Subgroups — C₂×C₅×C₇×D₇×C₃₇ #49136455

Order 36260.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₇×C₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₇×C₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₇×C₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₅×C₇×C₃₇	—	7	1	no	maximal
7	C₇×D₇×C₃₇	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₇²×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₇×C₃₇	C₂×C₇	1	2	yes	direct product factor
10	C₂×C₅×C₇×C₃₇	—	2	3	no	—
11	C₂×C₅×C₇×C₃₇	—	7	2	no	—
12	C₂×C₅×C₇×C₃₇	D₇	1	1	yes	characteristic, direct product factor
13	C₂×C₅×C₇×C₃₇	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇²×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×C₃₇	—	2	3	no	—
16	C₅×C₇×C₃₇	C₂×D₇	1	1	yes	characteristic, direct product factor
17	C₅×C₇×C₃₇	C₂²×C₇	1	1	yes	characteristic, complemented
18	C₂²×C₇×C₃₇	—	7	1	no	—
19	C₂×D₇×C₃₇	C₅×C₇	1	1	yes	characteristic, direct product factor
20	C₂×C₅×C₇×D₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×C₃₇	—	7	1	no	Hall
22	C₂×C₇×C₃₇	—	2	3	no	—
23	C₂×C₇×C₃₇	—	7	2	no	—
24	C₂×C₇×C₃₇	C₅×D₇	1	1	yes	characteristic, direct product factor
25	C₂×C₇×C₃₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented
26	D₇×C₃₇	C₂×C₅×C₇	1	2	yes	direct product factor
27	C₂×C₅×C₇²	C₂×C₃₇	1	1	yes	characteristic, complemented
28	C₅×C₇×D₇	C₂×C₃₇	1	2	yes	direct product factor
29	C₂×C₅×C₃₇	—	7	2	no	—
30	C₂×C₅×C₃₇	C₇×D₇	1	1	yes	characteristic, direct product factor
31	C₇×C₃₇	—	2	3	no	—
32	C₇×C₃₇	C₂×C₅×D₇	1	1	yes	characteristic, direct product factor
33	C₇×C₃₇	C₂²×C₅×C₇	1	1	yes	characteristic, complemented
34	C₅×C₇²	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₇×D₇	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
36	C₅×C₃₇	C₂×C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
37	C₂²×C₃₇	—	7	1	no	Hall
38	C₂²×C₅×C₇	—	7	1	no	—
39	C₂×C₅×D₇	C₇×C₃₇	1	1	yes	characteristic, direct product factor
40	C₂×C₇²	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented
41	C₇×D₇	C₂×C₅×C₃₇	1	2	yes	direct product factor
42	C₂×C₃₇	—	7	2	no	—
43	C₂×C₃₇	C₅×C₇×D₇	1	1	yes	characteristic, direct product factor
44	C₂×C₅×C₇	—	2	3	no	—
45	C₂×C₅×C₇	—	7	2	no	—
46	C₂×C₅×C₇	D₇×C₃₇	1	1	yes	characteristic, direct product factor
47	C₂×C₅×C₇	C₂×C₇×C₃₇	1	1	yes	characteristic, complemented
48	C₅×D₇	C₂×C₇×C₃₇	1	2	yes	direct product factor
49	C₇²	C₂²×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
50	C₃₇	C₂×C₅×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
51	C₅×C₇	—	2	3	no	—
52	C₅×C₇	C₂×D₇×C₃₇	1	1	yes	characteristic, direct product factor
53	C₅×C₇	C₂²×C₇×C₃₇	1	1	yes	characteristic, complemented
54	C₂²×C₇	—	7	1	no	—
55	C₂×D₇	C₅×C₇×C₃₇	1	1	yes	characteristic, direct product factor
56	C₂²×C₅	—	7	1	no	Hall
57	C₂×C₇	—	2	3	no	—
58	C₂×C₇	—	7	2	no	—
59	C₂×C₇	C₂×C₅×C₇×C₃₇	1	1	yes	characteristic, complemented
60	C₂×C₇	C₅×D₇×C₃₇	1	1	yes	characteristic, direct product factor
61	D₇	C₂×C₅×C₇×C₃₇	1	2	yes	direct product factor
62	C₂×C₅	—	7	2	no	—
63	C₂×C₅	C₇×D₇×C₃₇	1	1	yes	characteristic, direct product factor
64	C₇	—	2	3	no	—
65	C₇	C₂²×C₅×C₇×C₃₇	1	1	yes	characteristic, complemented
66	C₇	C₂×C₅×D₇×C₃₇	1	1	yes	characteristic, direct product factor
67	C₅	C₂×C₇×D₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
68	C₂²	—	7	1	no	Sylow
69	C₂	—	7	2	no	—
70	C₂	C₅×C₇×D₇×C₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₃₇	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₅×C₇×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₃₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₅×C₇×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₇×C₃₇	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₃₇	C₂	semidirect
3. C₅×C₇²×C₃₇	C₂²	semidirect
4. C₂×C₇×D₇×C₃₇	C₅	direct (N × H)
5. C₂×C₅×D₇×C₃₇	C₇	direct (N × H)
7. C₇×D₇×C₃₇	C₂×C₅	direct (N × H)
8. C₂×C₇²×C₃₇	C₂×C₅	semidirect
9. C₅×D₇×C₃₇	C₂×C₇	direct (N × H)
12. C₂×C₅×C₇×C₃₇	D₇	direct (N × H)
13. C₂×C₅×C₇×C₃₇	C₂×C₇	semidirect
14. C₇²×C₃₇	C₂²×C₅	semidirect
16. C₅×C₇×C₃₇	C₂×D₇	direct (N × H)
17. C₅×C₇×C₃₇	C₂²×C₇	semidirect
19. C₂×D₇×C₃₇	C₅×C₇	direct (N × H)
20. C₂×C₅×C₇×D₇	C₃₇	direct (N × H)
24. C₂×C₇×C₃₇	C₅×D₇	direct (N × H)
25. C₂×C₇×C₃₇	C₂×C₅×C₇	semidirect
26. D₇×C₃₇	C₂×C₅×C₇	direct (N × H)
27. C₂×C₅×C₇²	C₂×C₃₇	semidirect
28. C₅×C₇×D₇	C₂×C₃₇	direct (N × H)
30. C₂×C₅×C₃₇	C₇×D₇	direct (N × H)
32. C₇×C₃₇	C₂×C₅×D₇	direct (N × H)
33. C₇×C₃₇	C₂²×C₅×C₇	semidirect
34. C₅×C₇²	C₂²×C₃₇	semidirect
35. C₂×C₇×D₇	C₅×C₃₇	direct (N × H)
36. C₅×C₃₇	C₂×C₇×D₇	direct (N × H)
39. C₂×C₅×D₇	C₇×C₃₇	direct (N × H)
40. C₂×C₇²	C₂×C₅×C₃₇	semidirect
41. C₇×D₇	C₂×C₅×C₃₇	direct (N × H)
43. C₂×C₃₇	C₅×C₇×D₇	direct (N × H)
46. C₂×C₅×C₇	D₇×C₃₇	direct (N × H)
47. C₂×C₅×C₇	C₂×C₇×C₃₇	semidirect
48. C₅×D₇	C₂×C₇×C₃₇	direct (N × H)
49. C₇²	C₂²×C₅×C₃₇	semidirect
50. C₃₇	C₂×C₅×C₇×D₇	direct (N × H)
52. C₅×C₇	C₂×D₇×C₃₇	direct (N × H)
53. C₅×C₇	C₂²×C₇×C₃₇	semidirect
55. C₂×D₇	C₅×C₇×C₃₇	direct (N × H)
59. C₂×C₇	C₂×C₅×C₇×C₃₇	semidirect
60. C₂×C₇	C₅×D₇×C₃₇	direct (N × H)
61. D₇	C₂×C₅×C₇×C₃₇	direct (N × H)
63. C₂×C₅	C₇×D₇×C₃₇	direct (N × H)
65. C₇	C₂²×C₅×C₇×C₃₇	semidirect
66. C₇	C₂×C₅×D₇×C₃₇	direct (N × H)
67. C₅	C₂×C₇×D₇×C₃₇	direct (N × H)
70. C₂	C₅×C₇×D₇×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×D₇×C₃₇	2
C₂×C₅×C₇²×C₃₇	2
C₂×C₇×D₇×C₃₇	5
C₂×C₅×D₇×C₃₇	7
C₂²×C₅×C₇×C₃₇	7
C₂×C₅×C₇×D₇	37

Subgroups — C2×C5×C7×D7×C37 #49136455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×D₇×C₃₇ #49136455