Subgroups — C₂×C₇×C₃₁×D₃₉ #46799640

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×D₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₁₃×C₃₁	—	3	1	no	maximal, Hall
4	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₁₃×C₃₁	—	3	2	no	—
6	C₂×C₇×C₁₃×C₃₁	D₃	1	1	yes	characteristic, complemented
7	C₂×C₃₁×D₃₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×D₃×C₇×C₃₁	—	13	1	no	maximal, Hall
10	C₃₁×D₃₉	C₂×C₇	1	2	yes	direct product factor
11	C₂×C₃×C₁₃×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented
12	C₂×D₁₃×C₃₁	—	3	1	no	Hall
13	C₂×C₃×C₇×C₃₁	D₁₃	1	1	yes	characteristic, complemented
14	D₃×C₇×C₃₁	—	13	2	no	—
15	C₃×C₁₃×C₃₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×D₃₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₇×C₃₁	—	39	1	no	Hall
18	C₂×C₁₃×C₃₁	D₃×C₇	1	1	yes	characteristic, complemented
19	D₁₃×C₃₁	—	3	2	no	—
20	C₃×C₇×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×C₁₃	C₂×C₃₁	1	1	yes	characteristic, complemented
22	C₇×D₃₉	C₂×C₃₁	1	2	yes	direct product factor
23	C₂×C₇×C₃₁	—	39	2	no	—
24	C₂×C₇×C₃₁	D₃₉	1	1	yes	characteristic, direct product factor
25	C₁₃×C₃₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃×C₃₁	—	13	1	no	Hall
27	C₂×C₇×D₁₃	—	3	1	no	Hall
28	C₃×C₇×C₁₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
29	C₇×C₃₁	C₂×D₃₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₃₁	C₇×D₁₃	1	1	yes	characteristic, complemented
31	D₃×C₃₁	—	13	2	no	—
32	C₂×C₇×C₁₃	D₃×C₃₁	1	1	yes	characteristic, complemented
33	C₇×D₁₃	—	3	2	no	—
34	C₂×D₃₉	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
35	C₂²×C₃₁	—	39	1	no	Hall
36	C₃×C₃₁	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
37	C₇×C₁₃	C₂×D₃×C₃₁	1	1	yes	characteristic, complemented, Hall
38	C₂×D₃×C₇	—	13	1	no	Hall
39	C₂×C₃×C₁₃	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented
40	D₃₉	C₂×C₇×C₃₁	1	2	yes	direct product factor
41	C₂×C₃₁	—	39	2	no	—
42	C₂×C₃₁	C₇×D₃₉	1	1	yes	characteristic, direct product factor
43	C₂×D₁₃	—	3	1	no	Hall
44	C₂×C₃×C₇	D₁₃×C₃₁	1	1	yes	characteristic, complemented
45	D₃×C₇	—	13	2	no	—
46	C₃×C₁₃	C₂²×C₇×C₃₁	1	1	yes	characteristic, complemented, Hall
47	C₃₁	C₂×C₇×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₇	—	39	1	no	Hall
49	C₂×C₁₃	D₃×C₇×C₃₁	1	1	yes	characteristic, complemented
50	D₁₃	—	3	2	no	—
51	C₃×C₇	C₂×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Hall
52	C₂×C₇	—	39	2	no	—
53	C₂×C₇	C₃₁×D₃₉	1	1	yes	characteristic, direct product factor
54	C₁₃	C₂×D₃×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₃	—	13	1	no	Hall
56	C₇	C₂×C₃₁×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	C₇×D₁₃×C₃₁	1	1	yes	characteristic, complemented
58	D₃	—	13	2	no	—
59	C₂²	—	39	1	no	Sylow
60	C₃	C₂×C₇×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	39	2	no	—
62	C₂	C₇×C₃₁×D₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₃₁	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₃₁	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₁×D₃₉	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₃×C₃₁	C₂	semidirect
4. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
6. C₂×C₇×C₁₃×C₃₁	D₃	semidirect
7. C₂×C₃₁×D₃₉	C₇	direct (N × H)
8. C₇×C₁₃×C₃₁	C₂×D₃	semidirect
10. C₃₁×D₃₉	C₂×C₇	direct (N × H)
11. C₂×C₃×C₁₃×C₃₁	C₂×C₇	semidirect
13. C₂×C₃×C₇×C₃₁	D₁₃	semidirect
15. C₃×C₁₃×C₃₁	C₂²×C₇	semidirect
16. C₂×C₇×D₃₉	C₃₁	direct (N × H)
18. C₂×C₁₃×C₃₁	D₃×C₇	semidirect
20. C₃×C₇×C₃₁	C₂×D₁₃	semidirect
21. C₂×C₃×C₇×C₁₃	C₂×C₃₁	semidirect
22. C₇×D₃₉	C₂×C₃₁	direct (N × H)
24. C₂×C₇×C₃₁	D₃₉	direct (N × H)
25. C₁₃×C₃₁	C₂×D₃×C₇	semidirect
28. C₃×C₇×C₁₃	C₂²×C₃₁	semidirect
29. C₇×C₃₁	C₂×D₃₉	direct (N × H)
30. C₂×C₃×C₃₁	C₇×D₁₃	semidirect
32. C₂×C₇×C₁₃	D₃×C₃₁	semidirect
34. C₂×D₃₉	C₇×C₃₁	direct (N × H)
36. C₃×C₃₁	C₂×C₇×D₁₃	semidirect
37. C₇×C₁₃	C₂×D₃×C₃₁	semidirect
39. C₂×C₃×C₁₃	C₂×C₇×C₃₁	semidirect
40. D₃₉	C₂×C₇×C₃₁	direct (N × H)
42. C₂×C₃₁	C₇×D₃₉	direct (N × H)
44. C₂×C₃×C₇	D₁₃×C₃₁	semidirect
46. C₃×C₁₃	C₂²×C₇×C₃₁	semidirect
47. C₃₁	C₂×C₇×D₃₉	direct (N × H)
49. C₂×C₁₃	D₃×C₇×C₃₁	semidirect
51. C₃×C₇	C₂×D₁₃×C₃₁	semidirect
53. C₂×C₇	C₃₁×D₃₉	direct (N × H)
54. C₁₃	C₂×D₃×C₇×C₃₁	semidirect
56. C₇	C₂×C₃₁×D₃₉	direct (N × H)
57. C₂×C₃	C₇×D₁₃×C₃₁	semidirect
60. C₃	C₂×C₇×D₁₃×C₃₁	semidirect
62. C₂	C₇×C₃₁×D₃₉	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×C₃₁×D₃₉	2
C₂×C₃×C₇×C₁₃×C₃₁	2
C₂×C₇×D₁₃×C₃₁	3
C₂×C₃₁×D₃₉	7
C₂×D₃×C₇×C₃₁	13
C₂×C₇×D₃₉	31

Subgroups — C2×C7×C31×D39 #46799640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₃₁×D₃₉ #46799640