Subgroups — C₂×C₅²×D₃×C₇₁ #36319155

Order 21300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₃×C₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅²×C₇₁	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₃×C₇₁	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₅²×C₇₁	—	3	2	no	—
7	C₂×C₅²×C₇₁	D₃	1	1	yes	characteristic, direct product factor
8	C₅×D₃×C₇₁	C₂×C₅	1	12	yes	direct product factor
9	C₂×C₃×C₅×C₇₁	C₂×C₅	1	6	yes	complemented
10	C₅²×C₇₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₅×C₇₁	—	3	6	no	—
12	C₃×C₅×C₇₁	C₂²×C₅	1	6	yes	complemented
13	C₂×D₃×C₇₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₇₁	—	3	12	no	—
15	C₂×C₅×C₇₁	C₅×D₃	1	6	yes	direct product factor
16	C₂×C₃×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented
17	D₃×C₇₁	C₂×C₅²	1	2	yes	direct product factor
18	C₅×C₇₁	C₂×C₅×D₃	1	6	yes	direct product factor
19	C₂×C₅²×D₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₇₁	—	3	1	no	Hall
21	C₃×C₇₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅²	C₂×C₇₁	1	1	yes	characteristic, complemented
23	C₅²×D₃	C₂×C₇₁	1	2	yes	direct product factor
24	C₂×C₇₁	—	3	2	no	—
25	C₂×C₇₁	C₅²×D₃	1	1	yes	characteristic, direct product factor
26	C₂²×C₅²	—	3	1	no	Hall
27	C₃×C₅²	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
28	C₇₁	C₂×C₅²×D₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅×D₃	C₅×C₇₁	1	6	yes	direct product factor
30	C₂×C₅²	—	3	2	no	—
31	C₂×C₅²	D₃×C₇₁	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₅	C₂×C₅×C₇₁	1	6	yes	complemented
33	C₅×D₃	C₂×C₅×C₇₁	1	12	yes	direct product factor
34	C₅²	C₂×D₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²×C₅	—	3	6	no	—
36	C₃×C₅	C₂²×C₅×C₇₁	1	6	yes	complemented
37	C₂×D₃	C₅²×C₇₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₅	—	3	12	no	—
39	C₂×C₅	C₅×D₃×C₇₁	1	6	yes	direct product factor
40	C₂×C₃	C₂×C₅²×C₇₁	1	1	yes	characteristic, complemented
41	D₃	C₂×C₅²×C₇₁	1	2	yes	direct product factor
42	C₅	C₂×C₅×D₃×C₇₁	1	6	yes	direct product factor
43	C₂²	—	3	1	no	Sylow
44	C₃	C₂²×C₅²×C₇₁	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	3	2	no	—
46	C₂	C₅²×D₃×C₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₇₁	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅²×C₇₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₇₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅²×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₅²×D₃×C₇₁	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₇₁	C₂	semidirect
4. C₃×C₅²×C₇₁	C₂²	semidirect
5. C₂×C₅×D₃×C₇₁	C₅	direct (N × H)
7. C₂×C₅²×C₇₁	D₃	direct (N × H)
8. C₅×D₃×C₇₁	C₂×C₅	direct (N × H)
9. C₂×C₃×C₅×C₇₁	C₂×C₅	semidirect
10. C₅²×C₇₁	C₂×D₃	direct (N × H)
12. C₃×C₅×C₇₁	C₂²×C₅	semidirect
13. C₂×D₃×C₇₁	C₅²	direct (N × H)
15. C₂×C₅×C₇₁	C₅×D₃	direct (N × H)
16. C₂×C₃×C₇₁	C₂×C₅²	semidirect
17. D₃×C₇₁	C₂×C₅²	direct (N × H)
18. C₅×C₇₁	C₂×C₅×D₃	direct (N × H)
19. C₂×C₅²×D₃	C₇₁	direct (N × H)
21. C₃×C₇₁	C₂²×C₅²	semidirect
22. C₂×C₃×C₅²	C₂×C₇₁	semidirect
23. C₅²×D₃	C₂×C₇₁	direct (N × H)
25. C₂×C₇₁	C₅²×D₃	direct (N × H)
27. C₃×C₅²	C₂²×C₇₁	semidirect
28. C₇₁	C₂×C₅²×D₃	direct (N × H)
29. C₂×C₅×D₃	C₅×C₇₁	direct (N × H)
31. C₂×C₅²	D₃×C₇₁	direct (N × H)
32. C₂×C₃×C₅	C₂×C₅×C₇₁	semidirect
33. C₅×D₃	C₂×C₅×C₇₁	direct (N × H)
34. C₅²	C₂×D₃×C₇₁	direct (N × H)
36. C₃×C₅	C₂²×C₅×C₇₁	semidirect
37. C₂×D₃	C₅²×C₇₁	direct (N × H)
39. C₂×C₅	C₅×D₃×C₇₁	direct (N × H)
40. C₂×C₃	C₂×C₅²×C₇₁	semidirect
41. D₃	C₂×C₅²×C₇₁	direct (N × H)
42. C₅	C₂×C₅×D₃×C₇₁	direct (N × H)
44. C₃	C₂²×C₅²×C₇₁	semidirect
46. C₂	C₅²×D₃×C₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×D₃×C₇₁	2
C₂×C₃×C₅²×C₇₁	2
C₂²×C₅²×C₇₁	3
C₂×C₅×D₃×C₇₁	5
C₂×C₅²×D₃	71

Subgroups — C2×C52×D3×C71 #36319155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×D₃×C₇₁ #36319155