Subgroups — C₅²×C₃⋊(C₇⋊#595) #49087923

Order 35700.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇⋊#595	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃⋊(C₇⋊#595)	C₅	1	6	yes	maximal, direct product factor
5	C₅²×C₇×D₁₇	D₃	1	1	yes	characteristic
6	C₅²×C₃⋊#595	—	7	1	no	maximal, Hall
7	C₃×C₅×C₇×D₁₇	C₂×C₅	1	6	yes	—
8	C₅²×C₇×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅²×D₁₇	D₇	1	1	yes	characteristic
10	C₅×C₇⋊#595	—	3	6	no	—
11	C₅²×Dic₂₁	—	17	1	no	maximal, Hall
12	C₃×C₅×C₇×C₁₇	C₄×C₅	1	6	yes	complemented
13	C₅²×#595	—	21	1	no	Hall
14	C₃⋊(C₇⋊#595)	C₅²	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅²×C₁₇	Dic₇	1	1	yes	characteristic, complemented, Hall
16	C₅×C₇×D₁₇	C₅×D₃	1	6	yes	—
17	C₂×C₃×C₅²×C₇	—	17	1	no	—
18	C₅×C₃⋊#595	—	7	6	no	—
19	C₅²×D₁₇	D₂₁	1	1	yes	characteristic
20	C₃×C₇×D₁₇	C₂×C₅²	1	1	yes	characteristic
21	C₅²×Dic₇	—	51	1	no	Hall
22	C₅×C₇×C₁₇	C₅×Dic₃	1	6	yes	complemented
23	C₃×C₅²×C₇	#595	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×D₁₇	C₅×D₇	1	6	yes	—
25	C₇⋊#595	—	3	1	no	Hall
26	C₅²×C₁₇	Dic₂₁	1	1	yes	characteristic, complemented, Hall
27	C₅×Dic₂₁	—	17	6	no	—
28	C₃×C₇×C₁₇	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅²×C₇	—	17	1	no	—
30	C₅×#595	—	21	6	no	—
31	C₅²×Dic₃	—	119	1	no	Hall
32	C₃×C₅×C₁₇	C₅×Dic₇	1	6	yes	complemented
33	C₇×D₁₇	C₅²×D₃	1	1	yes	characteristic
34	C₂×C₃×C₅×C₇	—	17	6	no	—
35	C₃⋊#595	—	7	1	no	Hall
36	C₅²×C₇	C₃⋊#595	1	1	yes	characteristic, complemented, Hall
37	C₅×D₁₇	C₅×D₂₁	1	6	yes	—
38	C₂×C₃×C₅²	—	17	1	no	—
39	C₅×Dic₇	—	51	6	no	—
40	C₇×C₁₇	C₅²×Dic₃	1	1	yes	characteristic, complemented, Hall
41	C₃×C₅×C₇	C₅×#595	1	6	yes	complemented
42	C₃×D₁₇	C₅²×D₇	1	1	yes	characteristic
43	C₄×C₅²	—	357	1	no	Hall
44	C₅×C₁₇	C₅×Dic₂₁	1	6	yes	complemented
45	Dic₂₁	—	17	1	no	Hall
46	C₃×C₅²	C₇⋊#595	1	1	yes	characteristic, complemented, Hall
47	C₂×C₅×C₇	—	17	6	no	—
48	#595	—	21	1	no	Hall
49	C₅×Dic₃	—	119	6	no	—
50	C₃×C₁₇	C₅²×Dic₇	1	1	yes	characteristic, complemented, Hall
51	C₂×C₅²	—	17	1	no	—
52	C₂×C₃×C₇	—	17	1	no	—
53	C₅×C₇	C₅×C₃⋊#595	1	6	yes	complemented
54	D₁₇	C₅²×D₂₁	1	1	yes	characteristic
55	C₂×C₃×C₅	—	17	6	no	—
56	Dic₇	—	51	1	no	Hall
57	C₅²	C₃⋊(C₇⋊#595)	1	1	yes	characteristic, direct product factor, Sylow
58	C₃×C₇	C₅²×#595	1	1	yes	characteristic, complemented, Hall
59	C₄×C₅	—	357	6	no	—
60	C₁₇	C₅²×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₅	C₅×C₇⋊#595	1	6	yes	complemented
62	C₂×C₇	—	17	1	no	—
63	Dic₃	—	119	1	no	Hall
64	C₂×C₅	—	17	6	no	—
65	C₇	C₅²×C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	17	1	no	—
67	C₅	C₅×C₃⋊(C₇⋊#595)	1	6	yes	direct product factor
68	C₄	—	357	1	no	Sylow
69	C₃	C₅²×C₇⋊#595	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	C₃⋊(C₇⋊#595)
commutator, hypocenter	C₃×C₇×C₁₇	C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₇	C₄
prime radical	C₃×C₅²×C₇×D₁₇	C₂
cosocle	C₃×C₇×D₁₇	C₂×C₅²
LCS	G ▷ C₃×C₇×C₁₇
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₇×C₁₇	C₄	semidirect
4. C₅×C₃⋊(C₇⋊#595)	C₅	direct (N × H)
8. C₅²×C₇×C₁₇	Dic₃	semidirect
12. C₃×C₅×C₇×C₁₇	C₄×C₅	semidirect
14. C₃⋊(C₇⋊#595)	C₅²	direct (N × H)
15. C₃×C₅²×C₁₇	Dic₇	semidirect
22. C₅×C₇×C₁₇	C₅×Dic₃	semidirect
23. C₃×C₅²×C₇	#595	semidirect
26. C₅²×C₁₇	Dic₂₁	semidirect
28. C₃×C₇×C₁₇	C₄×C₅²	semidirect
32. C₃×C₅×C₁₇	C₅×Dic₇	semidirect
36. C₅²×C₇	C₃⋊#595	semidirect
40. C₇×C₁₇	C₅²×Dic₃	semidirect
41. C₃×C₅×C₇	C₅×#595	semidirect
44. C₅×C₁₇	C₅×Dic₂₁	semidirect
46. C₃×C₅²	C₇⋊#595	semidirect
50. C₃×C₁₇	C₅²×Dic₇	semidirect
53. C₅×C₇	C₅×C₃⋊#595	semidirect
57. C₅²	C₃⋊(C₇⋊#595)	direct (N × H)
58. C₃×C₇	C₅²×#595	semidirect
60. C₁₇	C₅²×Dic₂₁	semidirect
61. C₃×C₅	C₅×C₇⋊#595	semidirect
65. C₇	C₅²×C₃⋊#595	semidirect
67. C₅	C₅×C₃⋊(C₇⋊#595)	direct (N × H)
69. C₃	C₅²×C₇⋊#595	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₇×D₁₇	2
C₅²×C₇⋊#595	3
C₅×C₃⋊(C₇⋊#595)	5
C₅²×C₃⋊#595	7
C₅²×Dic₂₁	17

Subgroups — C52×C3⋊(C7⋊#595) #49087923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₃⋊(C₇⋊#595) #49087923