Group #50304342 — subgroups

Subgroups — C₃×C₅×C₁₃×D₇² #50304342

Order 38220.

208 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 80 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×C₇×C₁₃×D₇	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×D₇²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×D₇²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₇×C₁₃×D₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₃×C₅×C₁₃×D₇	—	7	2	no	maximal
9	C₃×C₁₃×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₇×C₁₃×D₇	C₂×C₅	1	2	yes	complemented
11	C₅×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×D₇²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×C₁₃×D₇	—	7	2	no	—
14	C₃×C₅×C₁₃×D₇	—	14	3	no	—
15	C₃×C₅×C₁₃×D₇	D₇	1	2	yes	direct product factor
16	C₂×C₃×C₅×C₇×C₁₃	—	7	2	no	—
17	C₁₃×D₇²	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₇²×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₁₃×D₇	—	7	2	no	—
20	C₃×C₅×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₇×D₇	C₂×C₁₃	1	2	yes	complemented
22	C₃×C₅×C₇×C₁₃	—	2	3	no	—
23	C₃×C₅×C₇×C₁₃	C₂×D₇	1	2	yes	complemented
24	C₁₃×C₇⋊D₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
25	C₇×C₁₃×D₇	C₂×C₃×C₅	1	2	yes	complemented
26	C₂×C₃×C₁₃×D₇	—	7	2	no	—
27	C₅×D₇²	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₅×C₇×C₁₃	—	7	2	no	—
29	C₅×C₁₃×D₇	—	7	2	no	—
30	C₅×C₁₃×D₇	—	14	3	no	—
31	C₅×C₁₃×D₇	C₃×D₇	1	2	yes	direct product factor
32	C₂²×C₃×C₅×C₁₃	—	49	1	no	Hall
33	C₃×C₅×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
34	C₇²×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
35	C₃×D₇²	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₇×C₁₃	—	7	2	no	—
37	C₃×C₁₃×D₇	—	7	2	no	—
38	C₃×C₁₃×D₇	—	14	3	no	—
39	C₃×C₁₃×D₇	C₅×D₇	1	2	yes	direct product factor
40	C₅×C₇⋊D₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
41	C₅×C₇×D₇	C₂×C₃×C₁₃	1	2	yes	complemented
42	C₅×C₇×C₁₃	—	2	3	no	—
43	C₅×C₇×C₁₃	C₂×C₃×D₇	1	2	yes	complemented
44	C₂×C₃×C₅×D₇	—	7	2	no	—
45	C₂×C₃×C₅×C₁₃	—	7	2	no	—
46	C₂×C₃×C₅×C₁₃	—	49	1	no	—
47	C₂×C₁₃×D₇	—	7	2	no	—
48	C₃×C₇⋊D₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
49	C₃×C₇×D₇	C₂×C₅×C₁₃	1	2	yes	complemented
50	C₃×C₇×C₁₃	—	2	3	no	—
51	C₃×C₇×C₁₃	C₂×C₅×D₇	1	2	yes	complemented
52	C₂²×C₅×C₁₃	—	49	1	no	Hall
53	C₅×C₇²	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅×C₇	—	7	2	no	—
55	C₃×C₅×D₇	—	7	2	no	—
56	C₃×C₅×D₇	—	14	3	no	—
57	C₃×C₅×D₇	C₁₃×D₇	1	2	yes	direct product factor
58	D₇²	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
59	C₃×C₅×C₁₃	D₇²	1	1	yes	characteristic, direct product factor, Hall
60	C₂×C₇×C₁₃	—	7	2	no	—
61	C₁₃×D₇	—	7	2	no	—
62	C₁₃×D₇	—	14	3	no	—
63	C₁₃×D₇	C₃×C₅×D₇	1	2	yes	direct product factor
64	C₂²×C₃×C₁₃	—	49	1	no	Hall
65	C₃×C₇²	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
66	C₂×C₅×D₇	—	7	2	no	—
67	C₂×C₅×C₁₃	—	7	2	no	—
68	C₂×C₅×C₁₃	—	49	1	no	—
69	C₃×C₅×C₇	—	2	3	no	—
70	C₃×C₅×C₇	C₂×C₁₃×D₇	1	2	yes	complemented
71	C₇⋊D₇	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
72	C₇×D₇	C₂×C₃×C₅×C₁₃	1	2	yes	complemented
73	C₇×C₁₃	—	2	3	no	—
74	C₇×C₁₃	C₂×C₃×C₅×D₇	1	2	yes	complemented
75	C₂×C₃×D₇	—	7	2	no	—
76	C₂×C₃×C₁₃	—	7	2	no	—
77	C₂×C₃×C₁₃	—	49	1	no	—
78	C₂×C₅×C₇	—	7	2	no	—
79	C₅×D₇	—	7	2	no	—
80	C₅×D₇	—	14	3	no	—
81	C₅×D₇	C₃×C₁₃×D₇	1	2	yes	direct product factor
82	C₅×C₁₃	C₃×D₇²	1	1	yes	characteristic, direct product factor, Hall
83	C₂²×C₃×C₅	—	49	1	no	Hall
84	C₂²×C₁₃	—	49	1	no	Hall
85	C₇²	C₂²×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
86	C₂×C₃×C₇	—	7	2	no	—
87	C₃×D₇	—	7	2	no	—
88	C₃×D₇	—	14	3	no	—
89	C₃×D₇	C₅×C₁₃×D₇	1	2	yes	direct product factor
90	C₃×C₁₃	C₅×D₇²	1	1	yes	characteristic, direct product factor, Hall
91	C₅×C₇	—	2	3	no	—
92	C₅×C₇	C₂×C₃×C₁₃×D₇	1	2	yes	complemented
93	C₂×C₃×C₅	—	7	2	no	—
94	C₂×C₃×C₅	—	49	1	no	—
95	C₂×D₇	—	7	2	no	—
96	C₂×C₁₃	—	7	2	no	—
97	C₂×C₁₃	—	49	1	no	—
98	C₃×C₇	—	2	3	no	—
99	C₃×C₇	C₂×C₅×C₁₃×D₇	1	2	yes	complemented
100	C₂²×C₅	—	49	1	no	Hall
101	C₃×C₅	C₁₃×D₇²	1	1	yes	characteristic, direct product factor, Hall
102	C₂×C₇	—	7	2	no	—
103	D₇	—	7	2	no	—
104	D₇	—	14	3	no	—
105	D₇	C₃×C₅×C₁₃×D₇	1	2	yes	direct product factor
106	C₁₃	C₃×C₅×D₇²	1	1	yes	characteristic, direct product factor, Sylow
107	C₂²×C₃	—	49	1	no	Hall
108	C₂×C₅	—	7	2	no	—
109	C₂×C₅	—	49	1	no	—
110	C₇	—	2	3	no	—
111	C₇	C₂×C₃×C₅×C₁₃×D₇	1	2	yes	complemented
112	C₂×C₃	—	7	2	no	—
113	C₂×C₃	—	49	1	no	—
114	C₅	C₃×C₁₃×D₇²	1	1	yes	characteristic, direct product factor, Sylow
115	C₂²	—	49	1	no	Sylow
116	C₃	C₅×C₁₃×D₇²	1	1	yes	characteristic, direct product factor, Sylow
117	C₂	—	7	2	no	—
118	C₂	—	49	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₇×C₁₃×D₇

C₂

yes

maximal, complemented

C₃×C₅×C₁₃×C₇⋊D₇

C₂

yes

maximal, characteristic, complemented

C₅×C₁₃×D₇²

C₃

yes

maximal, characteristic, direct product factor, Hall

C₃×C₅×C₇²×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₃×C₁₃×D₇²

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₃×C₇⋊D₇

C₂×C₃

yes

characteristic, complemented

C₅×C₇×C₁₃×D₇

C₂×C₃

yes

complemented

C₂×C₃×C₅×C₁₃×D₇

—

maximal

C₃×C₁₃×C₇⋊D₇

C₂×C₅

yes

characteristic, complemented

C₃×C₇×C₁₃×D₇

C₂×C₅

yes

complemented

C₅×C₇²×C₁₃

C₂²×C₃

yes

characteristic, complemented, Hall

C₃×C₅×D₇²

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₃×C₅×C₁₃×D₇

—

C₃×C₅×C₁₃×D₇

—

C₃×C₅×C₁₃×D₇

D₇

yes

direct product factor

C₂×C₃×C₅×C₇×C₁₃

—

C₁₃×D₇²

C₃×C₅

yes

characteristic, direct product factor, Hall

C₃×C₇²×C₁₃

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₅×C₁₃×D₇

—

C₃×C₅×C₇⋊D₇

C₂×C₁₃

yes

characteristic, complemented

C₃×C₅×C₇×D₇

C₂×C₁₃

yes

complemented

C₃×C₅×C₇×C₁₃

—

C₃×C₅×C₇×C₁₃

C₂×D₇

yes

complemented

C₁₃×C₇⋊D₇

C₂×C₃×C₅

yes

characteristic, complemented

C₇×C₁₃×D₇

C₂×C₃×C₅

yes

complemented

C₂×C₃×C₁₃×D₇

—

C₅×D₇²

C₃×C₁₃

yes

characteristic, direct product factor, Hall

C₂×C₅×C₇×C₁₃

—

C₅×C₁₃×D₇

—

C₅×C₁₃×D₇

—

C₅×C₁₃×D₇

C₃×D₇

yes

direct product factor

C₂²×C₃×C₅×C₁₃

—

Hall

C₃×C₅×C₇²

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₇²×C₁₃

C₂²×C₃×C₅

yes

characteristic, complemented, Hall

C₃×D₇²

C₅×C₁₃

yes

characteristic, direct product factor, Hall

C₂×C₃×C₇×C₁₃

—

C₃×C₁₃×D₇

—

C₃×C₁₃×D₇

—

C₃×C₁₃×D₇

C₅×D₇

yes

direct product factor

C₅×C₇⋊D₇

C₂×C₃×C₁₃

yes

characteristic, complemented

C₅×C₇×D₇

C₂×C₃×C₁₃

yes

complemented

C₅×C₇×C₁₃

—

C₅×C₇×C₁₃

C₂×C₃×D₇

yes

complemented

C₂×C₃×C₅×D₇

—

C₂×C₃×C₅×C₁₃

—

C₂×C₃×C₅×C₁₃

—

C₂×C₁₃×D₇

—

C₃×C₇⋊D₇

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃×C₇×D₇

C₂×C₅×C₁₃

yes

complemented

C₃×C₇×C₁₃

—

C₃×C₇×C₁₃

C₂×C₅×D₇

yes

complemented

C₂²×C₅×C₁₃

—

Hall

C₅×C₇²

C₂²×C₃×C₁₃

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₇

—

C₃×C₅×D₇

—

C₃×C₅×D₇

—

C₃×C₅×D₇

C₁₃×D₇

yes

direct product factor

D₇²

C₃×C₅×C₁₃

yes

characteristic, direct product factor, Hall

C₃×C₅×C₁₃

D₇²

yes

characteristic, direct product factor, Hall

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

—

C₁₃×D₇

C₃×C₅×D₇

yes

direct product factor

C₂²×C₃×C₁₃

—

Hall

C₃×C₇²

C₂²×C₅×C₁₃

yes

characteristic, complemented, Hall

C₂×C₅×D₇

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂×C₁₃×D₇

yes

complemented

C₇⋊D₇

C₂×C₃×C₅×C₁₃

yes

characteristic, complemented

C₇×D₇

C₂×C₃×C₅×C₁₃

yes

complemented

C₇×C₁₃

—

C₇×C₁₃

C₂×C₃×C₅×D₇

yes

complemented

C₂×C₃×D₇

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

C₂×C₅×C₇

—

C₅×D₇

—

C₅×D₇

—

C₅×D₇

C₃×C₁₃×D₇

yes

direct product factor

C₅×C₁₃

C₃×D₇²

yes

characteristic, direct product factor, Hall

C₂²×C₃×C₅

—

Hall

C₂²×C₁₃

—

Hall

C₇²

C₂²×C₃×C₅×C₁₃

yes

characteristic, complemented, Sylow

C₂×C₃×C₇

—

C₃×D₇

—

C₃×D₇

—

C₃×D₇

C₅×C₁₃×D₇

yes

direct product factor

C₃×C₁₃

C₅×D₇²

yes

characteristic, direct product factor, Hall

C₅×C₇

—

C₅×C₇

C₂×C₃×C₁₃×D₇

yes

complemented

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×D₇

—

C₂×C₁₃

—

C₂×C₁₃

—

C₃×C₇

—

C₃×C₇

C₂×C₅×C₁₃×D₇

yes

complemented

100

C₂²×C₅

—

Hall

101

C₃×C₅

C₁₃×D₇²

yes

characteristic, direct product factor, Hall

102

C₂×C₇

—

103

D₇

—

104

D₇

—

105

D₇

C₃×C₅×C₁₃×D₇

yes

direct product factor

106

C₁₃

C₃×C₅×D₇²

yes

characteristic, direct product factor, Sylow

107

C₂²×C₃

—

Hall

108

C₂×C₅

—

109

C₂×C₅

—

110

C₇

—

111

C₇

C₂×C₃×C₅×C₁₃×D₇

yes

complemented

112

C₂×C₃

—

113

C₂×C₃

—

114

C₅

C₃×C₁₃×D₇²

yes

characteristic, direct product factor, Sylow

115

C₂²

—

Sylow

116

C₃

C₅×C₁₃×D₇²

yes

characteristic, direct product factor, Sylow

117

C₂

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	D₇²
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₅×C₁₃

subgroup

G/H

center, hypercenter

C₃×C₅×C₁₃

D₇²

commutator, cosocle, hypocenter

C₇²

C₂²×C₃×C₅×C₁₃

Frattini

C₁

Fitting, socle

C₃×C₅×C₇²×C₁₃

C₂²

LCS

G ▷ C₇²

UCS

C₁ ◁ C₃×C₅×C₁₃

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₃×D₇	C₂	semidirect
2. C₃×C₅×C₁₃×C₇⋊D₇	C₂	semidirect
3. C₅×C₁₃×D₇²	C₃	direct (N × H)
4. C₃×C₅×C₇²×C₁₃	C₂²	semidirect
5. C₃×C₁₃×D₇²	C₅	direct (N × H)
6. C₅×C₁₃×C₇⋊D₇	C₂×C₃	semidirect
7. C₅×C₇×C₁₃×D₇	C₂×C₃	semidirect
9. C₃×C₁₃×C₇⋊D₇	C₂×C₅	semidirect
10. C₃×C₇×C₁₃×D₇	C₂×C₅	semidirect
11. C₅×C₇²×C₁₃	C₂²×C₃	semidirect
12. C₃×C₅×D₇²	C₁₃	direct (N × H)
15. C₃×C₅×C₁₃×D₇	D₇	direct (N × H)
17. C₁₃×D₇²	C₃×C₅	direct (N × H)
18. C₃×C₇²×C₁₃	C₂²×C₅	semidirect
20. C₃×C₅×C₇⋊D₇	C₂×C₁₃	semidirect
21. C₃×C₅×C₇×D₇	C₂×C₁₃	semidirect
23. C₃×C₅×C₇×C₁₃	C₂×D₇	semidirect
24. C₁₃×C₇⋊D₇	C₂×C₃×C₅	semidirect
25. C₇×C₁₃×D₇	C₂×C₃×C₅	semidirect
27. C₅×D₇²	C₃×C₁₃	direct (N × H)
31. C₅×C₁₃×D₇	C₃×D₇	direct (N × H)
33. C₃×C₅×C₇²	C₂²×C₁₃	semidirect
34. C₇²×C₁₃	C₂²×C₃×C₅	semidirect
35. C₃×D₇²	C₅×C₁₃	direct (N × H)
39. C₃×C₁₃×D₇	C₅×D₇	direct (N × H)
40. C₅×C₇⋊D₇	C₂×C₃×C₁₃	semidirect
41. C₅×C₇×D₇	C₂×C₃×C₁₃	semidirect
43. C₅×C₇×C₁₃	C₂×C₃×D₇	semidirect
48. C₃×C₇⋊D₇	C₂×C₅×C₁₃	semidirect
49. C₃×C₇×D₇	C₂×C₅×C₁₃	semidirect
51. C₃×C₇×C₁₃	C₂×C₅×D₇	semidirect
53. C₅×C₇²	C₂²×C₃×C₁₃	semidirect
57. C₃×C₅×D₇	C₁₃×D₇	direct (N × H)
58. D₇²	C₃×C₅×C₁₃	direct (N × H)
59. C₃×C₅×C₁₃	D₇²	direct (N × H)
63. C₁₃×D₇	C₃×C₅×D₇	direct (N × H)
65. C₃×C₇²	C₂²×C₅×C₁₃	semidirect
70. C₃×C₅×C₇	C₂×C₁₃×D₇	semidirect
71. C₇⋊D₇	C₂×C₃×C₅×C₁₃	semidirect
72. C₇×D₇	C₂×C₃×C₅×C₁₃	semidirect
74. C₇×C₁₃	C₂×C₃×C₅×D₇	semidirect
81. C₅×D₇	C₃×C₁₃×D₇	direct (N × H)
82. C₅×C₁₃	C₃×D₇²	direct (N × H)
85. C₇²	C₂²×C₃×C₅×C₁₃	semidirect
89. C₃×D₇	C₅×C₁₃×D₇	direct (N × H)
90. C₃×C₁₃	C₅×D₇²	direct (N × H)
92. C₅×C₇	C₂×C₃×C₁₃×D₇	semidirect
99. C₃×C₇	C₂×C₅×C₁₃×D₇	semidirect
101. C₃×C₅	C₁₃×D₇²	direct (N × H)
105. D₇	C₃×C₅×C₁₃×D₇	direct (N × H)
106. C₁₃	C₃×C₅×D₇²	direct (N × H)
111. C₇	C₂×C₃×C₅×C₁₃×D₇	semidirect
114. C₅	C₃×C₁₃×D₇²	direct (N × H)
116. C₃	C₅×C₁₃×D₇²	direct (N × H)

H ≅ G/N

type

1. C₃×C₅×C₇×C₁₃×D₇

C₂

semidirect

2. C₃×C₅×C₁₃×C₇⋊D₇

C₂

semidirect

3. C₅×C₁₃×D₇²

C₃

direct (N × H)

4. C₃×C₅×C₇²×C₁₃

C₂²

semidirect

5. C₃×C₁₃×D₇²

C₅

direct (N × H)

6. C₅×C₁₃×C₇⋊D₇

C₂×C₃

semidirect

7. C₅×C₇×C₁₃×D₇

C₂×C₃

semidirect

9. C₃×C₁₃×C₇⋊D₇

C₂×C₅

semidirect

10. C₃×C₇×C₁₃×D₇

C₂×C₅

semidirect

11. C₅×C₇²×C₁₃

C₂²×C₃

semidirect

12. C₃×C₅×D₇²

C₁₃

direct (N × H)

15. C₃×C₅×C₁₃×D₇

D₇

direct (N × H)

17. C₁₃×D₇²

C₃×C₅

direct (N × H)

18. C₃×C₇²×C₁₃

C₂²×C₅

semidirect

20. C₃×C₅×C₇⋊D₇

C₂×C₁₃

semidirect

21. C₃×C₅×C₇×D₇

C₂×C₁₃

semidirect

23. C₃×C₅×C₇×C₁₃

C₂×D₇

semidirect

24. C₁₃×C₇⋊D₇

C₂×C₃×C₅

semidirect

25. C₇×C₁₃×D₇

C₂×C₃×C₅

semidirect

27. C₅×D₇²

C₃×C₁₃

direct (N × H)

31. C₅×C₁₃×D₇

C₃×D₇

direct (N × H)

33. C₃×C₅×C₇²

C₂²×C₁₃

semidirect

34. C₇²×C₁₃

C₂²×C₃×C₅

semidirect

35. C₃×D₇²

C₅×C₁₃

direct (N × H)

39. C₃×C₁₃×D₇

C₅×D₇

direct (N × H)

40. C₅×C₇⋊D₇

C₂×C₃×C₁₃

semidirect

41. C₅×C₇×D₇

C₂×C₃×C₁₃

semidirect

43. C₅×C₇×C₁₃

C₂×C₃×D₇

semidirect

48. C₃×C₇⋊D₇

C₂×C₅×C₁₃

semidirect

49. C₃×C₇×D₇

C₂×C₅×C₁₃

semidirect

51. C₃×C₇×C₁₃

C₂×C₅×D₇

semidirect

53. C₅×C₇²

C₂²×C₃×C₁₃

semidirect

57. C₃×C₅×D₇

C₁₃×D₇

direct (N × H)

58. D₇²

C₃×C₅×C₁₃

direct (N × H)

59. C₃×C₅×C₁₃

D₇²

direct (N × H)

63. C₁₃×D₇

C₃×C₅×D₇

direct (N × H)

65. C₃×C₇²

C₂²×C₅×C₁₃

semidirect

70. C₃×C₅×C₇

C₂×C₁₃×D₇

semidirect

71. C₇⋊D₇

C₂×C₃×C₅×C₁₃

semidirect

72. C₇×D₇

C₂×C₃×C₅×C₁₃

semidirect

74. C₇×C₁₃

C₂×C₃×C₅×D₇

semidirect

81. C₅×D₇

C₃×C₁₃×D₇

direct (N × H)

82. C₅×C₁₃

C₃×D₇²

direct (N × H)

85. C₇²

C₂²×C₃×C₅×C₁₃

semidirect

89. C₃×D₇

C₅×C₁₃×D₇

direct (N × H)

90. C₃×C₁₃

C₅×D₇²

direct (N × H)

92. C₅×C₇

C₂×C₃×C₁₃×D₇

semidirect

99. C₃×C₇

C₂×C₅×C₁₃×D₇

semidirect

101. C₃×C₅

C₁₃×D₇²

direct (N × H)

105. D₇

C₃×C₅×C₁₃×D₇

direct (N × H)

106. C₁₃

C₃×C₅×D₇²

direct (N × H)

111. C₇

C₂×C₃×C₅×C₁₃×D₇

semidirect

114. C₅

C₃×C₁₃×D₇²

direct (N × H)

116. C₃

C₅×C₁₃×D₇²

direct (N × H)

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

subgroup	index
C₃×C₅×C₇×C₁₃×D₇	2
C₃×C₅×C₁₃×C₇⋊D₇	2
C₅×C₁₃×D₇²	3
C₃×C₁₃×D₇²	5
C₂×C₃×C₅×C₁₃×D₇	7
C₃×C₅×D₇²	13

subgroup

index

C₃×C₅×C₇×C₁₃×D₇

C₃×C₅×C₁₃×C₇⋊D₇

C₅×C₁₃×D₇²

C₃×C₁₃×D₇²

C₂×C₃×C₅×C₁₃×D₇

C₃×C₅×D₇²

Subgroups — C₃×C₅×C₁₃×D₇² #50304342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×C5×C13×D72 #50304342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₃×D₇² #50304342