Subgroups — C₅×C₇×A₄×C₇₁ #44447271

Order 29820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₇×C₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₇×C₇₁	—	4	1	no	maximal, Hall
3	C₇×A₄×C₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₇×C₇₁	—	3	1	no	—
5	C₅×A₄×C₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×C₇₁	A₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₇×C₇₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×C₇₁	—	4	1	no	Hall
9	C₂²×C₅×C₇₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₇₁	—	4	1	no	Hall
11	C₂×C₇×C₇₁	—	3	1	no	—
12	A₄×C₇₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₇₁	—	3	1	no	—
14	C₇×C₇₁	C₅×A₄	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₇×A₄	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅×C₇₁	C₇×A₄	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₇₁	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
18	C₃×C₇₁	—	4	1	no	Hall
19	C₂×C₇₁	—	3	1	no	—
20	C₂²×C₅×C₇	C₃×C₇₁	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₇	—	4	1	no	Hall
22	C₇×A₄	C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
23	C₇₁	C₅×C₇×A₄	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₅×C₇	—	3	1	no	—
25	C₅×A₄	C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
26	C₅×C₇	A₄×C₇₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂²×C₇	C₃×C₅×C₇₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₇	—	4	1	no	Hall
29	C₂²×C₅	C₃×C₇×C₇₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅	—	4	1	no	Hall
31	C₂×C₇	—	3	1	no	—
32	A₄	C₅×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₅	—	3	1	no	—
34	C₇	C₅×A₄×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
35	C₅	C₇×A₄×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₃×C₅×C₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	4	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇×C₇₁	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅×C₇×C₇₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₇×C₇₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₇×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₇×C₇₁	C₃	semidirect
3. C₇×A₄×C₇₁	C₅	direct (N × H)
5. C₅×A₄×C₇₁	C₇	direct (N × H)
6. C₅×C₇×C₇₁	A₄	direct (N × H)
7. C₂²×C₇×C₇₁	C₃×C₅	semidirect
9. C₂²×C₅×C₇₁	C₃×C₇	semidirect
12. A₄×C₇₁	C₅×C₇	direct (N × H)
14. C₇×C₇₁	C₅×A₄	direct (N × H)
15. C₅×C₇×A₄	C₇₁	direct (N × H)
16. C₅×C₇₁	C₇×A₄	direct (N × H)
17. C₂²×C₇₁	C₃×C₅×C₇	semidirect
20. C₂²×C₅×C₇	C₃×C₇₁	semidirect
22. C₇×A₄	C₅×C₇₁	direct (N × H)
23. C₇₁	C₅×C₇×A₄	direct (N × H)
25. C₅×A₄	C₇×C₇₁	direct (N × H)
26. C₅×C₇	A₄×C₇₁	direct (N × H)
27. C₂²×C₇	C₃×C₅×C₇₁	semidirect
29. C₂²×C₅	C₃×C₇×C₇₁	semidirect
32. A₄	C₅×C₇×C₇₁	direct (N × H)
34. C₇	C₅×A₄×C₇₁	direct (N × H)
35. C₅	C₇×A₄×C₇₁	direct (N × H)
36. C₂²	C₃×C₅×C₇×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₇×C₇₁	3
C₃×C₅×C₇×C₇₁	4
C₇×A₄×C₇₁	5
C₅×A₄×C₇₁	7
C₅×C₇×A₄	71

Subgroups — C5×C7×A4×C71 #44447271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×A₄×C₇₁ #44447271