Subgroups — C₂×C₇²×D₁₈₅ #49136460

Order 36260.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₈₅	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×C₇²×D₃₇	—	5	1	no	maximal, Hall
5	C₂×C₇×D₁₈₅	C₇	1	8	yes	maximal, direct product factor
6	C₇²×D₃₇	—	5	2	no	—
7	C₂×C₇²×C₃₇	D₅	1	1	yes	characteristic, complemented
8	C₇×D₁₈₅	C₂×C₇	1	16	yes	direct product factor
9	C₂×C₅×C₇×C₃₇	C₂×C₇	1	8	yes	complemented
10	C₇²×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇×C₃₇	C₂²×C₇	1	8	yes	complemented
12	C₂×C₇×D₃₇	—	5	8	no	—
13	C₂×C₇²×D₅	—	37	1	no	maximal, Hall
14	C₂×D₁₈₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₇×C₃₇	C₇×D₅	1	8	yes	complemented
16	C₇×D₃₇	—	5	16	no	—
17	C₂×C₅×C₇²	D₃₇	1	1	yes	characteristic, complemented
18	C₇²×D₅	—	37	2	no	—
19	C₂×C₅×C₃₇	C₂×C₇²	1	1	yes	characteristic, complemented
20	D₁₈₅	C₂×C₇²	1	2	yes	direct product factor
21	C₇×C₃₇	C₂×C₇×D₅	1	8	yes	complemented
22	C₅×C₇²	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₇²	—	185	1	no	Hall
24	C₅×C₃₇	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃₇	—	5	1	no	Hall
26	C₂×C₇×D₅	—	37	8	no	—
27	C₂×C₇²	—	185	2	no	—
28	C₂×C₇²	D₁₈₅	1	1	yes	characteristic, direct product factor
29	C₂×C₃₇	C₇²×D₅	1	1	yes	characteristic, complemented
30	D₃₇	—	5	2	no	—
31	C₂×C₅×C₇	C₇×D₃₇	1	8	yes	complemented
32	C₇×D₅	—	37	16	no	—
33	C₇²	C₂×D₁₈₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₃₇	C₂×C₇²×D₅	1	1	yes	characteristic, complemented, Sylow
35	C₅×C₇	C₂×C₇×D₃₇	1	8	yes	complemented
36	C₂²×C₇	—	185	8	no	—
37	C₂×D₅	—	37	1	no	Hall
38	C₂×C₇	—	185	16	no	—
39	C₂×C₇	C₇×D₁₈₅	1	8	yes	direct product factor
40	C₂×C₅	C₇²×D₃₇	1	1	yes	characteristic, complemented
41	D₅	—	37	2	no	—
42	C₇	C₂×C₇×D₁₈₅	1	8	yes	direct product factor
43	C₅	C₂×C₇²×D₃₇	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	185	1	no	Sylow
45	C₂	—	185	2	no	—
46	C₂	C₇²×D₁₈₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₁₈₅
commutator, cosocle, hypocenter	C₅×C₃₇	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₃₇	C₂
LCS	G ▷ C₅×C₃₇
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×D₁₈₅	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₃₇	C₂	semidirect
3. C₅×C₇²×C₃₇	C₂²	semidirect
5. C₂×C₇×D₁₈₅	C₇	direct (N × H)
7. C₂×C₇²×C₃₇	D₅	semidirect
8. C₇×D₁₈₅	C₂×C₇	direct (N × H)
9. C₂×C₅×C₇×C₃₇	C₂×C₇	semidirect
10. C₇²×C₃₇	C₂×D₅	semidirect
11. C₅×C₇×C₃₇	C₂²×C₇	semidirect
14. C₂×D₁₈₅	C₇²	direct (N × H)
15. C₂×C₇×C₃₇	C₇×D₅	semidirect
17. C₂×C₅×C₇²	D₃₇	semidirect
19. C₂×C₅×C₃₇	C₂×C₇²	semidirect
20. D₁₈₅	C₂×C₇²	direct (N × H)
21. C₇×C₃₇	C₂×C₇×D₅	semidirect
22. C₅×C₇²	C₂×D₃₇	semidirect
24. C₅×C₃₇	C₂²×C₇²	semidirect
28. C₂×C₇²	D₁₈₅	direct (N × H)
29. C₂×C₃₇	C₇²×D₅	semidirect
31. C₂×C₅×C₇	C₇×D₃₇	semidirect
33. C₇²	C₂×D₁₈₅	direct (N × H)
34. C₃₇	C₂×C₇²×D₅	semidirect
35. C₅×C₇	C₂×C₇×D₃₇	semidirect
39. C₂×C₇	C₇×D₁₈₅	direct (N × H)
40. C₂×C₅	C₇²×D₃₇	semidirect
42. C₇	C₂×C₇×D₁₈₅	direct (N × H)
43. C₅	C₂×C₇²×D₃₇	semidirect
46. C₂	C₇²×D₁₈₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×D₁₈₅	2
C₂×C₅×C₇²×C₃₇	2
C₂×C₇²×D₃₇	5
C₂×C₇×D₁₈₅	7
C₂×C₇²×D₅	37

Subgroups — C2×C72×D185 #49136460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×D₁₈₅ #49136460