	1	1	yes	characteristic, complemented, Hall
21	D₃×C₇	—	29	1	no	Hall
22	C₂×C₁₉	—	87	1	no	Hall
23	C₂₉	D₃×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₁₉×D₂₉	1	1	yes	characteristic, complemented, Hall
25	C₁₉	C₇×D₈₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	—	87	1	no	Hall
27	C₇	C₁₉×D₈₇	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	29	1	no	Hall
29	C₃	C₇×C₁₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	87	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₈₇
commutator, cosocle, hypocenter	C₃×C₂₉	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉×C₂₉	C₂
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₉×C₂₉	C₂	semidirect
3. C₇×C₁₉×C₂₉	D₃	semidirect
4. C₁₉×D₈₇	C₇	direct (N × H)
5. C₃×C₁₉×C₂₉	C₂×C₇	semidirect
6. C₇×D₈₇	C₁₉	direct (N × H)
9. C₃×C₇×C₂₉	C₂×C₁₉	semidirect
10. C₁₉×C₂₉	D₃×C₇	semidirect
12. C₃×C₇×C₁₉	D₂₉	semidirect
14. C₇×C₂₉	D₃×C₁₉	semidirect
15. D₈₇	C₇×C₁₉	direct (N × H)
16. C₇×C₁₉	D₈₇	direct (N × H)
18. C₃×C₂₉	C₂×C₇×C₁₉	semidirect
20. C₃×C₁₉	C₇×D₂₉	semidirect
23. C₂₉	D₃×C₇×C₁₉	semidirect
24. C₃×C₇	C₁₉×D₂₉	semidirect
25. C₁₉	C₇×D₈₇	direct (N × H)
27. C₇	C₁₉×D₈₇	direct (N × H)
29. C₃	C₇×C₁₉×D₂₉	semidirect

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
C₇×C₁₉×D₂₉	3
C₁₉×D₈₇	7
C₇×D₈₇	19
D₃×C₇×C₁₉	29

Subgroups — C7×C19×D87 #37529007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₉×D₈₇ #37529007