Subgroups — C₅×D₇²×C₃₇ #49136409

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, complemented
2	C₅×C₃₇×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₇²×C₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₇×C₃₇	—	7	2	no	maximal
6	C₃₇×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇×D₇×C₃₇	C₂×C₅	1	2	yes	complemented
8	C₅×D₇×C₃₇	—	7	2	no	—
9	C₅×D₇×C₃₇	—	14	3	no	—
10	C₅×D₇×C₃₇	D₇	1	2	yes	direct product factor
11	C₂×C₅×C₇×C₃₇	—	7	2	no	—
12	C₇²×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₅×C₇×C₃₇	—	2	3	no	—
14	C₅×C₇×C₃₇	C₂×D₇	1	2	yes	complemented
15	C₂×D₇×C₃₇	—	7	2	no	—
16	C₅×D₇²	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₅×C₃₇	—	49	1	no	Hall
18	C₂×C₇×C₃₇	—	7	2	no	—
19	D₇×C₃₇	—	7	2	no	—
20	D₇×C₃₇	—	14	3	no	—
21	D₇×C₃₇	C₅×D₇	1	2	yes	direct product factor
22	C₅×C₇⋊D₇	C₂×C₃₇	1	1	yes	characteristic, complemented
23	C₅×C₇×D₇	C₂×C₃₇	1	2	yes	complemented
24	C₂×C₅×C₃₇	—	7	2	no	—
25	C₂×C₅×C₃₇	—	49	1	no	—
26	C₇×C₃₇	—	2	3	no	—
27	C₇×C₃₇	C₂×C₅×D₇	1	2	yes	complemented
28	C₅×C₇²	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
29	D₇²	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
30	C₅×C₃₇	D₇²	1	1	yes	characteristic, direct product factor, Hall
31	C₂²×C₃₇	—	49	1	no	Hall
32	C₂×C₅×D₇	—	7	2	no	—
33	C₇⋊D₇	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented
34	C₇×D₇	C₂×C₅×C₃₇	1	2	yes	complemented
35	C₂×C₃₇	—	7	2	no	—
36	C₂×C₃₇	—	49	1	no	—
37	C₂×C₅×C₇	—	7	2	no	—
38	C₅×D₇	—	7	2	no	—
39	C₅×D₇	—	14	3	no	—
40	C₅×D₇	D₇×C₃₇	1	2	yes	direct product factor
41	C₇²	C₂²×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
42	C₃₇	C₅×D₇²	1	1	yes	characteristic, direct product factor, Sylow
43	C₅×C₇	—	2	3	no	—
44	C₅×C₇	C₂×D₇×C₃₇	1	2	yes	complemented
45	C₂×D₇	—	7	2	no	—
46	C₂²×C₅	—	49	1	no	Hall
47	C₂×C₇	—	7	2	no	—
48	D₇	—	7	2	no	—
49	D₇	—	14	3	no	—
50	D₇	C₅×D₇×C₃₇	1	2	yes	direct product factor
51	C₂×C₅	—	7	2	no	—
52	C₂×C₅	—	49	1	no	—
53	C₇	—	2	3	no	—
54	C₇	C₂×C₅×D₇×C₃₇	1	2	yes	complemented
55	C₅	D₇²×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²	—	49	1	no	Sylow
57	C₂	—	7	2	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₃₇	D₇²
commutator, cosocle, hypocenter	C₇²	C₂²×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₃₇	C₂²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₇×C₃₇	C₂	semidirect
2. C₅×C₃₇×C₇⋊D₇	C₂	semidirect
3. C₅×C₇²×C₃₇	C₂²	semidirect
4. D₇²×C₃₇	C₅	direct (N × H)
6. C₃₇×C₇⋊D₇	C₂×C₅	semidirect
7. C₇×D₇×C₃₇	C₂×C₅	semidirect
10. C₅×D₇×C₃₇	D₇	direct (N × H)
12. C₇²×C₃₇	C₂²×C₅	semidirect
14. C₅×C₇×C₃₇	C₂×D₇	semidirect
16. C₅×D₇²	C₃₇	direct (N × H)
21. D₇×C₃₇	C₅×D₇	direct (N × H)
22. C₅×C₇⋊D₇	C₂×C₃₇	semidirect
23. C₅×C₇×D₇	C₂×C₃₇	semidirect
27. C₇×C₃₇	C₂×C₅×D₇	semidirect
28. C₅×C₇²	C₂²×C₃₇	semidirect
29. D₇²	C₅×C₃₇	direct (N × H)
30. C₅×C₃₇	D₇²	direct (N × H)
33. C₇⋊D₇	C₂×C₅×C₃₇	semidirect
34. C₇×D₇	C₂×C₅×C₃₇	semidirect
40. C₅×D₇	D₇×C₃₇	direct (N × H)
41. C₇²	C₂²×C₅×C₃₇	semidirect
42. C₃₇	C₅×D₇²	direct (N × H)
44. C₅×C₇	C₂×D₇×C₃₇	semidirect
50. D₇	C₅×D₇×C₃₇	direct (N × H)
54. C₇	C₂×C₅×D₇×C₃₇	semidirect
55. C₅	D₇²×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
C₅×C₃₇×C₇⋊D₇	2
D₇²×C₃₇	5
C₂×C₅×D₇×C₃₇	7
C₅×D₇²	37

Subgroups — C5×D72×C37 #49136409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇²×C₃₇ #49136409