Subgroups — C₂×C₃×C₇×C₁₃×C₅₉ #44567247

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, direct product factor, Hall
2	C₂×C₇×C₁₃×C₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₅₉	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃×C₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₇×C₅₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₅₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₃×C₅₉	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₅₉	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₇×C₅₉	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₁₃×C₅₉	C₂×C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₁₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₅₉	C₂×C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₅₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇×C₁₃	C₂×C₅₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₇×C₁₃	C₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅₉	C₂×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅₉	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₃	C₂×C₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₁₃	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
20	C₅₉	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₃×C₇	C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₃	C₂×C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₃	C₃×C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇	C₂×C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	C₃×C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
26	C₁₃	C₂×C₃×C₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₃×C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	C₇×C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
29	C₃	C₂×C₇×C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₇×C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

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

Subgroups — C2×C3×C7×C13×C59 #44567247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₁₃×C₅₉ #44567247