Subgroups — C₃×C₅×D₅×D₇ #14523630

Order 2100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×C₇×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅×D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×D₇	—	5	1	no	maximal
7	C₃×D₅×D₇	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₇×D₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅²×D₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×D₅	—	7	1	no	maximal, Hall
12	C₂×C₃×C₅×C₇	—	5	1	no	—
13	C₃×D₃₅	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×C₇×D₅	C₂×C₅	1	1	yes	characteristic, complemented
15	C₃×C₅×D₇	—	2	2	no	—
16	C₃×C₅×D₇	—	5	1	no	—
17	C₃×C₅×D₇	D₅	1	1	yes	characteristic, direct product factor
18	C₃×C₅×D₇	C₂×C₅	1	1	yes	characteristic, complemented
19	C₅²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅²	—	7	1	no	—
21	C₃×C₅×D₅	—	7	1	no	—
22	C₃×C₅×D₅	D₇	1	1	yes	characteristic, direct product factor
23	C₂×C₅×D₇	—	5	1	no	—
24	D₅×D₇	C₃×C₅	1	1	yes	characteristic, direct product factor
25	C₃×C₅×C₇	—	2	2	no	—
26	C₃×C₅×C₇	C₂×D₅	1	1	yes	characteristic, complemented
27	C₃×C₅×C₇	C₂²×C₅	1	1	yes	characteristic, complemented
28	C₂×C₅×D₅	—	7	1	no	Hall
29	C₂×C₃×D₇	—	5	1	no	Hall
30	C₃×C₅²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₇	—	5	1	no	—
32	D₃₅	C₂×C₃×C₅	1	1	yes	characteristic, complemented
33	C₅×D₇	—	2	2	no	—
34	C₅×D₇	—	5	1	no	—
35	C₅×D₇	C₃×D₅	1	1	yes	characteristic, direct product factor
36	C₅×D₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
37	C₇×D₅	C₂×C₃×C₅	1	1	yes	characteristic, complemented
38	C₂²×C₃×C₅	—	35	1	no	—
39	C₂×C₃×D₅	—	7	1	no	—
40	C₂×C₅²	—	7	1	no	—
41	C₅×D₅	—	7	1	no	—
42	C₅×D₅	C₃×D₇	1	1	yes	characteristic, direct product factor
43	C₂×C₃×C₇	—	5	1	no	—
44	C₃×D₇	—	5	1	no	—
45	C₃×D₇	C₅×D₅	1	1	yes	characteristic, direct product factor
46	C₅×C₇	—	2	2	no	—
47	C₅×C₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
48	C₅×C₇	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
49	C₂×C₃×C₅	—	5	1	no	—
50	C₂×C₃×C₅	—	7	1	no	—
51	C₂×C₃×C₅	—	7	1	no	—
52	C₂×C₃×C₅	—	14	2	no	—
53	C₂×C₃×C₅	—	35	1	no	—
54	C₃×D₅	—	7	1	no	—
55	C₃×D₅	C₅×D₇	1	1	yes	characteristic, direct product factor
56	C₂×D₇	—	5	1	no	Hall
57	C₅²	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
58	C₃×C₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₅	—	35	1	no	—
60	C₂×D₅	—	7	1	no	—
61	C₃×C₅	—	2	2	no	—
62	C₃×C₅	D₅×D₇	1	1	yes	characteristic, direct product factor
63	C₃×C₅	C₂×C₅×D₇	1	1	yes	characteristic, complemented
64	C₂×C₇	—	5	1	no	—
65	D₇	—	5	1	no	—
66	D₇	C₃×C₅×D₅	1	1	yes	characteristic, direct product factor
67	C₂²×C₃	—	35	1	no	Hall
68	C₂×C₅	—	5	1	no	—
69	C₂×C₅	—	7	1	no	—
70	C₂×C₅	—	7	1	no	—
71	C₂×C₅	—	14	2	no	—
72	C₂×C₅	—	35	1	no	—
73	D₅	—	7	1	no	—
74	D₅	C₃×C₅×D₇	1	1	yes	characteristic, direct product factor
75	C₇	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	5	1	no	—
77	C₂×C₃	—	7	1	no	—
78	C₂×C₃	—	35	1	no	—
79	C₅	—	2	2	no	—
80	C₅	C₃×D₅×D₇	1	1	yes	characteristic, direct product factor
81	C₅	C₂×C₃×C₅×D₇	1	1	yes	characteristic, complemented
82	C₂²	—	35	1	no	Sylow
83	C₃	C₅×D₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	7	1	no	—
86	C₂	—	35	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	D₅×D₇
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₃₅	C₂	semidirect
2. C₃×C₅×C₇×D₅	C₂	semidirect
3. C₃×C₅²×D₇	C₂	semidirect
4. C₅×D₅×D₇	C₃	direct (N × H)
5. C₃×C₅²×C₇	C₂²	semidirect
7. C₃×D₅×D₇	C₅	direct (N × H)
8. C₅×D₃₅	C₂×C₃	semidirect
9. C₅×C₇×D₅	C₂×C₃	semidirect
10. C₅²×D₇	C₂×C₃	semidirect
13. C₃×D₃₅	C₂×C₅	semidirect
14. C₃×C₇×D₅	C₂×C₅	semidirect
17. C₃×C₅×D₇	D₅	direct (N × H)
18. C₃×C₅×D₇	C₂×C₅	semidirect
19. C₅²×C₇	C₂²×C₃	semidirect
22. C₃×C₅×D₅	D₇	direct (N × H)
24. D₅×D₇	C₃×C₅	direct (N × H)
26. C₃×C₅×C₇	C₂×D₅	semidirect
27. C₃×C₅×C₇	C₂²×C₅	semidirect
30. C₃×C₅²	C₂×D₇	semidirect
32. D₃₅	C₂×C₃×C₅	semidirect
35. C₅×D₇	C₃×D₅	direct (N × H)
36. C₅×D₇	C₂×C₃×C₅	semidirect
37. C₇×D₅	C₂×C₃×C₅	semidirect
42. C₅×D₅	C₃×D₇	direct (N × H)
45. C₃×D₇	C₅×D₅	direct (N × H)
47. C₅×C₇	C₂×C₃×D₅	semidirect
48. C₅×C₇	C₂²×C₃×C₅	semidirect
55. C₃×D₅	C₅×D₇	direct (N × H)
57. C₅²	C₂×C₃×D₇	semidirect
58. C₃×C₇	C₂×C₅×D₅	semidirect
62. C₃×C₅	D₅×D₇	direct (N × H)
63. C₃×C₅	C₂×C₅×D₇	semidirect
66. D₇	C₃×C₅×D₅	direct (N × H)
74. D₅	C₃×C₅×D₇	direct (N × H)
75. C₇	C₂×C₃×C₅×D₅	semidirect
80. C₅	C₃×D₅×D₇	direct (N × H)
81. C₅	C₂×C₃×C₅×D₇	semidirect
83. C₃	C₅×D₅×D₇	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×C₅×D₃₅	2
C₃×C₅×C₇×D₅	2
C₃×C₅²×D₇	2
C₅×D₅×D₇	3
C₂×C₃×C₅×D₇	5
C₃×D₅×D₇	5
C₂×C₃×C₅×D₅	7

Subgroups — C3×C5×D5×D7 #14523630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₅×D₇ #14523630