Subgroups — C₅×C₇×#10587716 #34062064

Order 19110.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×#63270	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇²×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×#10587716	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×#10587716	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₅×C₇×D₁₃⋊C₃	—	7	1	no	maximal
7	C₇×#63270	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×C₇×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
9	C₅×#63270	C₂×C₇	1	1	yes	characteristic, complemented
10	C₅×C₇×C₁₃⋊C₃	—	7	1	no	—
11	C₇²×D₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₇×D₁₃	—	3	2	no	—
13	C₅×C₇×D₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₅×C₇×D₁₃	C₃×C₇	1	1	yes	characteristic, complemented
15	C₅×C₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
16	C₇²×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
17	#10587716	C₅×C₇	1	1	yes	characteristic, direct product factor
18	C₇×D₁₃⋊C₃	—	7	1	no	—
19	C₂×C₅×C₇²	—	13	1	no	Hall
20	C₅×C₇×C₁₃	—	3	2	no	—
21	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₅×D₁₃⋊C₃	—	7	1	no	Hall
24	C₂×C₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
25	#63270	C₂×C₅×C₇	1	1	yes	characteristic, complemented
26	C₇×C₁₃⋊C₃	—	7	1	no	—
27	C₅×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₅×C₇	—	91	1	no	—
29	C₂×C₅×ΓL(1,𝔽₈)	—	13	1	no	—
30	C₅×C₁₃⋊C₃	—	7	1	no	Hall
31	C₇×D₁₃	—	3	2	no	—
32	C₇×D₁₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
33	C₇×D₁₃	C₃×C₅×C₇	1	1	yes	characteristic, complemented
34	C₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
35	C₅×D₁₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
36	C₃×C₅×C₇	—	91	1	no	—
37	C₅×ΓL(1,𝔽₈)	—	13	1	no	—
38	C₂×C₇²	—	13	1	no	Hall
39	C₇×C₁₃	—	3	2	no	—
40	C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
41	C₇×C₁₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
42	D₁₃⋊C₃	—	7	1	no	Hall
43	C₂×C₅×C₇	—	13	1	no	—
44	C₂×C₅×C₇	—	13	1	no	—
45	C₂×C₅×C₇	—	39	2	no	—
46	C₅×C₁₃	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
47	C₇²	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₇	—	91	1	no	—
49	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
50	C₁₃⋊C₃	—	7	1	no	Hall
51	C₅×C₇	—	3	2	no	—
52	C₅×C₇	C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
53	C₅×C₇	#10587716	1	1	yes	characteristic, direct product factor
54	C₂×C₃×C₅	—	91	1	no	Hall
55	D₁₃	C₅×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
56	C₃×C₇	—	91	1	no	—
57	ΓL(1,𝔽₈)	—	13	1	no	—
58	C₃×C₅	—	91	1	no	Hall
59	C₂×C₇	—	13	1	no	—
60	C₂×C₇	—	13	1	no	—
61	C₂×C₇	—	39	2	no	—
62	C₁₃	C₂×C₅×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₅	—	13	1	no	Hall
64	C₇	—	3	2	no	—
65	C₇	C₅×C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
66	C₇	C₅×#10587716	1	1	yes	characteristic, direct product factor
67	C₂×C₃	—	91	1	no	Hall
68	C₅	C₇×#10587716	1	1	yes	characteristic, direct product factor, Sylow
69	C₃	—	91	1	no	Sylow
70	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	#10587716
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×#63270	C₂	semidirect
2. C₅×C₇²×D₁₃	C₃	semidirect
3. C₇×#10587716	C₅	direct (N × H)
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
5. C₅×#10587716	C₇	direct (N × H)
7. C₇×#63270	C₂×C₅	semidirect
9. C₅×#63270	C₂×C₇	semidirect
11. C₇²×D₁₃	C₃×C₅	semidirect
13. C₅×C₇×D₁₃	ΓL(1,𝔽₈)	semidirect
14. C₅×C₇×D₁₃	C₃×C₇	semidirect
16. C₇²×C₁₃	C₂×C₃×C₅	semidirect
17. #10587716	C₅×C₇	direct (N × H)
21. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
22. C₅×C₇×C₁₃	C₂×C₃×C₇	semidirect
25. #63270	C₂×C₅×C₇	semidirect
27. C₅×C₇²	D₁₃⋊C₃	semidirect
32. C₇×D₁₃	C₅×ΓL(1,𝔽₈)	semidirect
33. C₇×D₁₃	C₃×C₅×C₇	semidirect
35. C₅×D₁₃	C₇×ΓL(1,𝔽₈)	semidirect
40. C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
41. C₇×C₁₃	C₂×C₃×C₅×C₇	semidirect
46. C₅×C₁₃	C₂×C₇×ΓL(1,𝔽₈)	semidirect
47. C₇²	C₅×D₁₃⋊C₃	semidirect
52. C₅×C₇	C₇×D₁₃⋊C₃	semidirect
53. C₅×C₇	#10587716	direct (N × H)
55. D₁₃	C₅×C₇×ΓL(1,𝔽₈)	semidirect
62. C₁₃	C₂×C₅×C₇×ΓL(1,𝔽₈)	semidirect
65. C₇	C₅×C₇×D₁₃⋊C₃	semidirect
66. C₇	C₅×#10587716	direct (N × H)
68. C₅	C₇×#10587716	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×#63270	2
C₅×C₇²×D₁₃	3
C₇×#10587716	5
C₅×#10587716	7
C₅×C₇×D₁₃⋊C₃	7
C₂×C₅×C₇×ΓL(1,𝔽₈)	13

Subgroups — C5×C7×#10587716 #34062064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×#10587716 #34062064