Subgroups — D₇×C₃₁×D₃₉ #46799592

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₂₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃₁×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₃×C₃₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₉₁	—	3	1	no	—
7	C₁₃×D₇×C₃₁	D₃	1	1	yes	characteristic, complemented
8	C₇×D₁₃×C₃₁	—	3	1	no	—
9	C₂×C₃₁×D₃₉	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×D₇×C₃₁	—	13	1	no	maximal, Hall
12	C₃₁×D₃₉	—	7	1	no	—
13	C₃₁×D₃₉	D₇	1	1	yes	characteristic, direct product factor
14	C₂×C₃×C₁₃×C₃₁	—	7	1	no	—
15	C₂×D₁₃×C₃₁	—	21	1	no	Hall
16	C₃₁×D₂₁	—	13	1	no	—
17	D₃×C₇×C₃₁	—	13	1	no	—
18	C₃×D₇×C₃₁	D₁₃	1	1	yes	characteristic, complemented
19	C₃×C₁₃×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₇×D₃₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×D₇×C₃₁	—	39	1	no	Hall
22	C₂×C₁₃×C₃₁	—	7	1	no	—
23	D₁₃×C₃₁	—	3	1	no	—
24	D₁₃×C₃₁	—	21	1	no	—
25	C₃×C₇×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	D₂₇₃	C₂×C₃₁	1	1	yes	characteristic, complemented
27	C₇×D₃₉	C₂×C₃₁	1	1	yes	characteristic, complemented
28	C₃×C₁₃×D₇	C₂×C₃₁	1	1	yes	characteristic, complemented
29	C₂×C₇×C₃₁	—	39	1	no	—
30	D₇×C₃₁	—	39	1	no	—
31	D₇×C₃₁	D₃₉	1	1	yes	characteristic, direct product factor
32	C₁₃×C₃₁	D₃×D₇	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃×C₃₁	—	91	1	no	Hall
34	D₇×D₁₃	—	3	1	no	Hall
35	C₃×C₇×C₁₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
36	C₇×C₃₁	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₃₁	—	7	1	no	—
38	D₃×C₃₁	—	13	1	no	—
39	D₃×C₃₁	—	91	1	no	—
40	D₉₁	—	3	1	no	—
41	C₇×D₁₃	—	3	1	no	—
42	C₁₃×D₇	D₃×C₃₁	1	1	yes	characteristic, complemented
43	C₂×D₃₉	—	7	1	no	Hall
44	C₂²×C₃₁	—	273	1	no	Hall
45	C₃×C₃₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
46	C₇×C₁₃	C₂×D₃×C₃₁	1	1	yes	characteristic, complemented, Hall
47	D₃×D₇	—	13	1	no	Hall
48	C₂×C₃×C₁₃	—	7	1	no	—
49	D₃₉	—	7	1	no	—
50	D₃₉	D₇×C₃₁	1	1	yes	characteristic, direct product factor
51	C₂×C₃₁	—	7	1	no	—
52	C₂×C₃₁	—	273	1	no	—
53	C₂×C₃₁	—	39	1	no	—
54	C₂×D₁₃	—	21	1	no	Hall
55	D₂₁	—	13	1	no	—
56	C₃×D₇	D₁₃×C₃₁	1	1	yes	characteristic, complemented
57	D₃×C₇	—	13	1	no	—
58	C₃×C₁₃	C₂×D₇×C₃₁	1	1	yes	characteristic, complemented, Hall
59	C₃₁	D₇×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×D₇	—	39	1	no	Hall
61	C₂×C₁₃	—	7	1	no	—
62	D₁₃	—	3	1	no	—
63	D₁₃	—	21	1	no	—
64	C₃×C₇	C₂×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	39	1	no	—
66	D₇	—	39	1	no	—
67	D₇	C₃₁×D₃₉	1	1	yes	characteristic, direct product factor
68	C₁₃	D₃×D₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	91	1	no	Hall
70	C₇	C₂×C₃₁×D₃₉	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	7	1	no	—
72	D₃	—	13	1	no	—
73	D₃	—	91	1	no	—
74	C₂²	—	273	1	no	Sylow
75	C₃	D₇×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	7	1	no	—
77	C₂	—	273	1	no	—
78	C₂	—	39	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₇×D₃₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₃₁	C₂²
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₂₇₃	C₂	semidirect
2. C₇×C₃₁×D₃₉	C₂	semidirect
3. C₃×C₁₃×D₇×C₃₁	C₂	semidirect
5. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
7. C₁₃×D₇×C₃₁	D₃	semidirect
10. C₇×C₁₃×C₃₁	C₂×D₃	semidirect
13. C₃₁×D₃₉	D₇	direct (N × H)
18. C₃×D₇×C₃₁	D₁₃	semidirect
19. C₃×C₁₃×C₃₁	C₂×D₇	semidirect
20. D₇×D₃₉	C₃₁	direct (N × H)
25. C₃×C₇×C₃₁	C₂×D₁₃	semidirect
26. D₂₇₃	C₂×C₃₁	semidirect
27. C₇×D₃₉	C₂×C₃₁	semidirect
28. C₃×C₁₃×D₇	C₂×C₃₁	semidirect
31. D₇×C₃₁	D₃₉	direct (N × H)
32. C₁₃×C₃₁	D₃×D₇	semidirect
35. C₃×C₇×C₁₃	C₂²×C₃₁	semidirect
36. C₇×C₃₁	C₂×D₃₉	semidirect
42. C₁₃×D₇	D₃×C₃₁	semidirect
45. C₃×C₃₁	D₇×D₁₃	semidirect
46. C₇×C₁₃	C₂×D₃×C₃₁	semidirect
50. D₃₉	D₇×C₃₁	direct (N × H)
56. C₃×D₇	D₁₃×C₃₁	semidirect
58. C₃×C₁₃	C₂×D₇×C₃₁	semidirect
59. C₃₁	D₇×D₃₉	direct (N × H)
64. C₃×C₇	C₂×D₁₃×C₃₁	semidirect
67. D₇	C₃₁×D₃₉	direct (N × H)
68. C₁₃	D₃×D₇×C₃₁	semidirect
70. C₇	C₂×C₃₁×D₃₉	semidirect
75. C₃	D₇×D₁₃×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×D₂₇₃	2
C₇×C₃₁×D₃₉	2
C₃×C₁₃×D₇×C₃₁	2
D₇×D₁₃×C₃₁	3
C₂×C₃₁×D₃₉	7
D₃×D₇×C₃₁	13
D₇×D₃₉	31

Subgroups — D7×C31×D39 #46799592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₃₁×D₃₉ #46799592