Subgroups — C₅⋊#16838468 #34062151

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⋊(C₇⋊D₉₁)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838468	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊#10587722	—	7	1	no	maximal
6	C₅⋊((C₁₃⋊C₃)⋊D₇)	—	7	1	no	maximal
7	C₇×#63270	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅⋊(ΓL(1,𝔽₈)⋊D₇)	—	13	1	no	maximal, Hall
9	C₅×#63270	D₇	1	1	yes	characteristic, complemented
10	C₅×C₇×C₁₃⋊C₃	—	7	1	no	—
11	C₇⋊D₉₁	—	5	1	no	Hall
12	D₄₅₅	—	7	1	no	—
13	D₄₅₅	—	7	1	no	—
14	D₄₅₅	—	21	2	no	—
15	C₅×C₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
16	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
17	#10587722	—	35	1	no	—
18	(C₁₃⋊C₃)⋊D₇	—	35	1	no	—
19	C₅⋊(C₇⋊D₇)	—	13	1	no	Hall
20	C₅×C₇×C₁₃	—	3	2	no	—
21	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
23	C₅⋊(D₁₃⋊C₃)	—	49	1	no	Hall
24	ΓL(1,𝔽₈)⋊D₇	—	65	1	no	Hall
25	#63270	D₃₅	1	1	yes	characteristic, complemented
26	C₇×C₁₃⋊C₃	—	7	1	no	—
27	C₅×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₃×D₃₅	—	91	1	no	—
29	C₅⋊AGL(1,𝔽₇)	—	91	1	no	—
30	C₅×C₁₃⋊C₃	—	7	1	no	Hall
31	D₉₁	—	35	1	no	—
32	D₉₁	—	35	1	no	—
33	D₉₁	—	105	2	no	—
34	C₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
35	D₆₅	—	49	1	no	Hall
36	C₃×C₅×C₇	—	91	1	no	—
37	C₅×ΓL(1,𝔽₈)	—	13	1	no	—
38	C₇⋊D₇	—	65	1	no	Hall
39	C₇×C₁₃	—	3	2	no	—
40	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
41	C₇×C₁₃	C₃×D₃₅	1	1	yes	characteristic, complemented
42	D₁₃⋊C₃	—	245	1	no	Hall
43	D₃₅	—	273	2	no	—
44	D₃₅	—	91	1	no	—
45	D₃₅	—	91	1	no	—
46	C₅×C₁₃	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented, Hall
47	C₇²	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
48	C₃×D₇	—	455	1	no	—
49	AGL(1,𝔽₇)	—	455	1	no	—
50	C₁₃⋊C₃	—	7	1	no	Hall
51	C₅×C₇	—	3	2	no	—
52	C₅×C₇	(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
53	C₅×C₇	#10587722	1	1	yes	characteristic, complemented
54	C₃×D₅	—	637	1	no	Hall
55	D₁₃	—	245	1	no	Hall
56	C₃×C₇	—	91	1	no	—
57	ΓL(1,𝔽₈)	—	13	1	no	—
58	C₃×C₅	—	91	1	no	Hall
59	D₇	—	1365	2	no	—
60	D₇	—	455	1	no	—
61	D₇	—	455	1	no	—
62	C₁₃	C₅⋊(ΓL(1,𝔽₈)⋊D₇)	1	1	yes	characteristic, complemented, Sylow
63	D₅	—	637	1	no	Hall
64	C₇	—	3	2	no	—
65	C₇	C₅⋊((C₁₃⋊C₃)⋊D₇)	1	1	yes	characteristic, complemented
66	C₇	C₅⋊#10587722	1	1	yes	characteristic, complemented
67	C₂×C₃	—	3185	1	no	Hall
68	C₅	#16838468	1	1	yes	characteristic, complemented, Sylow
69	C₃	—	91	1	no	Sylow
70	C₂	—	3185	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×#63270	C₂	semidirect
2. C₅⋊(C₇⋊D₉₁)	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
7. C₇×#63270	D₅	semidirect
9. C₅×#63270	D₇	semidirect
16. C₇²×C₁₃	C₃×D₅	semidirect
21. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
22. C₅×C₇×C₁₃	C₃×D₇	semidirect
25. #63270	D₃₅	semidirect
27. C₅×C₇²	D₁₃⋊C₃	semidirect
40. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
41. C₇×C₁₃	C₃×D₃₅	semidirect
46. C₅×C₁₃	ΓL(1,𝔽₈)⋊D₇	semidirect
47. C₇²	C₅⋊(D₁₃⋊C₃)	semidirect
52. C₅×C₇	(C₁₃⋊C₃)⋊D₇	semidirect
53. C₅×C₇	#10587722	semidirect
62. C₁₃	C₅⋊(ΓL(1,𝔽₈)⋊D₇)	semidirect
65. C₇	C₅⋊((C₁₃⋊C₃)⋊D₇)	semidirect
66. C₇	C₅⋊#10587722	semidirect
68. C₅	#16838468	semidirect

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⋊(C₇⋊D₉₁)	3
#16838468	5
C₅⋊#10587722	7
C₅⋊((C₁₃⋊C₃)⋊D₇)	7
C₅⋊(ΓL(1,𝔽₈)⋊D₇)	13

Subgroups — C5⋊#16838468 #34062151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#16838468 #34062151