Subgroups — D₂₁×D₇₁⋊C₅ #44447186

Order 29820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊(D₇₁⋊C₅))	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₁×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₇₁⋊C₅	—	3	1	no	maximal, Hall
5	C₃×C₇×C₇₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁×D₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₇⋊(D₇₁⋊C₅)	—	3	1	no	—
8	D₇×C₇₁⋊C₅	—	3	1	no	—
9	C₇×D₇₁⋊C₅	D₃	1	1	yes	characteristic, complemented
10	D₃×D₇₁⋊C₅	—	7	1	no	maximal, Hall
11	D₁₄₉₁	C₂×C₅	1	1	yes	characteristic, complemented
12	D₂₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×C₇×D₇₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₇×C₇₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(D₇₁⋊C₅)	—	7	1	no	—
16	D₃×C₇₁⋊C₅	—	7	1	no	—
17	C₃×D₇₁⋊C₅	D₇	1	1	yes	characteristic, complemented
18	D₇×D₇₁	—	3	1	no	Hall
19	C₃×C₇×C₇₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇₁⋊C₅	—	21	1	no	Hall
21	C₃×C₇₁⋊C₅	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₄₉₇	—	3	1	no	—
23	C₇×D₇₁	C₅×D₃	1	1	yes	characteristic, complemented
24	D₇×C₇₁	—	3	1	no	—
25	D₃×D₇₁	—	7	1	no	Hall
26	C₂×C₇₁⋊C₅	—	21	1	no	—
27	D₇₁⋊C₅	—	21	1	no	—
28	D₇₁⋊C₅	D₂₁	1	1	yes	characteristic, direct product factor
29	C₇×C₇₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
30	D₂₁₃	—	7	1	no	—
31	C₃×D₇₁	C₅×D₇	1	1	yes	characteristic, complemented
32	D₃×C₇₁	—	7	1	no	—
33	C₂×C₅×D₂₁	—	71	1	no	maximal, Hall
34	C₇₁⋊C₅	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₁	—	21	1	no	Hall
36	C₃×C₇₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₇	—	71	1	no	—
38	C₅×D₂₁	—	71	1	no	—
39	C₅×D₂₁	—	71	1	no	—
40	C₂×C₇₁	—	21	1	no	—
41	D₇₁	—	21	1	no	—
42	D₇₁	C₅×D₂₁	1	1	yes	characteristic, complemented
43	C₂×C₅×D₇	—	213	1	no	Hall
44	C₃×C₅×C₇	—	71	1	no	Hall
45	C₂×D₂₁	—	71	1	no	Hall
46	C₇₁	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅×C₇	—	71	1	no	—
48	C₅×D₇	—	213	1	no	—
49	C₅×D₇	—	213	1	no	—
50	C₂×C₅×D₃	—	497	1	no	Hall
51	C₂×C₃×C₇	—	71	1	no	—
52	D₂₁	—	71	1	no	—
53	D₂₁	D₇₁⋊C₅	1	1	yes	characteristic, direct product factor
54	C₅×C₇	—	71	1	no	Hall
55	C₂×C₃×C₅	—	71	1	no	—
56	C₅×D₃	—	497	1	no	—
57	C₅×D₃	—	497	1	no	—
58	C₂×D₇	—	213	1	no	Hall
59	C₃×C₇	C₂×D₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₅	—	1491	1	no	Hall
61	C₃×C₅	—	71	1	no	Hall
62	C₂×C₇	—	71	1	no	—
63	D₇	—	3	1	no	—
64	D₇	—	213	1	no	—
65	C₂×D₃	—	497	1	no	Hall
66	C₂×C₅	—	71	1	no	—
67	C₂×C₅	—	1491	1	no	—
68	C₂×C₅	—	1491	1	no	—
69	C₇	D₃×D₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	71	1	no	—
71	D₃	—	7	1	no	—
72	D₃	—	497	1	no	—
73	C₅	—	71	1	no	Sylow
74	C₂²	—	1491	1	no	Sylow
75	C₃	D₇×D₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	71	1	no	—
78	C₂	—	1491	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₇⋊(D₇₁⋊C₅))	C₂	semidirect
2. D₂₁×C₇₁⋊C₅	C₂	semidirect
3. C₃×C₇×D₇₁⋊C₅	C₂	semidirect
5. C₃×C₇×C₇₁⋊C₅	C₂²	semidirect
6. D₂₁×D₇₁	C₅	semidirect
9. C₇×D₇₁⋊C₅	D₃	semidirect
11. D₁₄₉₁	C₂×C₅	semidirect
12. D₂₁×C₇₁	C₂×C₅	semidirect
13. C₃×C₇×D₇₁	C₂×C₅	semidirect
14. C₇×C₇₁⋊C₅	C₂×D₃	semidirect
17. C₃×D₇₁⋊C₅	D₇	semidirect
19. C₃×C₇×C₇₁	C₂²×C₅	semidirect
21. C₃×C₇₁⋊C₅	C₂×D₇	semidirect
23. C₇×D₇₁	C₅×D₃	semidirect
28. D₇₁⋊C₅	D₂₁	direct (N × H)
29. C₇×C₇₁	C₂×C₅×D₃	semidirect
31. C₃×D₇₁	C₅×D₇	semidirect
34. C₇₁⋊C₅	C₂×D₂₁	semidirect
36. C₃×C₇₁	C₂×C₅×D₇	semidirect
42. D₇₁	C₅×D₂₁	semidirect
46. C₇₁	C₂×C₅×D₂₁	semidirect
53. D₂₁	D₇₁⋊C₅	direct (N × H)
59. C₃×C₇	C₂×D₇₁⋊C₅	semidirect
69. C₇	D₃×D₇₁⋊C₅	semidirect
75. C₃	D₇×D₇₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₇⋊(D₇₁⋊C₅))	2
D₂₁×C₇₁⋊C₅	2
C₃×C₇×D₇₁⋊C₅	2
D₇×D₇₁⋊C₅	3
D₂₁×D₇₁	5
D₃×D₇₁⋊C₅	7
C₂×C₅×D₂₁	71

Subgroups — D21×D71⋊C5 #44447186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁×D₇₁⋊C₅ #44447186