Subgroups — C₂×C₇×C₁₃⋊C₃×C₅₉ #44567248

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, direct product factor, Hall
2	C₂×C₇×C₁₃×C₅₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃⋊C₃×C₅₉	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, direct product factor, Hall
7	C₂×C₁₃×C₅₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×C₅₉	—	13	1	no	Hall
9	C₂×C₇×C₅₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₁₃×C₅₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₁₃⋊C₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₅₉	C₂×C₁₃⋊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, direct product factor, Hall
15	C₂×C₇×C₁₃	C₃×C₅₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅₉	—	13	1	no	Hall
17	C₂×C₅₉	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₃	C₂×C₃×C₅₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₃⋊C₃	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
20	C₅₉	C₂×C₇×C₁₃⋊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, direct product factor, Hall
23	C₂×C₁₃	C₃×C₇×C₅₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇	—	13	1	no	Hall
25	C₂×C₇	C₁₃⋊C₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
26	C₁₃	C₂×C₃×C₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₂×C₁₃⋊C₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	13	1	no	Hall
29	C₃	—	13	1	no	Sylow
30	C₂	C₇×C₁₃⋊C₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃⋊C₃×C₅₉	C₂	direct (N × H)
2. C₂×C₇×C₁₃×C₅₉	C₃	semidirect
3. C₇×C₁₃×C₅₉	C₂×C₃	semidirect
4. C₂×C₁₃⋊C₃×C₅₉	C₇	direct (N × H)
6. C₁₃⋊C₃×C₅₉	C₂×C₇	direct (N × H)
7. C₂×C₁₃×C₅₉	C₃×C₇	semidirect
9. C₂×C₇×C₅₉	C₁₃⋊C₃	direct (N × H)
10. C₁₃×C₅₉	C₂×C₃×C₇	semidirect
11. C₂×C₇×C₁₃⋊C₃	C₅₉	direct (N × H)
12. C₇×C₅₉	C₂×C₁₃⋊C₃	direct (N × H)
14. C₇×C₁₃⋊C₃	C₂×C₅₉	direct (N × H)
15. C₂×C₇×C₁₃	C₃×C₅₉	semidirect
17. C₂×C₅₉	C₇×C₁₃⋊C₃	direct (N × H)
18. C₇×C₁₃	C₂×C₃×C₅₉	semidirect
19. C₂×C₁₃⋊C₃	C₇×C₅₉	direct (N × H)
20. C₅₉	C₂×C₇×C₁₃⋊C₃	direct (N × H)
22. C₁₃⋊C₃	C₂×C₇×C₅₉	direct (N × H)
23. C₂×C₁₃	C₃×C₇×C₅₉	semidirect
25. C₂×C₇	C₁₃⋊C₃×C₅₉	direct (N × H)
26. C₁₃	C₂×C₃×C₇×C₅₉	semidirect
27. C₇	C₂×C₁₃⋊C₃×C₅₉	direct (N × H)
30. C₂	C₇×C₁₃⋊C₃×C₅₉	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
C₂×C₇×C₁₃×C₅₉	3
C₂×C₁₃⋊C₃×C₅₉	7
C₂×C₃×C₇×C₅₉	13
C₂×C₇×C₁₃⋊C₃	59

Subgroups — C2×C7×C13⋊C3×C59 #44567248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₃⋊C₃×C₅₉ #44567248