Subgroups — C₃×C₇⋊#13133348 #49087920

Order 35700.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#13133348	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇⋊#66774	—	5	2	no	maximal
5	C₇×C₁₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×#13133348	—	7	1	no	maximal, Hall
7	C₃×C₇×D₅×C₁₇	—	5	2	no	—
8	C₃×C₇×D₅×C₁₇	—	10	2	no	—
9	C₅²×C₇×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₇×C₅⋊D₅	D₇	1	1	yes	characteristic
11	C₇⋊#66774	—	5	2	no	—
12	C₃×C₇⋊#1044	—	17	1	no	maximal, Hall
13	C₃×C₅×C₇×C₁₇	—	2	2	no	—
14	C₃×C₅×C₇×C₁₇	AGL(1,𝔽₅)	1	2	yes	complemented
15	#13133348	—	7	1	no	Hall
16	C₃×Dic₁₁₉	—	25	1	no	Hall
17	C₃×C₅²×C₁₇	Dic₇	1	1	yes	characteristic, complemented, Hall
18	C₇×D₅×C₁₇	—	5	2	no	—
19	C₇×D₅×C₁₇	—	10	2	no	—
20	C₃×C₇×C₅⋊D₅	D₁₇	1	1	yes	characteristic
21	C₃×#66774	—	35	2	no	—
22	C₁₇×C₅⋊D₅	C₃×D₇	1	1	yes	characteristic
23	C₂×C₃×C₇×C₁₇	—	25	1	no	—
24	C₇⋊#1044	—	17	1	no	Hall
25	C₅×C₇×C₁₇	—	2	2	no	—
26	C₅×C₇×C₁₇	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
27	C₃×C₅²×C₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
28	C₃×D₅×C₁₇	—	5	2	no	—
29	C₃×D₅×C₁₇	—	10	2	no	—
30	Dic₁₁₉	—	25	1	no	Hall
31	C₅²×C₁₇	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇⋊AGL(1,𝔽₅)	—	85	2	no	—
33	C₃×C₇×C₁₇	#1044	1	1	yes	characteristic, complemented, Hall
34	C₇×C₅⋊D₅	C₃×D₁₇	1	1	yes	characteristic
35	#66774	—	35	2	no	—
36	C₃×#1044	—	119	1	no	Hall
37	C₃×C₅×C₁₇	—	2	2	no	—
38	C₃×C₅×C₁₇	C₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
39	C₂×C₇×C₁₇	—	25	1	no	—
40	C₃×C₇×D₅	—	5	2	no	—
41	C₃×C₇×D₅	—	10	2	no	—
42	C₃×Dic₁₇	—	175	1	no	Hall
43	C₅²×C₇	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Hall
44	D₅×C₁₇	—	5	2	no	—
45	D₅×C₁₇	—	10	2	no	—
46	C₃×C₅⋊D₅	D₁₁₉	1	1	yes	characteristic
47	C₇⋊AGL(1,𝔽₅)	—	85	2	no	—
48	C₇×C₁₇	C₃×#1044	1	1	yes	characteristic, complemented, Hall
49	C₃×C₅×C₇	—	2	2	no	—
50	C₃×C₅×C₇	#66774	1	2	yes	complemented
51	C₂×C₃×C₁₇	—	25	1	no	—
52	#1044	—	119	1	no	Hall
53	C₅×C₁₇	—	2	2	no	—
54	C₅×C₁₇	C₃×C₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
55	C₃×Dic₇	—	425	1	no	Hall
56	C₃×C₅²	Dic₁₁₉	1	1	yes	characteristic, complemented, Hall
57	C₇×D₅	—	5	2	no	—
58	C₇×D₅	—	10	2	no	—
59	Dic₁₇	—	175	1	no	Hall
60	C₃×AGL(1,𝔽₅)	—	595	2	no	—
61	C₃×C₁₇	C₇⋊#1044	1	1	yes	characteristic, complemented, Hall
62	C₅⋊D₅	C₃×D₁₁₉	1	1	yes	characteristic
63	C₂×C₃×C₇	—	25	1	no	—
64	C₅×C₇	—	2	2	no	—
65	C₅×C₇	C₃×#66774	1	2	yes	complemented
66	C₂×C₁₇	—	25	1	no	—
67	C₃×D₅	—	5	2	no	—
68	C₃×D₅	—	10	2	no	—
69	Dic₇	—	425	1	no	Hall
70	C₅²	C₃×Dic₁₁₉	1	1	yes	characteristic, complemented, Sylow
71	C₃×C₇	#13133348	1	1	yes	characteristic, complemented, Hall
72	AGL(1,𝔽₅)	—	595	2	no	—
73	C₁₇	C₃×C₇⋊#1044	1	1	yes	characteristic, complemented, Sylow
74	C₃×C₅	—	2	2	no	—
75	C₃×C₅	C₇⋊#66774	1	2	yes	complemented
76	C₂×C₇	—	25	1	no	—
77	C₃×C₄	—	2975	1	no	Hall
78	D₅	—	5	2	no	—
79	D₅	—	10	2	no	—
80	C₇	C₃×#13133348	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	25	1	no	—
82	C₅	—	2	2	no	—
83	C₅	C₃×C₇⋊#66774	1	2	yes	complemented
84	C₄	—	2975	1	no	Sylow
85	C₃	C₇⋊#13133348	1	1	yes	characteristic, direct product factor, Sylow
86	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₇⋊#13133348
commutator, hypocenter	C₅²×C₇×C₁₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₇	C₄
prime radical	C₃×C₇×C₁₇×C₅⋊D₅	C₂
cosocle	C₇×C₁₇×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₇×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₇⋊#13133348	C₃	direct (N × H)
3. C₃×C₅²×C₇×C₁₇	C₄	semidirect
9. C₅²×C₇×C₁₇	C₃×C₄	semidirect
14. C₃×C₅×C₇×C₁₇	AGL(1,𝔽₅)	semidirect
17. C₃×C₅²×C₁₇	Dic₇	semidirect
26. C₅×C₇×C₁₇	C₃×AGL(1,𝔽₅)	semidirect
27. C₃×C₅²×C₇	Dic₁₇	semidirect
31. C₅²×C₁₇	C₃×Dic₇	semidirect
33. C₃×C₇×C₁₇	#1044	semidirect
38. C₃×C₅×C₁₇	C₇⋊AGL(1,𝔽₅)	semidirect
43. C₅²×C₇	C₃×Dic₁₇	semidirect
48. C₇×C₁₇	C₃×#1044	semidirect
50. C₃×C₅×C₇	#66774	semidirect
54. C₅×C₁₇	C₃×C₇⋊AGL(1,𝔽₅)	semidirect
56. C₃×C₅²	Dic₁₁₉	semidirect
61. C₃×C₁₇	C₇⋊#1044	semidirect
65. C₅×C₇	C₃×#66774	semidirect
70. C₅²	C₃×Dic₁₁₉	semidirect
71. C₃×C₇	#13133348	semidirect
73. C₁₇	C₃×C₇⋊#1044	semidirect
75. C₃×C₅	C₇⋊#66774	semidirect
80. C₇	C₃×#13133348	semidirect
83. C₅	C₃×C₇⋊#66774	semidirect
85. C₃	C₇⋊#13133348	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇×C₅⋊D₅	2
C₇⋊#13133348	3
C₃×C₇⋊#66774	5
C₃×#13133348	7
C₃×C₇⋊#1044	17

Subgroups — C3×C7⋊#13133348 #49087920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇⋊#13133348 #49087920