Subgroups — C₂×D₃×(C₇₁⋊C₅)⋊C₇ #44447166

Order 29820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×(C₇₁⋊C₅)⋊C₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×(C₇₁⋊C₅)⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×(C₇₁⋊C₅)⋊C₇	—	3	1	no	maximal, Hall
4	C₃×(C₇₁⋊C₅)⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₇₁⋊C₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×(C₇₁⋊C₅)⋊C₇	—	3	2	no	—
7	C₂×(C₇₁⋊C₅)⋊C₇	D₃	1	1	yes	characteristic, direct product factor
8	C₂×D₃×C₇₁⋊C₅	C₇	1	1	yes	maximal, characteristic, complemented, Hall
9	D₃×C₇₁⋊C₇	C₂×C₅	1	2	yes	complemented
10	C₂×C₃×C₇₁⋊C₇	C₂×C₅	1	1	yes	characteristic, complemented
11	(C₇₁⋊C₅)⋊C₇	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
12	D₃×C₇₁⋊C₅	C₂×C₇	1	2	yes	complemented
13	C₂×C₃×C₇₁⋊C₅	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂²×C₇₁⋊C₇	—	3	1	no	Hall
15	C₃×C₇₁⋊C₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₇₁⋊C₅	—	3	1	no	Hall
17	C₃×C₇₁⋊C₅	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇₁⋊C₇	—	3	2	no	—
19	C₂×C₇₁⋊C₇	C₅×D₃	1	1	yes	characteristic, complemented
20	C₂×D₃×C₇₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇₁⋊C₅	—	3	2	no	—
22	C₂×C₇₁⋊C₅	D₃×C₇	1	1	yes	characteristic, complemented
23	C₇₁⋊C₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
25	D₃×C₇₁	C₂×C₅×C₇	1	2	yes	complemented
26	C₂×C₅×D₃×C₇	—	71	1	no	maximal, Hall
27	C₇₁⋊C₅	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₇₁	—	3	1	no	Hall
29	C₃×C₇₁	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅×C₇	—	71	1	no	—
31	C₅×D₃×C₇	—	71	2	no	—
32	C₂×C₇₁	—	3	2	no	—
33	C₂×C₇₁	C₅×D₃×C₇	1	1	yes	characteristic, complemented
34	C₂²×C₅×C₇	—	213	1	no	Hall
35	C₃×C₅×C₇	—	71	1	no	Hall
36	C₂×D₃×C₇	—	71	1	no	Hall
37	C₇₁	C₂×C₅×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₅×C₇	—	71	1	no	—
39	C₂×C₅×C₇	—	213	2	no	—
40	C₂×C₅×D₃	—	497	1	no	Hall
41	C₂×C₃×C₇	—	71	1	no	—
42	D₃×C₇	—	71	2	no	—
43	C₅×C₇	—	71	1	no	Hall
44	C₂×C₃×C₅	—	497	1	no	—
45	C₅×D₃	—	497	2	no	—
46	C₂²×C₇	—	213	1	no	Hall
47	C₃×C₇	—	71	1	no	Hall
48	C₂²×C₅	—	1491	1	no	Hall
49	C₃×C₅	—	497	1	no	Hall
50	C₂×C₇	—	71	1	no	—
51	C₂×C₇	—	213	2	no	—
52	C₂×D₃	(C₇₁⋊C₅)⋊C₇	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₅	—	1491	2	no	—
54	C₂×C₅	—	497	1	no	—
55	C₇	—	71	1	no	Sylow
56	C₂×C₃	C₂×(C₇₁⋊C₅)⋊C₇	1	1	yes	characteristic, complemented
57	D₃	C₂×(C₇₁⋊C₅)⋊C₇	1	2	yes	direct product factor
58	C₅	—	497	1	no	Sylow
59	C₂²	—	3	1	no	Sylow
60	C₃	C₂²×(C₇₁⋊C₅)⋊C₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	3	2	no	—
62	C₂	D₃×(C₇₁⋊C₅)⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×(C₇₁⋊C₅)⋊C₇
commutator, cosocle, hypocenter	C₃×C₇₁	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇₁	C₂×C₅×C₇
LCS	G ▷ C₃×C₇₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₃×(C₇₁⋊C₅)⋊C₇	C₂	direct (N × H)
2. C₂×C₃×(C₇₁⋊C₅)⋊C₇	C₂	semidirect
4. C₃×(C₇₁⋊C₅)⋊C₇	C₂²	semidirect
5. C₂×D₃×C₇₁⋊C₇	C₅	semidirect
7. C₂×(C₇₁⋊C₅)⋊C₇	D₃	direct (N × H)
8. C₂×D₃×C₇₁⋊C₅	C₇	semidirect
9. D₃×C₇₁⋊C₇	C₂×C₅	semidirect
10. C₂×C₃×C₇₁⋊C₇	C₂×C₅	semidirect
11. (C₇₁⋊C₅)⋊C₇	C₂×D₃	direct (N × H)
12. D₃×C₇₁⋊C₅	C₂×C₇	semidirect
13. C₂×C₃×C₇₁⋊C₅	C₂×C₇	semidirect
15. C₃×C₇₁⋊C₇	C₂²×C₅	semidirect
17. C₃×C₇₁⋊C₅	C₂²×C₇	semidirect
19. C₂×C₇₁⋊C₇	C₅×D₃	semidirect
20. C₂×D₃×C₇₁	C₅×C₇	semidirect
22. C₂×C₇₁⋊C₅	D₃×C₇	semidirect
23. C₇₁⋊C₇	C₂×C₅×D₃	semidirect
24. C₂×C₃×C₇₁	C₂×C₅×C₇	semidirect
25. D₃×C₇₁	C₂×C₅×C₇	semidirect
27. C₇₁⋊C₅	C₂×D₃×C₇	semidirect
29. C₃×C₇₁	C₂²×C₅×C₇	semidirect
33. C₂×C₇₁	C₅×D₃×C₇	semidirect
37. C₇₁	C₂×C₅×D₃×C₇	semidirect
52. C₂×D₃	(C₇₁⋊C₅)⋊C₇	direct (N × H)
56. C₂×C₃	C₂×(C₇₁⋊C₅)⋊C₇	semidirect
57. D₃	C₂×(C₇₁⋊C₅)⋊C₇	direct (N × H)
60. C₃	C₂²×(C₇₁⋊C₅)⋊C₇	semidirect
62. C₂	D₃×(C₇₁⋊C₅)⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃×(C₇₁⋊C₅)⋊C₇	2
C₂×C₃×(C₇₁⋊C₅)⋊C₇	2
C₂²×(C₇₁⋊C₅)⋊C₇	3
C₂×D₃×C₇₁⋊C₇	5
C₂×D₃×C₇₁⋊C₅	7
C₂×C₅×D₃×C₇	71

Subgroups — C2×D3×(C71⋊C5)⋊C7 #44447166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×(C₇₁⋊C₅)⋊C₇ #44447166