Subgroups — C₇×#15690395 #36339429

Order 21420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#10597480	—	5	1	no	maximal, Hall
4	C₅×D₃×C₇×C₁₇	—	6	2	no	—
5	#15690395	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×Dic₈₅	—	9	1	no	maximal, Hall
7	C₇×C₁₇×C₃⋊D₃	D₅	1	1	yes	characteristic
8	C₃×C₅×C₇×C₁₇	—	2	2	no	—
9	C₅×C₁₇×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
10	C₇×#4379	—	17	1	no	maximal, Hall
11	C₂×C₅×C₇×C₁₇	—	9	1	no	—
12	C₃²×C₇×C₁₇	Dic₅	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₅×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇×C₁₇	—	6	2	no	—
15	C₅×C₇×C₃⋊D₃	D₁₇	1	1	yes	characteristic
16	#10597480	—	5	1	no	Hall
17	C₅×C₇×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
18	C₅×D₃×C₁₇	—	6	2	no	—
19	C₇×Dic₁₇	—	45	1	no	Hall
20	C₃×C₇×C₁₇	—	2	2	no	—
21	Dic₈₅	—	9	1	no	Hall
22	C₃²×C₅×C₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
23	C₁₇×C₃⋊D₃	C₇×D₅	1	1	yes	characteristic
24	C₃×C₅×C₁₇	—	2	2	no	—
25	C₇×#157	—	85	1	no	Hall
26	C₂×C₇×C₁₇	—	9	1	no	—
27	C₅×D₃×C₇	—	6	2	no	—
28	#4379	—	17	1	no	Hall
29	C₂×C₅×C₁₇	—	9	1	no	—
30	C₃²×C₁₇	C₇×Dic₅	1	1	yes	characteristic, complemented, Hall
31	C₇×Dic₅	—	153	1	no	Hall
32	C₇×C₃⋊D₃	D₈₅	1	1	yes	characteristic
33	C₇×C₁₇	#4379	1	1	yes	characteristic, complemented, Hall
34	C₃×C₅×C₇	—	2	2	no	—
35	D₃×C₁₇	—	6	2	no	—
36	C₅×C₃⋊D₃	C₇×D₁₇	1	1	yes	characteristic
37	C₅×C₁₇	C₇×#157	1	1	yes	characteristic, complemented, Hall
38	C₂×C₅×C₇	—	9	1	no	—
39	Dic₁₇	—	45	1	no	Hall
40	C₃²×C₇	Dic₈₅	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₇	—	2	2	no	—
42	C₃²×C₅	C₇×Dic₁₇	1	1	yes	characteristic, complemented, Hall
43	D₃×C₇	—	6	2	no	—
44	#157	—	85	1	no	Hall
45	C₅×C₇	#10597480	1	1	yes	characteristic, complemented, Hall
46	C₂×C₁₇	—	9	1	no	—
47	C₅×D₃	—	6	2	no	—
48	C₄×C₇	—	765	1	no	Hall
49	C₃×C₇	—	2	2	no	—
50	Dic₅	—	153	1	no	Hall
51	C₃⋊D₃	C₇×D₈₅	1	1	yes	characteristic
52	C₁₇	C₇×#4379	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₅	—	2	2	no	—
54	C₂×C₇	—	9	1	no	—
55	C₂×C₅	—	9	1	no	—
56	C₃²	C₇×Dic₈₅	1	1	yes	characteristic, complemented, Sylow
57	C₇	#15690395	1	1	yes	characteristic, direct product factor, Sylow
58	D₃	—	6	2	no	—
59	C₅	C₇×#10597480	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	765	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#15690395
commutator, hypocenter	C₃²×C₅×C₁₇	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₄
prime radical	C₅×C₇×C₁₇×C₃⋊D₃	C₂
cosocle	C₅×C₁₇×C₃⋊D₃	C₂×C₇
LCS	G ▷ C₃²×C₅×C₁₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₇×C₁₇	C₄	semidirect
5. #15690395	C₇	direct (N × H)
12. C₃²×C₇×C₁₇	Dic₅	semidirect
13. C₃²×C₅×C₁₇	C₄×C₇	semidirect
17. C₅×C₇×C₁₇	#157	semidirect
22. C₃²×C₅×C₇	Dic₁₇	semidirect
30. C₃²×C₁₇	C₇×Dic₅	semidirect
33. C₇×C₁₇	#4379	semidirect
37. C₅×C₁₇	C₇×#157	semidirect
40. C₃²×C₇	Dic₈₅	semidirect
42. C₃²×C₅	C₇×Dic₁₇	semidirect
45. C₅×C₇	#10597480	semidirect
52. C₁₇	C₇×#4379	semidirect
56. C₃²	C₇×Dic₈₅	semidirect
57. C₇	#15690395	direct (N × H)
59. C₅	C₇×#10597480	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₇×C₃⋊D₃	2
C₇×#10597480	5
#15690395	7
C₇×Dic₈₅	9
C₇×#4379	17

Subgroups — C7×#15690395 #36339429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#15690395 #36339429