Group #50304407 — subgroups

Subgroups — C₅×D₃×C₁₃×C₇⋊D₇ #50304407

Order 38220.

400 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₁₃×C₇⋊D₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₃×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×C₇⋊D₇	—	3	1	no	—
8	C₅×C₁₃×C₇⋊D₇	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₇²×C₁₃	—	3	1	no	—
10	C₅×D₃×C₁₃×D₇	—	7	8	no	maximal
11	C₁₃×C₃⋊(C₇⋊D₇)	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₇²×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×C₁₃×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₃×C₇⋊D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅×C₁₃×D₂₁	—	7	8	no	—
17	C₅×D₃×C₇×C₁₃	D₇	1	8	yes	complemented
18	C₃×C₅×C₁₃×D₇	—	7	8	no	—
19	C₂×C₁₃×C₇⋊D₇	—	3	1	no	Hall
20	C₃×C₇²×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₁₃×D₇	—	21	8	no	—
22	C₅×C₃⋊(C₇⋊D₇)	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₅×D₃×C₇²	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₃×C₅×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₃×C₅×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
26	C₂×C₇²×C₁₃	—	3	1	no	—
27	C₁₃×C₇⋊D₇	—	3	1	no	—
28	C₁₃×C₇⋊D₇	C₅×D₃	1	1	yes	characteristic, direct product factor
29	D₃×C₁₃×D₇	—	7	8	no	—
30	C₂×C₅×C₇⋊D₇	—	3	1	no	Hall
31	C₂×C₅×C₇×C₁₃	—	3	8	no	—
32	C₅×C₁₃×D₇	—	7	8	no	—
33	C₅×C₁₃×D₇	—	21	8	no	—
34	C₂×C₅×D₃×C₁₃	—	49	1	no	Hall
35	C₃×C₅×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
36	C₇²×C₁₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
37	D₃×C₇⋊D₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
38	C₁₃×D₂₁	—	7	8	no	—
39	D₃×C₇×C₁₃	C₅×D₇	1	8	yes	complemented
40	C₃×C₁₃×D₇	—	7	8	no	—
41	C₂×C₅×C₇²	—	3	1	no	—
42	C₅×C₇⋊D₇	—	3	1	no	—
43	C₅×C₇⋊D₇	D₃×C₁₃	1	1	yes	characteristic, direct product factor
44	C₅×C₇×C₁₃	D₃×D₇	1	8	yes	complemented
45	C₅×D₃×D₇	—	7	8	no	—
46	C₂×C₃×C₅×C₁₃	—	49	1	no	—
47	C₅×D₃×C₁₃	—	49	1	no	—
48	C₅×D₃×C₁₃	C₇⋊D₇	1	1	yes	characteristic, direct product factor
49	C₂×C₁₃×D₇	—	21	8	no	—
50	C₃⋊(C₇⋊D₇)	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
51	D₃×C₇²	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
52	C₃×C₇⋊D₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
53	C₃×C₇×C₁₃	C₂×C₅×D₇	1	8	yes	complemented
54	C₂²×C₅×C₁₃	—	147	1	no	Hall
55	C₅×C₇²	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
56	C₅×D₂₁	—	7	8	no	—
57	C₅×D₃×C₇	C₁₃×D₇	1	8	yes	complemented
58	C₃×C₅×D₇	—	7	8	no	—
59	C₂×C₇⋊D₇	—	3	1	no	Hall
60	C₃×C₅×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
61	C₂×C₇×C₁₃	—	3	8	no	—
62	C₁₃×D₇	—	7	8	no	—
63	C₁₃×D₇	—	21	8	no	—
64	C₂×D₃×C₁₃	—	49	1	no	Hall
65	C₃×C₇²	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
66	C₂×C₅×D₇	—	21	8	no	—
67	C₂×C₅×C₁₃	—	3	1	no	—
68	C₂×C₅×C₁₃	—	49	1	no	—
69	C₂×C₅×C₁₃	—	147	1	no	—
70	C₃×C₅×C₇	C₂×C₁₃×D₇	1	8	yes	complemented
71	C₂×C₇²	—	3	1	no	—
72	C₇⋊D₇	—	3	1	no	—
73	C₇⋊D₇	C₅×D₃×C₁₃	1	1	yes	characteristic, direct product factor
74	C₇×C₁₃	C₅×D₃×D₇	1	8	yes	complemented
75	D₃×D₇	—	7	8	no	—
76	C₂×C₃×C₁₃	—	49	1	no	—
77	D₃×C₁₃	—	49	1	no	—
78	D₃×C₁₃	C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor
79	C₂×C₅×C₇	—	3	8	no	—
80	C₅×D₇	—	7	8	no	—
81	C₅×D₇	—	21	8	no	—
82	C₅×C₁₃	D₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
83	C₂×C₅×D₃	—	49	1	no	Hall
84	C₂²×C₁₃	—	147	1	no	Hall
85	C₇²	C₂×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
86	D₂₁	—	7	8	no	—
87	C₃×D₇	—	7	8	no	—
88	D₃×C₇	C₅×C₁₃×D₇	1	8	yes	complemented
89	C₃×C₁₃	C₂×C₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
90	C₅×C₇	D₃×C₁₃×D₇	1	8	yes	complemented
91	C₂×C₃×C₅	—	49	1	no	—
92	C₅×D₃	—	49	1	no	—
93	C₅×D₃	C₁₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor
94	C₂×D₇	—	21	8	no	—
95	C₂×C₁₃	—	3	1	no	—
96	C₂×C₁₃	—	49	1	no	—
97	C₂×C₁₃	—	147	1	no	—
98	C₃×C₇	C₂×C₅×C₁₃×D₇	1	8	yes	complemented
99	C₂²×C₅	—	147	1	no	Hall
100	C₃×C₅	C₂×C₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
101	C₂×C₇	—	3	8	no	—
102	D₇	—	7	8	no	—
103	D₇	—	21	8	no	—
104	C₁₃	C₅×D₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
105	C₂×D₃	—	49	1	no	Hall
106	C₂×C₅	—	3	1	no	—
107	C₂×C₅	—	49	1	no	—
108	C₂×C₅	—	147	1	no	—
109	C₇	C₅×D₃×C₁₃×D₇	1	8	yes	complemented
110	C₂×C₃	—	49	1	no	—
111	D₃	—	49	1	no	—
112	D₃	C₅×C₁₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor
113	C₅	D₃×C₁₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²	—	147	1	no	Sylow
115	C₃	C₂×C₅×C₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
116	C₂	—	3	1	no	—
117	C₂	—	49	1	no	—
118	C₂	—	147	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₁₃×C₇⋊D₇

C₂

yes

maximal, characteristic, complemented

C₅×D₃×C₇²×C₁₃

C₂

yes

maximal, characteristic, complemented

C₅×C₁₃×C₃⋊(C₇⋊D₇)

C₂

yes

maximal, characteristic, complemented

C₂×C₅×C₁₃×C₇⋊D₇

—

maximal, Hall

C₃×C₅×C₇²×C₁₃

C₂²

yes

characteristic, complemented, Hall

D₃×C₁₃×C₇⋊D₇

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₃×C₇⋊D₇

—

C₅×C₁₃×C₇⋊D₇

D₃

yes

characteristic, direct product factor

C₂×C₅×C₇²×C₁₃

—

C₅×D₃×C₁₃×D₇

—

maximal

C₁₃×C₃⋊(C₇⋊D₇)

C₂×C₅

yes

characteristic, complemented

D₃×C₇²×C₁₃

C₂×C₅

yes

characteristic, complemented

C₃×C₁₃×C₇⋊D₇

C₂×C₅

yes

characteristic, complemented

C₅×C₇²×C₁₃

C₂×D₃

yes

characteristic, complemented, Hall

C₅×D₃×C₇⋊D₇

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₃×D₂₁

—

C₅×D₃×C₇×C₁₃

D₇

yes

complemented

C₃×C₅×C₁₃×D₇

—

C₂×C₁₃×C₇⋊D₇

—

Hall

C₃×C₇²×C₁₃

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₅×C₁₃×D₇

—

C₅×C₃⋊(C₇⋊D₇)

C₂×C₁₃

yes

characteristic, complemented

C₅×D₃×C₇²

C₂×C₁₃

yes

characteristic, complemented

C₃×C₅×C₇⋊D₇

C₂×C₁₃

yes

characteristic, complemented

C₃×C₅×C₇×C₁₃

C₂×D₇

yes

complemented

C₂×C₇²×C₁₃

—

C₁₃×C₇⋊D₇

—

C₁₃×C₇⋊D₇

C₅×D₃

yes

characteristic, direct product factor

D₃×C₁₃×D₇

—

C₂×C₅×C₇⋊D₇

—

Hall

C₂×C₅×C₇×C₁₃

—

C₅×C₁₃×D₇

—

C₅×C₁₃×D₇

—

C₂×C₅×D₃×C₁₃

—

Hall

C₃×C₅×C₇²

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₇²×C₁₃

C₂×C₅×D₃

yes

characteristic, complemented, Hall

D₃×C₇⋊D₇

C₅×C₁₃

yes

characteristic, direct product factor, Hall

C₁₃×D₂₁

—

D₃×C₇×C₁₃

C₅×D₇

yes

complemented

C₃×C₁₃×D₇

—

C₂×C₅×C₇²

—

C₅×C₇⋊D₇

—

C₅×C₇⋊D₇

D₃×C₁₃

yes

characteristic, direct product factor

C₅×C₇×C₁₃

D₃×D₇

yes

complemented

C₅×D₃×D₇

—

C₂×C₃×C₅×C₁₃

—

C₅×D₃×C₁₃

—

C₅×D₃×C₁₃

C₇⋊D₇

yes

characteristic, direct product factor

C₂×C₁₃×D₇

—

C₃⋊(C₇⋊D₇)

C₂×C₅×C₁₃

yes

characteristic, complemented

D₃×C₇²

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃×C₇⋊D₇

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃×C₇×C₁₃

C₂×C₅×D₇

yes

complemented

C₂²×C₅×C₁₃

—

147

Hall

C₅×C₇²

C₂×D₃×C₁₃

yes

characteristic, complemented, Hall

C₅×D₂₁

—

C₅×D₃×C₇

C₁₃×D₇

yes

complemented

C₃×C₅×D₇

—

C₂×C₇⋊D₇

—

Hall

C₃×C₅×C₁₃

C₂×C₇⋊D₇

yes

characteristic, complemented, Hall

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

—

C₂×D₃×C₁₃

—

Hall

C₃×C₇²

C₂²×C₅×C₁₃

yes

characteristic, complemented, Hall

C₂×C₅×D₇

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

147

—

C₃×C₅×C₇

C₂×C₁₃×D₇

yes

complemented

C₂×C₇²

—

C₇⋊D₇

—

C₇⋊D₇

C₅×D₃×C₁₃

yes

characteristic, direct product factor

C₇×C₁₃

C₅×D₃×D₇

yes

complemented

D₃×D₇

—

C₂×C₃×C₁₃

—

D₃×C₁₃

—

D₃×C₁₃

C₅×C₇⋊D₇

yes

characteristic, direct product factor

C₂×C₅×C₇

—

C₅×D₇

—

C₅×D₇

—

C₅×C₁₃

D₃×C₇⋊D₇

yes

characteristic, direct product factor, Hall

C₂×C₅×D₃

—

Hall

C₂²×C₁₃

—

147

Hall

C₇²

C₂×C₅×D₃×C₁₃

yes

characteristic, complemented, Sylow

D₂₁

—

C₃×D₇

—

D₃×C₇

C₅×C₁₃×D₇

yes

complemented

C₃×C₁₃

C₂×C₅×C₇⋊D₇

yes

characteristic, complemented, Hall

C₅×C₇

D₃×C₁₃×D₇

yes

complemented

C₂×C₃×C₅

—

C₅×D₃

—

C₅×D₃

C₁₃×C₇⋊D₇

yes

characteristic, direct product factor

C₂×D₇

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

—

147

—

C₃×C₇

C₂×C₅×C₁₃×D₇

yes

complemented

C₂²×C₅

—

147

Hall

100

C₃×C₅

C₂×C₁₃×C₇⋊D₇

yes

characteristic, complemented, Hall

101

C₂×C₇

—

102

D₇

—

103

D₇

—

104

C₁₃

C₅×D₃×C₇⋊D₇

yes

characteristic, direct product factor, Sylow

105

C₂×D₃

—

Hall

106

C₂×C₅

—

107

C₂×C₅

—

108

C₂×C₅

—

147

—

109

C₇

C₅×D₃×C₁₃×D₇

yes

complemented

110

C₂×C₃

—

111

D₃

—

112

D₃

C₅×C₁₃×C₇⋊D₇

yes

characteristic, direct product factor

113

C₅

D₃×C₁₃×C₇⋊D₇

yes

characteristic, direct product factor, Sylow

114

C₂²

—

147

Sylow

115

C₃

C₂×C₅×C₁₃×C₇⋊D₇

yes

characteristic, complemented, Sylow

116

C₂

—

117

C₂

—

118

C₂

—

147

—

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₃×C₇⋊D₇
commutator, cosocle, hypocenter	C₃×C₇²	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₅×C₁₃

subgroup

G/H

center, hypercenter

C₅×C₁₃

D₃×C₇⋊D₇

commutator, cosocle, hypocenter

C₃×C₇²

C₂²×C₅×C₁₃

Frattini

C₁

Fitting, socle

C₃×C₅×C₇²×C₁₃

C₂²

LCS

G ▷ C₃×C₇²

UCS

C₁ ◁ C₅×C₁₃

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×C₇⋊D₇	C₂	semidirect
2. C₅×D₃×C₇²×C₁₃	C₂	semidirect
3. C₅×C₁₃×C₃⋊(C₇⋊D₇)	C₂	semidirect
5. C₃×C₅×C₇²×C₁₃	C₂²	semidirect
6. D₃×C₁₃×C₇⋊D₇	C₅	direct (N × H)
8. C₅×C₁₃×C₇⋊D₇	D₃	direct (N × H)
11. C₁₃×C₃⋊(C₇⋊D₇)	C₂×C₅	semidirect
12. D₃×C₇²×C₁₃	C₂×C₅	semidirect
13. C₃×C₁₃×C₇⋊D₇	C₂×C₅	semidirect
14. C₅×C₇²×C₁₃	C₂×D₃	semidirect
15. C₅×D₃×C₇⋊D₇	C₁₃	direct (N × H)
17. C₅×D₃×C₇×C₁₃	D₇	semidirect
20. C₃×C₇²×C₁₃	C₂²×C₅	semidirect
22. C₅×C₃⋊(C₇⋊D₇)	C₂×C₁₃	semidirect
23. C₅×D₃×C₇²	C₂×C₁₃	semidirect
24. C₃×C₅×C₇⋊D₇	C₂×C₁₃	semidirect
25. C₃×C₅×C₇×C₁₃	C₂×D₇	semidirect
28. C₁₃×C₇⋊D₇	C₅×D₃	direct (N × H)
35. C₃×C₅×C₇²	C₂²×C₁₃	semidirect
36. C₇²×C₁₃	C₂×C₅×D₃	semidirect
37. D₃×C₇⋊D₇	C₅×C₁₃	direct (N × H)
39. D₃×C₇×C₁₃	C₅×D₇	semidirect
43. C₅×C₇⋊D₇	D₃×C₁₃	direct (N × H)
44. C₅×C₇×C₁₃	D₃×D₇	semidirect
48. C₅×D₃×C₁₃	C₇⋊D₇	direct (N × H)
50. C₃⋊(C₇⋊D₇)	C₂×C₅×C₁₃	semidirect
51. D₃×C₇²	C₂×C₅×C₁₃	semidirect
52. C₃×C₇⋊D₇	C₂×C₅×C₁₃	semidirect
53. C₃×C₇×C₁₃	C₂×C₅×D₇	semidirect
55. C₅×C₇²	C₂×D₃×C₁₃	semidirect
57. C₅×D₃×C₇	C₁₃×D₇	semidirect
60. C₃×C₅×C₁₃	C₂×C₇⋊D₇	semidirect
65. C₃×C₇²	C₂²×C₅×C₁₃	semidirect
70. C₃×C₅×C₇	C₂×C₁₃×D₇	semidirect
73. C₇⋊D₇	C₅×D₃×C₁₃	direct (N × H)
74. C₇×C₁₃	C₅×D₃×D₇	semidirect
78. D₃×C₁₃	C₅×C₇⋊D₇	direct (N × H)
82. C₅×C₁₃	D₃×C₇⋊D₇	direct (N × H)
85. C₇²	C₂×C₅×D₃×C₁₃	semidirect
88. D₃×C₇	C₅×C₁₃×D₇	semidirect
89. C₃×C₁₃	C₂×C₅×C₇⋊D₇	semidirect
90. C₅×C₇	D₃×C₁₃×D₇	semidirect
93. C₅×D₃	C₁₃×C₇⋊D₇	direct (N × H)
98. C₃×C₇	C₂×C₅×C₁₃×D₇	semidirect
100. C₃×C₅	C₂×C₁₃×C₇⋊D₇	semidirect
104. C₁₃	C₅×D₃×C₇⋊D₇	direct (N × H)
109. C₇	C₅×D₃×C₁₃×D₇	semidirect
112. D₃	C₅×C₁₃×C₇⋊D₇	direct (N × H)
113. C₅	D₃×C₁₃×C₇⋊D₇	direct (N × H)
115. C₃	C₂×C₅×C₁₃×C₇⋊D₇	semidirect

H ≅ G/N

type

1. C₃×C₅×C₁₃×C₇⋊D₇

C₂

semidirect

2. C₅×D₃×C₇²×C₁₃

C₂

semidirect

3. C₅×C₁₃×C₃⋊(C₇⋊D₇)

C₂

semidirect

5. C₃×C₅×C₇²×C₁₃

C₂²

semidirect

6. D₃×C₁₃×C₇⋊D₇

C₅

direct (N × H)

8. C₅×C₁₃×C₇⋊D₇

D₃

direct (N × H)

11. C₁₃×C₃⋊(C₇⋊D₇)

C₂×C₅

semidirect

12. D₃×C₇²×C₁₃

C₂×C₅

semidirect

13. C₃×C₁₃×C₇⋊D₇

C₂×C₅

semidirect

14. C₅×C₇²×C₁₃

C₂×D₃

semidirect

15. C₅×D₃×C₇⋊D₇

C₁₃

direct (N × H)

17. C₅×D₃×C₇×C₁₃

D₇

semidirect

20. C₃×C₇²×C₁₃

C₂²×C₅

semidirect

22. C₅×C₃⋊(C₇⋊D₇)

C₂×C₁₃

semidirect

23. C₅×D₃×C₇²

C₂×C₁₃

semidirect

24. C₃×C₅×C₇⋊D₇

C₂×C₁₃

semidirect

25. C₃×C₅×C₇×C₁₃

C₂×D₇

semidirect

28. C₁₃×C₇⋊D₇

C₅×D₃

direct (N × H)

35. C₃×C₅×C₇²

C₂²×C₁₃

semidirect

36. C₇²×C₁₃

C₂×C₅×D₃

semidirect

37. D₃×C₇⋊D₇

C₅×C₁₃

direct (N × H)

39. D₃×C₇×C₁₃

C₅×D₇

semidirect

43. C₅×C₇⋊D₇

D₃×C₁₃

direct (N × H)

44. C₅×C₇×C₁₃

D₃×D₇

semidirect

48. C₅×D₃×C₁₃

C₇⋊D₇

direct (N × H)

50. C₃⋊(C₇⋊D₇)

C₂×C₅×C₁₃

semidirect

51. D₃×C₇²

C₂×C₅×C₁₃

semidirect

52. C₃×C₇⋊D₇

C₂×C₅×C₁₃

semidirect

53. C₃×C₇×C₁₃

C₂×C₅×D₇

semidirect

55. C₅×C₇²

C₂×D₃×C₁₃

semidirect

57. C₅×D₃×C₇

C₁₃×D₇

semidirect

60. C₃×C₅×C₁₃

C₂×C₇⋊D₇

semidirect

65. C₃×C₇²

C₂²×C₅×C₁₃

semidirect

70. C₃×C₅×C₇

C₂×C₁₃×D₇

semidirect

73. C₇⋊D₇

C₅×D₃×C₁₃

direct (N × H)

74. C₇×C₁₃

C₅×D₃×D₇

semidirect

78. D₃×C₁₃

C₅×C₇⋊D₇

direct (N × H)

82. C₅×C₁₃

D₃×C₇⋊D₇

direct (N × H)

85. C₇²

C₂×C₅×D₃×C₁₃

semidirect

88. D₃×C₇

C₅×C₁₃×D₇

semidirect

89. C₃×C₁₃

C₂×C₅×C₇⋊D₇

semidirect

90. C₅×C₇

D₃×C₁₃×D₇

semidirect

93. C₅×D₃

C₁₃×C₇⋊D₇

direct (N × H)

98. C₃×C₇

C₂×C₅×C₁₃×D₇

semidirect

100. C₃×C₅

C₂×C₁₃×C₇⋊D₇

semidirect

104. C₁₃

C₅×D₃×C₇⋊D₇

direct (N × H)

109. C₇

C₅×D₃×C₁₃×D₇

semidirect

112. D₃

C₅×C₁₃×C₇⋊D₇

direct (N × H)

113. C₅

D₃×C₁₃×C₇⋊D₇

direct (N × H)

115. C₃

C₂×C₅×C₁₃×C₇⋊D₇

semidirect

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

subgroup	index
C₃×C₅×C₁₃×C₇⋊D₇	2
C₅×D₃×C₇²×C₁₃	2
C₅×C₁₃×C₃⋊(C₇⋊D₇)	2
C₂×C₅×C₁₃×C₇⋊D₇	3
D₃×C₁₃×C₇⋊D₇	5
C₅×D₃×C₁₃×D₇	7
C₅×D₃×C₇⋊D₇	13

subgroup

index

C₃×C₅×C₁₃×C₇⋊D₇

C₅×D₃×C₇²×C₁₃

C₅×C₁₃×C₃⋊(C₇⋊D₇)

C₂×C₅×C₁₃×C₇⋊D₇

D₃×C₁₃×C₇⋊D₇

C₅×D₃×C₁₃×D₇

C₅×D₃×C₇⋊D₇

Subgroups — C₅×D₃×C₁₃×C₇⋊D₇ #50304407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D3×C13×C7⋊D7 #50304407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₃×C₇⋊D₇ #50304407