Subgroups — C₅⋊#16838449 #34062132

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274262	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₅⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838449	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊#10587721	—	7	1	no	maximal
6	C₅⋊#10587721	—	7	1	no	maximal
7	C₅⋊#10587721	—	7	1	no	maximal
8	C₅⋊#10587721	—	7	5	no	maximal
9	#14274262	D₅	1	1	yes	characteristic, complemented, Hall
10	C₅⋊#64424	—	13	1	no	maximal, Hall
11	C₅×#63271	—	7	1	no	—
12	C₅×#63271	—	7	1	no	—
13	C₅×#63271	—	7	1	no	—
14	C₅×#63271	—	7	5	no	—
15	C₁₃×C₇⋊D₇	—	5	1	no	Hall
16	C₁₃×D₃₅	—	7	1	no	—
17	C₁₃×D₃₅	—	7	1	no	—
18	C₁₃×D₃₅	—	21	1	no	—
19	C₁₃×D₃₅	—	21	5	no	—
20	C₅×#3861	—	13	1	no	Hall
21	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
22	#10587721	—	35	1	no	—
23	#10587721	—	35	1	no	—
24	#10587721	—	35	1	no	—
25	#10587721	—	35	5	no	—
26	C₅⋊(C₇⋊D₇)	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
28	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
29	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
30	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	5	yes	complemented
31	D₅×C₁₃⋊C₃	—	49	1	no	Hall
32	#64424	—	65	1	no	Hall
33	#63271	—	7	1	no	—
34	#63271	—	7	1	no	—
35	#63271	—	7	1	no	—
36	#63271	—	7	5	no	—
37	C₅×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
38	C₅⋊AGL(1,𝔽₇)	—	91	1	no	—
39	C₅⋊AGL(1,𝔽₇)	—	91	1	no	—
40	C₅⋊AGL(1,𝔽₇)	—	91	1	no	—
41	C₅⋊AGL(1,𝔽₇)	—	91	5	no	—
42	C₅×C₁₃⋊C₃	—	49	1	no	Hall
43	C₁₃×D₇	—	35	1	no	—
44	C₁₃×D₇	—	35	1	no	—
45	C₁₃×D₇	—	105	1	no	—
46	C₁₃×D₇	—	105	5	no	—
47	#3861	—	13	1	no	Hall
48	D₅×C₁₃	—	147	1	no	Hall
49	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
50	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
51	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
52	C₅×ΓL(1,𝔽₈)	—	91	5	no	—
53	C₇⋊D₇	—	5	1	no	Hall
54	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
55	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
56	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
57	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	5	yes	complemented
58	C₂×C₁₃⋊C₃	—	245	1	no	Hall
59	D₃₅	—	7	1	no	—
60	D₃₅	—	21	1	no	—
61	D₃₅	—	21	1	no	—
62	D₃₅	—	21	5	no	—
63	C₅×C₁₃	#64424	1	1	yes	characteristic, complemented, Hall
64	C₇²	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	AGL(1,𝔽₇)	—	455	1	no	—
66	AGL(1,𝔽₇)	—	455	1	no	—
67	AGL(1,𝔽₇)	—	455	1	no	—
68	AGL(1,𝔽₇)	—	455	5	no	—
69	C₁₃⋊C₃	—	49	1	no	Hall
70	C₅×C₇	#10587721	1	1	yes	characteristic, complemented
71	C₅×C₇	#10587721	1	1	yes	characteristic, complemented
72	C₅×C₇	#10587721	1	1	yes	characteristic, complemented
73	C₅×C₇	#10587721	1	5	yes	complemented
74	C₃×D₅	—	637	1	no	Hall
75	C₂×C₁₃	—	735	1	no	Hall
76	ΓL(1,𝔽₈)	—	91	1	no	—
77	ΓL(1,𝔽₈)	—	91	1	no	—
78	ΓL(1,𝔽₈)	—	91	1	no	—
79	ΓL(1,𝔽₈)	—	91	5	no	—
80	C₃×C₅	—	637	1	no	Hall
81	D₇	—	105	1	no	—
82	D₇	—	105	1	no	—
83	D₇	—	105	1	no	—
84	D₇	—	105	5	no	—
85	C₁₃	C₅⋊#64424	1	1	yes	characteristic, complemented, Sylow
86	D₅	—	147	1	no	Hall
87	C₇	C₅⋊#10587721	1	1	yes	characteristic, complemented
88	C₇	C₅⋊#10587721	1	1	yes	characteristic, complemented
89	C₇	C₅⋊#10587721	1	1	yes	characteristic, complemented
90	C₇	C₅⋊#10587721	1	5	yes	complemented
91	C₂×C₃	—	3185	1	no	Hall
92	C₅	#16838449	1	1	yes	characteristic, complemented, Sylow
93	C₃	—	637	1	no	Sylow
94	C₂	—	735	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×#14274262	C₂	semidirect
2. C₁₃×C₅⋊(C₇⋊D₇)	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
9. #14274262	D₅	semidirect
21. C₇²×C₁₃	C₃×D₅	semidirect
26. C₅⋊(C₇⋊D₇)	C₁₃⋊C₃	semidirect
27. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
28. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
29. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
30. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
37. C₅×C₇²	C₂×C₁₃⋊C₃	semidirect
54. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
55. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
56. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
57. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
63. C₅×C₁₃	#64424	semidirect
64. C₇²	D₅×C₁₃⋊C₃	semidirect
70. C₅×C₇	#10587721	semidirect
71. C₅×C₇	#10587721	semidirect
72. C₅×C₇	#10587721	semidirect
73. C₅×C₇	#10587721	semidirect
85. C₁₃	C₅⋊#64424	semidirect
87. C₇	C₅⋊#10587721	semidirect
88. C₇	C₅⋊#10587721	semidirect
89. C₇	C₅⋊#10587721	semidirect
90. C₇	C₅⋊#10587721	semidirect
92. C₅	#16838449	semidirect

Maximal subgroups

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

subgroup	index
C₅×#14274262	2
C₁₃×C₅⋊(C₇⋊D₇)	3
#16838449	5
C₅⋊#10587721	7
C₅⋊#64424	13

Subgroups — C5⋊#16838449 #34062132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#16838449 #34062132