Subgroups — C₅×A₄×D₇ #11719857

Order 840.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×C₅×D₇	—	4	1	no	maximal
4	A₄×D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₅×C₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₅×D₇	—	3	1	no	—
7	C₂×C₅×D₇	—	3	1	no	—
8	C₂×C₅×A₄	—	7	1	no	maximal, Hall
9	C₃×C₅×C₇	—	4	1	no	Hall
10	C₇×A₄	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₇	—	3	1	no	—
12	C₅×D₇	—	3	1	no	—
13	C₅×D₇	A₄	1	1	yes	characteristic, direct product factor
14	C₅×A₄	D₇	1	1	yes	characteristic, direct product factor
15	C₂²×D₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₃×D₇	—	4	1	no	—
17	C₂³×C₅	—	7	1	no	Hall
18	C₅×C₇	C₂×A₄	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅	—	28	1	no	—
20	C₂²×C₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	C₂×D₇	—	3	1	no	—
22	C₂×D₇	—	3	1	no	—
23	C₂×A₄	—	7	1	no	Hall
24	C₃×C₇	—	4	1	no	Hall
25	C₂²×C₅	—	21	1	no	—
26	C₂²×C₅	—	21	1	no	—
27	C₂²×C₅	C₃×D₇	1	1	yes	characteristic, complemented
28	C₃×C₅	—	4	1	no	Hall
29	C₂×C₇	—	3	1	no	—
30	D₇	—	3	1	no	—
31	D₇	C₅×A₄	1	1	yes	characteristic, direct product factor
32	A₄	C₅×D₇	1	1	yes	characteristic, direct product factor
33	C₂×C₅	—	3	1	no	—
34	C₂×C₅	—	7	1	no	—
35	C₂×C₅	—	21	1	no	—
36	C₂³	—	7	1	no	Sylow
37	C₇	C₂×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃	—	28	1	no	—
39	C₅	A₄×D₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	21	1	no	—
41	C₂²	—	21	1	no	—
42	C₂²	C₃×C₅×D₇	1	1	yes	characteristic, complemented
43	C₃	—	4	1	no	Sylow
44	C₂	—	3	1	no	—
45	C₂	—	7	1	no	—
46	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₅	A₄×D₇
commutator, cosocle, hypocenter	C₂²×C₇	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₇	C₂×C₃
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×A₄	C₂	semidirect
2. C₂²×C₅×D₇	C₃	semidirect
4. A₄×D₇	C₅	direct (N × H)
5. C₂²×C₅×C₇	C₂×C₃	semidirect
10. C₇×A₄	C₂×C₅	semidirect
13. C₅×D₇	A₄	direct (N × H)
14. C₅×A₄	D₇	direct (N × H)
15. C₂²×D₇	C₃×C₅	semidirect
18. C₅×C₇	C₂×A₄	semidirect
20. C₂²×C₇	C₂×C₃×C₅	semidirect
27. C₂²×C₅	C₃×D₇	semidirect
31. D₇	C₅×A₄	direct (N × H)
32. A₄	C₅×D₇	direct (N × H)
37. C₇	C₂×C₅×A₄	semidirect
39. C₅	A₄×D₇	direct (N × H)
42. C₂²	C₃×C₅×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×A₄	2
C₂²×C₅×D₇	3
C₃×C₅×D₇	4
A₄×D₇	5
C₂×C₅×A₄	7

Subgroups — C5×A4×D7 #11719857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×A₄×D₇ #11719857