Subgroups — C₃×C₄×C₅×C₇×C₇₁ #44447113

Order 29820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₇×C₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇×C₇₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₄×C₇×C₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇×C₇₁	C₂×C₃	1	1	yes	characteristic
6	C₃×C₄×C₅×C₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇×C₇₁	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇×C₇₁	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₅×C₇₁	C₂×C₇	1	1	yes	characteristic
10	C₄×C₇×C₇₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇×C₇₁	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₅×C₇₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇₁	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₇×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic
15	C₃×C₄×C₇₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×C₇₁	C₂×C₃×C₇	1	1	yes	characteristic
17	C₇×C₇₁	C₃×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₇₁	C₂×C₅×C₇	1	1	yes	characteristic
19	C₃×C₄×C₅×C₇	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₅×C₇₁	C₃×C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₇₁	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₇₁	C₄×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅×C₇	C₂×C₇₁	1	1	yes	characteristic
24	C₂×C₇₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic
25	C₄×C₅×C₇	C₃×C₇₁	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅×C₇	C₄×C₇₁	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₄×C₇	C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
28	C₇₁	C₃×C₄×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅×C₇	C₂×C₃×C₇₁	1	1	yes	characteristic
30	C₃×C₄×C₅	C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₇	C₂×C₅×C₇₁	1	1	yes	characteristic
32	C₅×C₇	C₃×C₄×C₇₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₅	C₂×C₇×C₇₁	1	1	yes	characteristic
34	C₄×C₇	C₃×C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₇	C₄×C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
36	C₄×C₅	C₃×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅	C₄×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₇	C₂×C₃×C₅×C₇₁	1	1	yes	characteristic
39	C₃×C₄	C₅×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	C₂×C₃×C₇×C₇₁	1	1	yes	characteristic
41	C₇	C₃×C₄×C₅×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	C₂×C₅×C₇×C₇₁	1	1	yes	characteristic
43	C₅	C₃×C₄×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	C₃×C₅×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₄×C₅×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂×C₃×C₅×C₇×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₅×C₇×C₇₁
socle, prime radical	C₂×C₃×C₅×C₇×C₇₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₇×C₇₁	C₃	direct (N × H)
3. C₃×C₅×C₇×C₇₁	C₄	direct (N × H)
4. C₃×C₄×C₇×C₇₁	C₅	direct (N × H)
6. C₃×C₄×C₅×C₇₁	C₇	direct (N × H)
8. C₅×C₇×C₇₁	C₃×C₄	direct (N × H)
10. C₄×C₇×C₇₁	C₃×C₅	direct (N × H)
11. C₃×C₇×C₇₁	C₄×C₅	direct (N × H)
12. C₄×C₅×C₇₁	C₃×C₇	direct (N × H)
13. C₃×C₅×C₇₁	C₄×C₇	direct (N × H)
15. C₃×C₄×C₇₁	C₅×C₇	direct (N × H)
17. C₇×C₇₁	C₃×C₄×C₅	direct (N × H)
19. C₃×C₄×C₅×C₇	C₇₁	direct (N × H)
20. C₅×C₇₁	C₃×C₄×C₇	direct (N × H)
21. C₄×C₇₁	C₃×C₅×C₇	direct (N × H)
22. C₃×C₇₁	C₄×C₅×C₇	direct (N × H)
25. C₄×C₅×C₇	C₃×C₇₁	direct (N × H)
26. C₃×C₅×C₇	C₄×C₇₁	direct (N × H)
27. C₃×C₄×C₇	C₅×C₇₁	direct (N × H)
28. C₇₁	C₃×C₄×C₅×C₇	direct (N × H)
30. C₃×C₄×C₅	C₇×C₇₁	direct (N × H)
32. C₅×C₇	C₃×C₄×C₇₁	direct (N × H)
34. C₄×C₇	C₃×C₅×C₇₁	direct (N × H)
35. C₃×C₇	C₄×C₅×C₇₁	direct (N × H)
36. C₄×C₅	C₃×C₇×C₇₁	direct (N × H)
37. C₃×C₅	C₄×C₇×C₇₁	direct (N × H)
39. C₃×C₄	C₅×C₇×C₇₁	direct (N × H)
41. C₇	C₃×C₄×C₅×C₇₁	direct (N × H)
43. C₅	C₃×C₄×C₇×C₇₁	direct (N × H)
44. C₄	C₃×C₅×C₇×C₇₁	direct (N × H)
45. C₃	C₄×C₅×C₇×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
C₂×C₃×C₅×C₇×C₇₁	2
C₄×C₅×C₇×C₇₁	3
C₃×C₄×C₇×C₇₁	5
C₃×C₄×C₅×C₇₁	7
C₃×C₄×C₅×C₇	71

Subgroups — C3×C4×C5×C7×C71 #44447113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×C₇×C₇₁ #44447113