Subgroups — C₇×C₅₉×D₃₉ #44567261

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₃×C₅₉	—	3	1	no	maximal, Hall
3	C₇×C₁₃×C₅₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₅₉×D₃₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₇×C₅₉	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₁₃×C₅₉	—	3	1	no	Hall
8	C₃×C₇×C₅₉	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₅₉	—	39	1	no	Hall
10	C₁₃×C₅₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₉	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₅₉	D₃₉	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₅₉	—	13	1	no	Hall
14	C₃×C₇×C₁₃	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
15	C₇×D₁₃	—	3	1	no	Hall
16	C₃×C₅₉	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅₉	—	39	1	no	Hall
18	C₇×C₁₃	D₃×C₅₉	1	1	yes	characteristic, complemented, Hall
19	D₃₉	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
20	C₅₉	C₇×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
21	D₃×C₇	—	13	1	no	Hall
22	C₃×C₁₃	C₂×C₇×C₅₉	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	3	1	no	Hall
24	C₃×C₇	D₁₃×C₅₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇	—	39	1	no	Hall
26	C₁₃	D₃×C₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₅₉×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	13	1	no	Hall
29	C₃	C₇×D₁₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₅₉	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₇×C₅₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₅₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₇×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₅₉	C₂	semidirect
3. C₇×C₁₃×C₅₉	D₃	semidirect
4. C₅₉×D₃₉	C₇	direct (N × H)
6. C₃×C₁₃×C₅₉	C₂×C₇	semidirect
8. C₃×C₇×C₅₉	D₁₃	semidirect
10. C₁₃×C₅₉	D₃×C₇	semidirect
11. C₇×D₃₉	C₅₉	direct (N × H)
12. C₇×C₅₉	D₃₉	direct (N × H)
14. C₃×C₇×C₁₃	C₂×C₅₉	semidirect
16. C₃×C₅₉	C₇×D₁₃	semidirect
18. C₇×C₁₃	D₃×C₅₉	semidirect
19. D₃₉	C₇×C₅₉	direct (N × H)
20. C₅₉	C₇×D₃₉	direct (N × H)
22. C₃×C₁₃	C₂×C₇×C₅₉	semidirect
24. C₃×C₇	D₁₃×C₅₉	semidirect
26. C₁₃	D₃×C₇×C₅₉	semidirect
27. C₇	C₅₉×D₃₉	direct (N × H)
29. C₃	C₇×D₁₃×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₅₉	2
C₇×D₁₃×C₅₉	3
C₅₉×D₃₉	7
D₃×C₇×C₅₉	13
C₇×D₃₉	59

Subgroups — C7×C59×D39 #44567261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₅₉×D₃₉ #44567261