Subgroups — C₂×C₇×C₁₇×#3874 #49087839

Order 35700.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₇×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₇×#3874	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₇×D₅×C₁₇	—	3	1	no	maximal, Hall
4	C₇×C₁₇×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×D₅×C₁₇	—	3	2	no	—
6	C₂×C₅²×C₇×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₂×C₁₇×#3874	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅²×C₇×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇×C₅²⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
10	C₁₇×#3874	C₂×C₇	1	2	yes	direct product factor
11	C₂×C₇×D₅×C₁₇	—	3	1	no	—
12	C₂²×C₅×C₇×C₁₇	—	15	1	no	—
13	C₂×C₇×#3874	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅×D₅×C₁₇	—	3	1	no	Hall
15	C₂×D₃×C₇×C₁₇	—	25	1	no	maximal, Hall
16	C₁₇×C₅²⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₇×C₁₇	—	3	1	no	—
18	C₂×C₅×C₇×C₁₇	—	3	1	no	—
19	C₂×C₅×C₇×C₁₇	—	15	2	no	—
20	C₇×D₅×C₁₇	—	3	2	no	—
21	C₂×C₇×C₅²⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented
22	C₇×#3874	C₂×C₁₇	1	2	yes	direct product factor
23	C₂×C₅²×C₁₇	D₃×C₇	1	1	yes	characteristic, complemented
24	C₅×D₅×C₁₇	—	3	2	no	—
25	C₂×C₃×C₇×C₁₇	—	25	1	no	—
26	D₃×C₇×C₁₇	—	25	2	no	—
27	C₂×C₅×C₇×D₅	—	3	1	no	Hall
28	C₅×C₇×C₁₇	—	3	1	no	—
29	C₅×C₇×C₁₇	—	3	1	no	—
30	C₇×C₅²⋊C₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₇×C₁₇	—	15	1	no	Hall
32	C₅²×C₁₇	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
33	C₃×C₇×C₁₇	—	25	1	no	Hall
34	C₂×C₅²×C₇	D₃×C₁₇	1	1	yes	characteristic, complemented
35	C₅×C₇×D₅	—	3	2	no	—
36	C₂²×C₅×C₁₇	—	15	1	no	—
37	C₂×D₅×C₁₇	—	3	1	no	—
38	C₂×#3874	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇×C₁₇	—	15	2	no	—
40	C₂×C₇×C₁₇	#3874	1	1	yes	characteristic, direct product factor
41	C₂×D₃×C₁₇	—	25	1	no	Hall
42	C₅²×C₇	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
43	C₂×C₅×C₁₇	—	3	1	no	—
44	C₂×C₅×C₁₇	—	3	1	no	—
45	C₂×C₅×C₁₇	—	15	2	no	—
46	D₅×C₁₇	—	3	2	no	—
47	C₂×C₅²⋊C₃	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented
48	#3874	C₂×C₇×C₁₇	1	2	yes	direct product factor
49	C₂²×C₅×C₇	—	15	1	no	—
50	C₂×C₇×D₅	—	3	1	no	—
51	C₇×C₁₇	C₂×#3874	1	1	yes	characteristic, direct product factor, Hall
52	C₂×C₃×C₁₇	—	25	1	no	—
53	D₃×C₁₇	—	25	2	no	—
54	C₂×C₅×D₅	—	3	1	no	Hall
55	C₅×C₁₇	—	3	1	no	—
56	C₅×C₁₇	—	3	1	no	—
57	C₂×D₃×C₇	—	25	1	no	Hall
58	C₅²⋊C₃	C₂²×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₅×C₇	—	3	1	no	—
60	C₂×C₅×C₇	—	3	1	no	—
61	C₂×C₅×C₇	—	15	2	no	—
62	C₇×D₅	—	3	2	no	—
63	C₂²×C₁₇	—	15	1	no	Hall
64	C₃×C₁₇	—	25	1	no	Hall
65	C₂×C₅²	D₃×C₇×C₁₇	1	1	yes	characteristic, complemented
66	C₅×D₅	—	3	2	no	—
67	C₂×C₃×C₇	—	25	1	no	—
68	D₃×C₇	—	25	2	no	—
69	C₅×C₇	—	3	1	no	—
70	C₅×C₇	—	3	1	no	—
71	C₂×C₁₇	—	15	2	no	—
72	C₂×C₁₇	C₇×#3874	1	1	yes	characteristic, direct product factor
73	C₂²×C₇	—	15	1	no	Hall
74	C₅²	C₂×D₃×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
75	C₃×C₇	—	25	1	no	Hall
76	C₂²×C₅	—	15	1	no	—
77	C₂×D₅	—	3	1	no	—
78	C₁₇	C₂×C₇×#3874	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₇	—	15	2	no	—
80	C₂×C₇	C₁₇×#3874	1	1	yes	characteristic, direct product factor
81	C₂×D₃	—	25	1	no	Hall
82	C₂×C₅	—	3	1	no	—
83	C₂×C₅	—	3	1	no	—
84	C₂×C₅	—	15	2	no	—
85	D₅	—	3	2	no	—
86	C₇	C₂×C₁₇×#3874	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×C₃	—	25	1	no	—
88	D₃	—	25	2	no	—
89	C₅	—	3	1	no	—
90	C₅	—	3	1	no	—
91	C₂²	—	15	1	no	Sylow
92	C₃	—	25	1	no	Sylow
93	C₂	—	15	2	no	—
94	C₂	C₇×C₁₇×#3874	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₇	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂²×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₇	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₁₇×C₅²⋊C₃	C₂	semidirect
2. C₇×C₁₇×#3874	C₂	direct (N × H)
4. C₇×C₁₇×C₅²⋊C₃	C₂²	semidirect
6. C₂×C₅²×C₇×C₁₇	D₃	semidirect
7. C₂×C₁₇×#3874	C₇	direct (N × H)
8. C₅²×C₇×C₁₇	C₂×D₃	semidirect
9. C₂×C₁₇×C₅²⋊C₃	C₂×C₇	semidirect
10. C₁₇×#3874	C₂×C₇	direct (N × H)
13. C₂×C₇×#3874	C₁₇	direct (N × H)
16. C₁₇×C₅²⋊C₃	C₂²×C₇	semidirect
21. C₂×C₇×C₅²⋊C₃	C₂×C₁₇	semidirect
22. C₇×#3874	C₂×C₁₇	direct (N × H)
23. C₂×C₅²×C₁₇	D₃×C₇	semidirect
30. C₇×C₅²⋊C₃	C₂²×C₁₇	semidirect
32. C₅²×C₁₇	C₂×D₃×C₇	semidirect
34. C₂×C₅²×C₇	D₃×C₁₇	semidirect
38. C₂×#3874	C₇×C₁₇	direct (N × H)
40. C₂×C₇×C₁₇	#3874	direct (N × H)
42. C₅²×C₇	C₂×D₃×C₁₇	semidirect
47. C₂×C₅²⋊C₃	C₂×C₇×C₁₇	semidirect
48. #3874	C₂×C₇×C₁₇	direct (N × H)
51. C₇×C₁₇	C₂×#3874	direct (N × H)
58. C₅²⋊C₃	C₂²×C₇×C₁₇	semidirect
65. C₂×C₅²	D₃×C₇×C₁₇	semidirect
72. C₂×C₁₇	C₇×#3874	direct (N × H)
74. C₅²	C₂×D₃×C₇×C₁₇	semidirect
78. C₁₇	C₂×C₇×#3874	direct (N × H)
80. C₂×C₇	C₁₇×#3874	direct (N × H)
86. C₇	C₂×C₁₇×#3874	direct (N × H)
94. C₂	C₇×C₁₇×#3874	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×C₇×C₁₇×C₅²⋊C₃	2
C₇×C₁₇×#3874	2
C₂×C₅×C₇×D₅×C₁₇	3
C₂×C₁₇×#3874	7
C₂×C₇×#3874	17
C₂×D₃×C₇×C₁₇	25

Subgroups — C2×C7×C17×#3874 #49087839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₇×#3874 #49087839