Subgroups — C₇×C₅₉×D₁₃⋊C₃ #44567271

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₇×C₅₉	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₇×C₅₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₅₉	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₇×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃⋊C₃×C₅₉	C₂	semidirect
2. C₇×D₁₃×C₅₉	C₃	semidirect
3. C₇×C₁₃×C₅₉	C₂×C₃	semidirect
4. C₅₉×D₁₃⋊C₃	C₇	direct (N × H)
6. C₁₃⋊C₃×C₅₉	C₂×C₇	semidirect
7. D₁₃×C₅₉	C₃×C₇	semidirect
10. C₁₃×C₅₉	C₂×C₃×C₇	semidirect
11. C₇×D₁₃⋊C₃	C₅₉	direct (N × H)
12. C₇×C₅₉	D₁₃⋊C₃	direct (N × H)
14. C₇×C₁₃⋊C₃	C₂×C₅₉	semidirect
15. C₇×D₁₃	C₃×C₅₉	semidirect
18. C₇×C₁₃	C₂×C₃×C₅₉	semidirect
19. D₁₃⋊C₃	C₇×C₅₉	direct (N × H)
20. C₅₉	C₇×D₁₃⋊C₃	direct (N × H)
22. C₁₃⋊C₃	C₂×C₇×C₅₉	semidirect
23. D₁₃	C₃×C₇×C₅₉	semidirect
26. C₁₃	C₂×C₃×C₇×C₅₉	semidirect
27. C₇	C₅₉×D₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₃⋊C₃×C₅₉	2
C₇×D₁₃×C₅₉	3
C₅₉×D₁₃⋊C₃	7
C₂×C₃×C₇×C₅₉	13
C₇×D₁₃⋊C₃	59

Subgroups — C7×C59×D13⋊C3 #44567271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₅₉×D₁₃⋊C₃ #44567271