Subgroups — C₃×C₇×D₅×D₇₁ #44447233

Order 29820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₃₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₅×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₅×D₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇×D₇₁	—	5	1	no	maximal, Hall
7	C₇×D₃₅₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₅×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₇×D₇₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₅×D₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₇×D₇₁	—	5	1	no	—
12	C₃×C₇×D₇₁	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₃×C₇×C₇₁	—	5	1	no	—
14	C₅×C₇×C₇₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×D₃₅₅	C₂×C₇	1	1	yes	characteristic, complemented
16	C₃×D₅×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×C₅×D₇₁	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇×D₇₁	—	5	1	no	Hall
19	C₃×C₇×C₇₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅×D₇₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅×C₇₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₇₁	—	5	1	no	—
23	C₇×D₇₁	—	5	1	no	—
24	C₇×D₇₁	C₃×D₅	1	1	yes	characteristic, direct product factor
25	C₂×C₃×D₇₁	—	5	1	no	Hall
26	D₃₅₅	C₂×C₃×C₇	1	1	yes	characteristic, complemented
27	C₅×D₇₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
28	D₅×C₇₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
29	C₇×C₇₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇₁	—	5	1	no	—
31	C₃×D₇₁	—	5	1	no	—
32	C₃×D₇₁	C₇×D₅	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₇×D₅	—	71	1	no	maximal, Hall
34	C₅×C₇₁	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₁	—	5	1	no	Hall
36	C₃×C₇₁	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₇	—	71	1	no	—
38	C₃×C₇×D₅	—	71	1	no	—
39	C₃×C₇×D₅	D₇₁	1	1	yes	characteristic, direct product factor
40	C₂×C₇₁	—	5	1	no	—
41	D₇₁	—	5	1	no	—
42	D₇₁	C₃×C₇×D₅	1	1	yes	characteristic, direct product factor
43	C₂×C₇×D₅	—	71	1	no	Hall
44	C₃×C₅×C₇	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃×C₇	—	355	1	no	Hall
46	C₇₁	C₂×C₃×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅×C₇	—	71	1	no	—
48	C₇×D₅	—	71	1	no	—
49	C₇×D₅	C₃×D₇₁	1	1	yes	characteristic, direct product factor
50	C₂×C₃×D₅	—	71	1	no	Hall
51	C₂×C₃×C₇	—	5	1	no	—
52	C₂×C₃×C₇	—	71	1	no	—
53	C₂×C₃×C₇	—	355	1	no	—
54	C₅×C₇	C₂×C₃×D₇₁	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	71	1	no	—
56	C₃×D₅	—	71	1	no	—
57	C₃×D₅	C₇×D₇₁	1	1	yes	characteristic, direct product factor
58	C₂²×C₇	—	355	1	no	Hall
59	C₃×C₇	D₅×D₇₁	1	1	yes	characteristic, direct product factor, Hall
60	C₂×D₅	—	71	1	no	Hall
61	C₃×C₅	C₂×C₇×D₇₁	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	5	1	no	—
63	C₂×C₇	—	71	1	no	—
64	C₂×C₇	—	355	1	no	—
65	C₂²×C₃	—	355	1	no	Hall
66	C₂×C₅	—	71	1	no	—
67	D₅	—	71	1	no	—
68	D₅	C₃×C₇×D₇₁	1	1	yes	characteristic, direct product factor
69	C₇	C₃×D₅×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	5	1	no	—
71	C₂×C₃	—	71	1	no	—
72	C₂×C₃	—	355	1	no	—
73	C₅	C₂×C₃×C₇×D₇₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	355	1	no	Sylow
75	C₃	C₇×D₅×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	71	1	no	—
78	C₂	—	355	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇	D₅×D₇₁
commutator, cosocle, hypocenter	C₅×C₇₁	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₁	C₂²
LCS	G ▷ C₅×C₇₁
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₃₅₅	C₂	semidirect
2. C₃×C₇×D₅×C₇₁	C₂	semidirect
3. C₃×C₅×C₇×D₇₁	C₂	semidirect
4. C₇×D₅×D₇₁	C₃	direct (N × H)
5. C₃×C₅×C₇×C₇₁	C₂²	semidirect
7. C₇×D₃₅₅	C₂×C₃	semidirect
8. C₇×D₅×C₇₁	C₂×C₃	semidirect
9. C₅×C₇×D₇₁	C₂×C₃	semidirect
10. C₃×D₅×D₇₁	C₇	direct (N × H)
12. C₃×C₇×D₇₁	D₅	direct (N × H)
14. C₅×C₇×C₇₁	C₂²×C₃	semidirect
15. C₃×D₃₅₅	C₂×C₇	semidirect
16. C₃×D₅×C₇₁	C₂×C₇	semidirect
17. C₃×C₅×D₇₁	C₂×C₇	semidirect
19. C₃×C₇×C₇₁	C₂×D₅	semidirect
20. D₅×D₇₁	C₃×C₇	direct (N × H)
21. C₃×C₅×C₇₁	C₂²×C₇	semidirect
24. C₇×D₇₁	C₃×D₅	direct (N × H)
26. D₃₅₅	C₂×C₃×C₇	semidirect
27. C₅×D₇₁	C₂×C₃×C₇	semidirect
28. D₅×C₇₁	C₂×C₃×C₇	semidirect
29. C₇×C₇₁	C₂×C₃×D₅	semidirect
32. C₃×D₇₁	C₇×D₅	direct (N × H)
34. C₅×C₇₁	C₂²×C₃×C₇	semidirect
36. C₃×C₇₁	C₂×C₇×D₅	semidirect
39. C₃×C₇×D₅	D₇₁	direct (N × H)
42. D₇₁	C₃×C₇×D₅	direct (N × H)
44. C₃×C₅×C₇	C₂×D₇₁	semidirect
46. C₇₁	C₂×C₃×C₇×D₅	semidirect
49. C₇×D₅	C₃×D₇₁	direct (N × H)
54. C₅×C₇	C₂×C₃×D₇₁	semidirect
57. C₃×D₅	C₇×D₇₁	direct (N × H)
59. C₃×C₇	D₅×D₇₁	direct (N × H)
61. C₃×C₅	C₂×C₇×D₇₁	semidirect
68. D₅	C₃×C₇×D₇₁	direct (N × H)
69. C₇	C₃×D₅×D₇₁	direct (N × H)
73. C₅	C₂×C₃×C₇×D₇₁	semidirect
75. C₃	C₇×D₅×D₇₁	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×D₃₅₅	2
C₃×C₇×D₅×C₇₁	2
C₃×C₅×C₇×D₇₁	2
C₇×D₅×D₇₁	3
C₂×C₃×C₇×D₇₁	5
C₃×D₅×D₇₁	7
C₂×C₃×C₇×D₅	71

Subgroups — C3×C7×D5×D71 #44447233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₅×D₇₁ #44447233