Subgroups — C₅×C₇×Dic₁₈₅ #39905973

Order 25900.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₇×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×Dic₁₈₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₇×Dic₃₇	—	5	1	no	maximal
5	C₅×Dic₁₈₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₃₇	—	2	2	no	—
7	C₂×C₅×C₇×C₃₇	D₅	1	1	yes	characteristic
8	C₂×C₅×C₇×C₃₇	C₂×C₅	1	1	yes	characteristic
9	C₂×C₅²×C₃₇	C₂×C₇	1	1	yes	characteristic
10	C₅×C₇×C₃₇	—	2	2	no	—
11	C₅×C₇×C₃₇	Dic₅	1	1	yes	characteristic, complemented
12	C₅×C₇×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented
13	C₇×Dic₃₇	—	5	1	no	Hall
14	C₅²×C₃₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
15	Dic₁₈₅	C₅×C₇	1	1	yes	characteristic, direct product factor
16	C₅×Dic₃₇	—	5	1	no	—
17	C₅×C₇×Dic₅	—	37	1	no	maximal, Hall
18	C₂×C₇×C₃₇	C₅×D₅	1	1	yes	characteristic
19	C₂×C₅×C₃₇	—	2	2	no	—
20	C₂×C₅×C₃₇	C₇×D₅	1	1	yes	characteristic
21	C₂×C₅×C₃₇	C₂×C₅×C₇	1	1	yes	characteristic
22	C₂×C₅²×C₇	D₃₇	1	1	yes	characteristic
23	C₇×C₃₇	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
24	C₅×C₃₇	—	2	2	no	—
25	C₅×C₃₇	C₇×Dic₅	1	1	yes	characteristic, complemented
26	C₅×C₃₇	C₄×C₅×C₇	1	1	yes	characteristic, complemented
27	C₅²×C₇	Dic₃₇	1	1	yes	characteristic, complemented, Hall
28	Dic₃₇	—	5	1	no	Hall
29	C₄×C₅×C₇	—	185	1	no	—
30	C₇×Dic₅	—	37	1	no	—
31	C₅×Dic₅	—	37	1	no	Hall
32	C₂×C₃₇	C₅×C₇×D₅	1	1	yes	characteristic
33	C₂×C₅×C₇	—	2	2	no	—
34	C₂×C₅×C₇	C₅×D₃₇	1	1	yes	characteristic
35	C₂×C₅×C₇	D₁₈₅	1	1	yes	characteristic
36	C₂×C₅²	C₇×D₃₇	1	1	yes	characteristic
37	C₃₇	C₅×C₇×Dic₅	1	1	yes	characteristic, complemented, Sylow
38	C₅×C₇	—	2	2	no	—
39	C₅×C₇	C₅×Dic₃₇	1	1	yes	characteristic, complemented
40	C₅×C₇	Dic₁₈₅	1	1	yes	characteristic, direct product factor
41	C₄×C₇	—	185	1	no	Hall
42	C₅²	C₇×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
43	C₄×C₅	—	185	1	no	—
44	Dic₅	—	37	1	no	—
45	C₂×C₇	C₅×D₁₈₅	1	1	yes	characteristic
46	C₂×C₅	—	2	2	no	—
47	C₂×C₅	C₅×C₇×D₃₇	1	1	yes	characteristic
48	C₂×C₅	C₇×D₁₈₅	1	1	yes	characteristic
49	C₇	C₅×Dic₁₈₅	1	1	yes	characteristic, direct product factor, Sylow
50	C₅	—	2	2	no	—
51	C₅	C₅×C₇×Dic₃₇	1	1	yes	characteristic, complemented
52	C₅	C₇×Dic₁₈₅	1	1	yes	characteristic, direct product factor
53	C₄	—	185	1	no	Sylow
54	C₂	C₅×C₇×D₁₈₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	D₁₈₅
commutator, hypocenter	C₅×C₃₇	C₄×C₅×C₇
Frattini	C₂	C₅×C₇×D₁₈₅
Fitting, socle, prime radical	C₂×C₅²×C₇×C₃₇	C₂
cosocle	C₂×C₅×C₃₇	C₂×C₅×C₇
LCS	G ▷ C₅×C₃₇
UCS	C₁ ◁ C₂×C₅×C₇

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇×C₃₇	C₄	semidirect
3. C₇×Dic₁₈₅	C₅	direct (N × H)
5. C₅×Dic₁₈₅	C₇	direct (N × H)
11. C₅×C₇×C₃₇	Dic₅	semidirect
12. C₅×C₇×C₃₇	C₄×C₅	semidirect
14. C₅²×C₃₇	C₄×C₇	semidirect
15. Dic₁₈₅	C₅×C₇	direct (N × H)
23. C₇×C₃₇	C₅×Dic₅	semidirect
25. C₅×C₃₇	C₇×Dic₅	semidirect
26. C₅×C₃₇	C₄×C₅×C₇	semidirect
27. C₅²×C₇	Dic₃₇	semidirect
37. C₃₇	C₅×C₇×Dic₅	semidirect
39. C₅×C₇	C₅×Dic₃₇	semidirect
40. C₅×C₇	Dic₁₈₅	direct (N × H)
42. C₅²	C₇×Dic₃₇	semidirect
49. C₇	C₅×Dic₁₈₅	direct (N × H)
51. C₅	C₅×C₇×Dic₃₇	semidirect
52. C₅	C₇×Dic₁₈₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₇×C₃₇	2
C₇×Dic₁₈₅	5
C₅×C₇×Dic₃₇	5
C₅×Dic₁₈₅	7
C₅×C₇×Dic₅	37

Subgroups — C5×C7×Dic185 #39905973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×Dic₁₈₅ #39905973