Subgroups — C₂×C₃₇×C₅⋊(C₇⋊D₇) #49136463

Order 36260.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₅⋊(C₇⋊D₇)	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×C₃₇×C₇⋊D₇	—	5	1	no	maximal, Hall
5	C₂×C₃₇×D₃₅	—	7	8	no	maximal
6	C₃₇×C₇⋊D₇	—	5	2	no	—
7	C₂×C₇²×C₃₇	D₅	1	1	yes	characteristic, complemented
8	C₃₇×D₃₅	—	7	16	no	—
9	C₂×C₅×C₇×C₃₇	D₇	1	8	yes	complemented
10	C₇²×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇×C₃₇	C₂×D₇	1	8	yes	complemented
12	C₂×D₇×C₃₇	—	35	8	no	—
13	C₂×C₅⋊(C₇⋊D₇)	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×D₅×C₃₇	—	49	1	no	Hall
15	C₂×C₇×C₃₇	D₃₅	1	8	yes	complemented
16	D₇×C₃₇	—	35	16	no	—
17	C₂×C₅×C₇²	C₂×C₃₇	1	1	yes	characteristic, complemented
18	C₅⋊(C₇⋊D₇)	C₂×C₃₇	1	2	yes	direct product factor
19	C₂×C₅×C₃₇	C₇⋊D₇	1	1	yes	characteristic, complemented
20	D₅×C₃₇	—	49	2	no	—
21	C₇×C₃₇	C₂×D₃₅	1	8	yes	complemented
22	C₅×C₇²	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇⋊D₇	—	5	1	no	Hall
24	C₅×C₃₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₃₇	—	245	1	no	Hall
26	C₂×D₃₅	—	7	8	no	—
27	C₂×C₇²	D₅×C₃₇	1	1	yes	characteristic, complemented
28	C₇⋊D₇	—	5	2	no	—
29	C₂×C₃₇	—	245	2	no	—
30	C₂×C₃₇	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
31	C₂×C₅×C₇	D₇×C₃₇	1	8	yes	complemented
32	D₃₅	—	7	16	no	—
33	C₇²	C₂×D₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
34	C₃₇	C₂×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
35	C₅×C₇	C₂×D₇×C₃₇	1	8	yes	complemented
36	C₂×D₇	—	35	8	no	—
37	C₂×D₅	—	49	1	no	Hall
38	C₂×C₇	C₃₇×D₃₅	1	8	yes	complemented
39	D₇	—	35	16	no	—
40	C₂×C₅	C₃₇×C₇⋊D₇	1	1	yes	characteristic, complemented
41	D₅	—	49	2	no	—
42	C₇	C₂×C₃₇×D₃₅	1	8	yes	complemented
43	C₅	C₂×C₃₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	245	1	no	Sylow
45	C₂	—	245	2	no	—
46	C₂	C₃₇×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₃₇×C₅⋊(C₇⋊D₇)	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₃₇	C₂	semidirect
3. C₅×C₇²×C₃₇	C₂²	semidirect
7. C₂×C₇²×C₃₇	D₅	semidirect
9. C₂×C₅×C₇×C₃₇	D₇	semidirect
10. C₇²×C₃₇	C₂×D₅	semidirect
11. C₅×C₇×C₃₇	C₂×D₇	semidirect
13. C₂×C₅⋊(C₇⋊D₇)	C₃₇	direct (N × H)
15. C₂×C₇×C₃₇	D₃₅	semidirect
17. C₂×C₅×C₇²	C₂×C₃₇	semidirect
18. C₅⋊(C₇⋊D₇)	C₂×C₃₇	direct (N × H)
19. C₂×C₅×C₃₇	C₇⋊D₇	semidirect
21. C₇×C₃₇	C₂×D₃₅	semidirect
22. C₅×C₇²	C₂²×C₃₇	semidirect
24. C₅×C₃₇	C₂×C₇⋊D₇	semidirect
27. C₂×C₇²	D₅×C₃₇	semidirect
30. C₂×C₃₇	C₅⋊(C₇⋊D₇)	direct (N × H)
31. C₂×C₅×C₇	D₇×C₃₇	semidirect
33. C₇²	C₂×D₅×C₃₇	semidirect
34. C₃₇	C₂×C₅⋊(C₇⋊D₇)	direct (N × H)
35. C₅×C₇	C₂×D₇×C₃₇	semidirect
38. C₂×C₇	C₃₇×D₃₅	semidirect
40. C₂×C₅	C₃₇×C₇⋊D₇	semidirect
42. C₇	C₂×C₃₇×D₃₅	semidirect
43. C₅	C₂×C₃₇×C₇⋊D₇	semidirect
46. C₂	C₃₇×C₅⋊(C₇⋊D₇)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×C₅⋊(C₇⋊D₇)	2
C₂×C₅×C₇²×C₃₇	2
C₂×C₃₇×C₇⋊D₇	5
C₂×C₃₇×D₃₅	7
C₂×C₅⋊(C₇⋊D₇)	37

Subgroups — C2×C37×C5⋊(C7⋊D7) #49136463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×C₅⋊(C₇⋊D₇) #49136463