Subgroups — C₅×#16838458 #34062082

Order 19110.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274263	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×C₁₃×D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838458	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×#10587720	—	7	1	no	maximal
6	C₂×C₅×#63270	—	7	1	no	maximal
7	#14274263	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×#64423	—	13	1	no	maximal, Hall
9	C₅×#63270	—	7	1	no	—
10	C₅×#63270	—	7	1	no	—
11	C₅×#63270	—	14	3	no	—
12	C₇×C₁₃×D₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₇×C₁₃	—	7	1	no	—
14	C₅×C₁₃×D₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
15	C₅×#3861	—	13	1	no	Hall
16	C₇²×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×#63270	—	7	1	no	—
18	#10587720	—	7	1	no	—
19	C₅×C₇×D₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₅×C₇×C₁₃	—	2	3	no	—
21	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₂×C₅×C₁₃⋊C₃	—	49	1	no	Hall
24	#64423	—	13	1	no	Hall
25	#63270	—	7	1	no	—
26	#63270	—	7	1	no	—
27	#63270	—	14	3	no	—
28	C₅×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×ΓL(1,𝔽₈)	—	91	1	no	—
30	C₅×AGL(1,𝔽₇)	—	91	1	no	—
31	C₅×C₁₃⋊C₃	—	49	1	no	Hall
32	C₂×C₇×C₁₃	—	7	1	no	—
33	C₁₃×D₇	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
34	#3861	—	13	1	no	Hall
35	C₂×C₅×C₁₃	—	7	1	no	Hall
36	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
37	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
38	C₅×ΓL(1,𝔽₈)	—	182	3	no	—
39	C₇×D₇	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₇×C₁₃	—	2	3	no	—
41	C₇×C₁₃	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
42	C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
43	C₂×C₁₃⋊C₃	—	49	1	no	Hall
44	C₂×C₅×C₇	—	7	1	no	—
45	C₅×D₇	#63270	1	1	yes	characteristic, complemented
46	C₅×C₁₃	#64423	1	1	yes	characteristic, complemented, Hall
47	C₇²	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×ΓL(1,𝔽₈)	—	91	1	no	—
49	AGL(1,𝔽₇)	—	91	1	no	—
50	C₁₃⋊C₃	—	49	1	no	Hall
51	C₅×C₇	—	2	3	no	—
52	C₅×C₇	#10587720	1	1	yes	characteristic, complemented
53	C₅×C₇	C₂×#63270	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅	—	637	1	no	Hall
55	C₂×C₁₃	—	7	1	no	Hall
56	ΓL(1,𝔽₈)	—	91	1	no	—
57	ΓL(1,𝔽₈)	—	91	1	no	—
58	ΓL(1,𝔽₈)	—	182	3	no	—
59	C₃×C₅	—	637	1	no	Hall
60	C₂×C₇	—	7	1	no	—
61	D₇	C₅×#63270	1	1	yes	characteristic, complemented
62	C₁₃	C₅×#64423	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₅	—	7	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	C₂×C₅×#63270	1	1	yes	characteristic, complemented
66	C₇	C₅×#10587720	1	1	yes	characteristic, complemented
67	C₂×C₃	—	637	1	no	Hall
68	C₅	#16838458	1	1	yes	characteristic, direct product factor, Sylow
69	C₃	—	637	1	no	Sylow
70	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#16838458
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14274263	C₂	semidirect
2. C₅×C₇×C₁₃×D₇	C₃	semidirect
3. #16838458	C₅	direct (N × H)
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
7. #14274263	C₂×C₅	semidirect
12. C₇×C₁₃×D₇	C₃×C₅	semidirect
14. C₅×C₁₃×D₇	ΓL(1,𝔽₈)	semidirect
16. C₇²×C₁₃	C₂×C₃×C₅	semidirect
19. C₅×C₇×D₇	C₁₃⋊C₃	semidirect
21. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
22. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
28. C₅×C₇²	C₂×C₁₃⋊C₃	semidirect
33. C₁₃×D₇	C₅×ΓL(1,𝔽₈)	semidirect
39. C₇×D₇	C₅×C₁₃⋊C₃	semidirect
41. C₇×C₁₃	C₅×AGL(1,𝔽₇)	semidirect
42. C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
45. C₅×D₇	#63270	semidirect
46. C₅×C₁₃	#64423	semidirect
47. C₇²	C₂×C₅×C₁₃⋊C₃	semidirect
52. C₅×C₇	#10587720	semidirect
53. C₅×C₇	C₂×#63270	semidirect
61. D₇	C₅×#63270	semidirect
62. C₁₃	C₅×#64423	semidirect
65. C₇	C₂×C₅×#63270	semidirect
66. C₇	C₅×#10587720	semidirect
68. C₅	#16838458	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×#14274263	2
C₅×C₇×C₁₃×D₇	3
#16838458	5
C₅×#10587720	7
C₂×C₅×#63270	7
C₅×#64423	13

Subgroups — C5×#16838458 #34062082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#16838458 #34062082