Subgroups — C₇×C₅⋊(#41⋊C₃) #13132591

Order 1680.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#713	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×C₇×Dic₅	—	4	1	no	maximal
4	C₇×#41⋊C₃	—	5	1	no	maximal, Hall
5	C₅×C₇×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₇×D₂₀	—	3	1	no	—
7	C₄×C₇×D₅	—	3	1	no	—
8	C₅⋊(#41⋊C₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×C₇	—	4	1	no	—
10	C₇×SL(2,𝔽₃)	D₅	1	1	yes	characteristic, complemented
11	C₂×C₇×D₅	—	3	1	no	—
12	C₄×C₅×C₇	—	3	1	no	—
13	C₇×Dic₅	A₄	1	1	yes	characteristic
14	C₅×SL(2,𝔽₃)	C₂×C₇	1	1	yes	characteristic, complemented
15	C₇×#41	—	5	1	no	Hall
16	C₃×C₅×C₇	—	4	1	no	Hall
17	C₃×C₄×C₇	—	20	1	no	—
18	#713	C₃×C₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₇	C₂×A₄	1	1	yes	characteristic
20	C₇×D₅	—	6	1	no	—
21	C₃×Dic₅	—	4	1	no	—
22	C₇×Q₈	C₃×D₅	1	1	yes	characteristic
23	C₇×D₄	—	15	1	no	—
24	C₂×C₄×C₇	—	15	1	no	—
25	#41⋊C₃	—	5	1	no	Hall
26	C₂×C₃×C₇	—	4	1	no	—
27	C₅×Q₈	C₂×C₃×C₇	1	1	yes	characteristic
28	D₂₀	—	3	1	no	—
29	C₄×D₅	—	3	1	no	—
30	C₅×C₇	#41⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₅	—	4	1	no	—
32	C₂²×C₇	—	15	1	no	—
33	C₄×C₇	—	3	1	no	—
34	C₄×C₇	—	5	1	no	—
35	SL(2,𝔽₃)	C₇×D₅	1	1	yes	characteristic, complemented
36	C₃×C₇	—	4	1	no	Hall
37	C₂×D₅	—	3	1	no	—
38	C₄×C₅	—	3	1	no	—
39	Dic₅	C₇×A₄	1	1	yes	characteristic
40	#41	—	5	1	no	Sylow
41	C₃×C₅	—	4	1	no	Hall
42	C₂×C₇	—	30	1	no	—
43	C₂×C₇	D₅×A₄	1	1	yes	characteristic
44	C₃×C₄	—	20	1	no	—
45	C₂×C₅	C₂×C₇×A₄	1	1	yes	characteristic
46	D₅	—	6	1	no	—
47	Q₈	C₃×C₇×D₅	1	1	yes	characteristic
48	D₄	—	15	1	no	—
49	C₂×C₄	—	15	1	no	—
50	C₇	C₅⋊(#41⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	4	1	no	—
52	C₅	C₇×#41⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	15	1	no	—
54	C₄	—	3	1	no	—
55	C₄	—	5	1	no	—
56	C₃	—	4	1	no	Sylow
57	C₂	—	30	1	no	—
58	C₂	C₇×D₅×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	D₅×A₄
commutator, cosocle, hypocenter	C₅×Q₈	C₂×C₃×C₇
Frattini	C₂	C₇×D₅×A₄
Fitting	C₅×C₇×Q₈	C₂×C₃
socle	C₂×C₅×C₇	C₂×A₄
LCS	G ▷ C₅×Q₈
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×SL(2,𝔽₃)	C₂	semidirect
2. C₇×#713	C₃	semidirect
8. C₅⋊(#41⋊C₃)	C₇	direct (N × H)
10. C₇×SL(2,𝔽₃)	D₅	semidirect
14. C₅×SL(2,𝔽₃)	C₂×C₇	semidirect
18. #713	C₃×C₇	semidirect
30. C₅×C₇	#41⋊C₃	semidirect
35. SL(2,𝔽₃)	C₇×D₅	semidirect
50. C₇	C₅⋊(#41⋊C₃)	direct (N × H)
52. C₅	C₇×#41⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×SL(2,𝔽₃)	2
C₇×#713	3
C₃×C₇×Dic₅	4
C₇×#41⋊C₃	5
C₅⋊(#41⋊C₃)	7

Subgroups — C7×C5⋊(#41⋊C3) #13132591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₅⋊(#41⋊C₃) #13132591