Group #30655678 — subgroups

Subgroups — C₅×C₁₃×D₇×C₃⋊D₃ #30655678

Order 16380.

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 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	C₅×C₁₃×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×C₁₃×D₇	—	3	4	no	maximal
5	C₃²×C₅×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₇×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×D₂₁	—	3	4	no	—
8	C₅×D₃×C₇×C₁₃	—	3	4	no	—
9	C₃×C₅×C₁₃×D₇	D₃	1	4	yes	complemented
10	C₂×C₅×C₁₃×C₃⋊D₃	—	7	1	no	maximal, Hall
11	C₂×C₅×C₁₃×D₇	—	9	1	no	Hall
12	C₁₃×C₃⋊D₂₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₇×C₁₃×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃²×C₁₃×D₇	C₂×C₅	1	1	yes	characteristic, complemented
15	C₃×C₅×C₇×C₁₃	C₂×D₃	1	4	yes	complemented
16	C₅×D₇×C₃⋊D₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃²×C₅×C₁₃	—	7	1	no	—
18	C₅×C₁₃×C₃⋊D₃	—	7	1	no	—
19	C₅×C₁₃×C₃⋊D₃	D₇	1	1	yes	characteristic, direct product factor
20	D₃×C₁₃×D₇	—	3	4	no	—
21	C₂×C₅×C₇×C₁₃	—	9	1	no	—
22	C₅×C₁₃×D₇	—	9	1	no	—
23	C₅×C₁₃×D₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
24	C₃²×C₇×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×D₃×C₁₃	—	21	4	no	—
26	C₅×C₃⋊D₂₁	C₂×C₁₃	1	1	yes	characteristic, complemented
27	C₅×C₇×C₃⋊D₃	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₃²×C₅×D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
29	C₃²×C₅×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
30	C₁₃×D₂₁	—	3	4	no	—
31	D₃×C₇×C₁₃	—	3	4	no	—
32	C₃×C₁₃×D₇	C₅×D₃	1	4	yes	complemented
33	C₂×C₁₃×C₃⋊D₃	—	7	1	no	Hall
34	C₅×C₇×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
35	C₅×D₃×D₇	—	3	4	no	—
36	C₂×C₃×C₅×C₁₃	—	7	4	no	—
37	C₅×D₃×C₁₃	—	3	4	no	—
38	C₅×D₃×C₁₃	—	21	4	no	—
39	C₂×C₁₃×D₇	—	9	1	no	Hall
40	C₃²×C₅×C₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
41	C₃×C₇×C₁₃	C₂×C₅×D₃	1	4	yes	complemented
42	C₂²×C₅×C₁₃	—	63	1	no	Hall
43	D₇×C₃⋊D₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃²×C₁₃	—	7	1	no	—
45	C₁₃×C₃⋊D₃	—	7	1	no	—
46	C₁₃×C₃⋊D₃	C₅×D₇	1	1	yes	characteristic, direct product factor
47	C₅×D₂₁	—	3	4	no	—
48	C₅×D₃×C₇	—	3	4	no	—
49	C₃×C₅×D₇	D₃×C₁₃	1	4	yes	complemented
50	C₃×C₅×C₁₃	D₃×D₇	1	4	yes	complemented
51	C₂×C₇×C₁₃	—	9	1	no	—
52	C₁₃×D₇	—	9	1	no	—
53	C₁₃×D₇	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
54	C₂×C₅×C₃⋊D₃	—	7	1	no	Hall
55	C₂×D₃×C₁₃	—	21	4	no	—
56	C₂×C₅×D₇	—	9	1	no	Hall
57	C₂×C₅×C₁₃	—	7	1	no	—
58	C₂×C₅×C₁₃	—	9	1	no	—
59	C₂×C₅×C₁₃	—	63	1	no	—
60	C₃⋊D₂₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
61	C₇×C₃⋊D₃	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
62	C₃²×D₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
63	C₃²×C₁₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
64	C₃×C₅×C₇	C₂×D₃×C₁₃	1	4	yes	complemented
65	C₇×C₁₃	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
66	C₂×C₃²×C₅	—	7	1	no	—
67	C₅×C₃⋊D₃	—	7	1	no	—
68	C₅×C₃⋊D₃	C₁₃×D₇	1	1	yes	characteristic, direct product factor
69	D₃×D₇	—	3	4	no	—
70	C₂×C₃×C₁₃	—	7	4	no	—
71	D₃×C₁₃	—	3	4	no	—
72	D₃×C₁₃	—	21	4	no	—
73	C₂×C₅×C₇	—	9	1	no	—
74	C₅×D₇	—	9	1	no	—
75	C₅×D₇	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
76	C₅×C₁₃	D₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
77	C₃²×C₇	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
78	C₂×C₅×D₃	—	21	4	no	—
79	C₂²×C₁₃	—	63	1	no	Hall
80	C₃²×C₅	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
81	D₂₁	—	3	4	no	—
82	C₃×D₇	C₅×D₃×C₁₃	1	4	yes	complemented
83	D₃×C₇	—	3	4	no	—
84	C₃×C₁₃	C₅×D₃×D₇	1	4	yes	complemented
85	C₂×C₃⋊D₃	—	7	1	no	Hall
86	C₅×C₇	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
87	C₂×C₃×C₅	—	7	4	no	—
88	C₅×D₃	—	3	4	no	—
89	C₅×D₃	—	21	4	no	—
90	C₂×D₇	—	9	1	no	Hall
91	C₂×C₁₃	—	7	1	no	—
92	C₂×C₁₃	—	9	1	no	—
93	C₂×C₁₃	—	63	1	no	—
94	C₃×C₇	C₂×C₅×D₃×C₁₃	1	4	yes	complemented
95	C₂²×C₅	—	63	1	no	Hall
96	C₂×C₃²	—	7	1	no	—
97	C₃⋊D₃	—	7	1	no	—
98	C₃⋊D₃	C₅×C₁₃×D₇	1	1	yes	characteristic, direct product factor
99	C₃×C₅	D₃×C₁₃×D₇	1	4	yes	complemented
100	C₂×C₇	—	9	1	no	—
101	D₇	—	9	1	no	—
102	D₇	C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
103	C₁₃	C₅×D₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
104	C₂×D₃	—	21	4	no	—
105	C₂×C₅	—	7	1	no	—
106	C₂×C₅	—	9	1	no	—
107	C₂×C₅	—	63	1	no	—
108	C₃²	C₂×C₅×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
109	C₇	C₂×C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	7	4	no	—
111	D₃	—	3	4	no	—
112	D₃	—	21	4	no	—
113	C₅	C₁₃×D₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²	—	63	1	no	Sylow
115	C₃	C₅×D₃×C₁₃×D₇	1	4	yes	complemented
116	C₂	—	7	1	no	—
117	C₂	—	9	1	no	—
118	C₂	—	63	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₁₃×C₃⋊D₂₁

C₂

yes

maximal, characteristic, complemented

C₅×C₇×C₁₃×C₃⋊D₃

C₂

yes

maximal, characteristic, complemented

C₃²×C₅×C₁₃×D₇

C₂

yes

maximal, characteristic, complemented

C₅×D₃×C₁₃×D₇

—

maximal

C₃²×C₅×C₇×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₁₃×D₇×C₃⋊D₃

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₃×D₂₁

—

C₅×D₃×C₇×C₁₃

—

C₃×C₅×C₁₃×D₇

D₃

yes

complemented

C₂×C₅×C₁₃×C₃⋊D₃

—

maximal, Hall

C₂×C₅×C₁₃×D₇

—

Hall

C₁₃×C₃⋊D₂₁

C₂×C₅

yes

characteristic, complemented

C₇×C₁₃×C₃⋊D₃

C₂×C₅

yes

characteristic, complemented

C₃²×C₁₃×D₇

C₂×C₅

yes

characteristic, complemented

C₃×C₅×C₇×C₁₃

C₂×D₃

yes

complemented

C₅×D₇×C₃⋊D₃

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃²×C₅×C₁₃

—

C₅×C₁₃×C₃⋊D₃

—

C₅×C₁₃×C₃⋊D₃

D₇

yes

characteristic, direct product factor

D₃×C₁₃×D₇

—

C₂×C₅×C₇×C₁₃

—

C₅×C₁₃×D₇

—

C₅×C₁₃×D₇

C₃⋊D₃

yes

characteristic, direct product factor

C₃²×C₇×C₁₃

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₁₃

—

C₅×C₃⋊D₂₁

C₂×C₁₃

yes

characteristic, complemented

C₅×C₇×C₃⋊D₃

C₂×C₁₃

yes

characteristic, complemented

C₃²×C₅×D₇

C₂×C₁₃

yes

characteristic, complemented

C₃²×C₅×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

C₁₃×D₂₁

—

D₃×C₇×C₁₃

—

C₃×C₁₃×D₇

C₅×D₃

yes

complemented

C₂×C₁₃×C₃⋊D₃

—

Hall

C₅×C₇×C₁₃

C₂×C₃⋊D₃

yes

characteristic, complemented, Hall

C₅×D₃×D₇

—

C₂×C₃×C₅×C₁₃

—

C₅×D₃×C₁₃

—

C₅×D₃×C₁₃

—

C₂×C₁₃×D₇

—

Hall

C₃²×C₅×C₇

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₃×C₇×C₁₃

C₂×C₅×D₃

yes

complemented

C₂²×C₅×C₁₃

—

Hall

D₇×C₃⋊D₃

C₅×C₁₃

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₁₃

—

C₁₃×C₃⋊D₃

—

C₁₃×C₃⋊D₃

C₅×D₇

yes

characteristic, direct product factor

C₅×D₂₁

—

C₅×D₃×C₇

—

C₃×C₅×D₇

D₃×C₁₃

yes

complemented

C₃×C₅×C₁₃

D₃×D₇

yes

complemented

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

C₅×C₃⋊D₃

yes

characteristic, direct product factor

C₂×C₅×C₃⋊D₃

—

Hall

C₂×D₃×C₁₃

—

C₂×C₅×D₇

—

Hall

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₃⋊D₂₁

C₂×C₅×C₁₃

yes

characteristic, complemented

C₇×C₃⋊D₃

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃²×D₇

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃²×C₁₃

C₂×C₅×D₇

yes

characteristic, complemented, Hall

C₃×C₅×C₇

C₂×D₃×C₁₃

yes

complemented

C₇×C₁₃

C₂×C₅×C₃⋊D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅

—

C₅×C₃⋊D₃

—

C₅×C₃⋊D₃

C₁₃×D₇

yes

characteristic, direct product factor

D₃×D₇

—

C₂×C₃×C₁₃

—

D₃×C₁₃

—

D₃×C₁₃

—

C₂×C₅×C₇

—

C₅×D₇

—

C₅×D₇

C₁₃×C₃⋊D₃

yes

characteristic, direct product factor

C₅×C₁₃

D₇×C₃⋊D₃

yes

characteristic, direct product factor, Hall

C₃²×C₇

C₂²×C₅×C₁₃

yes

characteristic, complemented, Hall

C₂×C₅×D₃

—

C₂²×C₁₃

—

Hall

C₃²×C₅

C₂×C₁₃×D₇

yes

characteristic, complemented, Hall

D₂₁

—

C₃×D₇

C₅×D₃×C₁₃

yes

complemented

D₃×C₇

—

C₃×C₁₃

C₅×D₃×D₇

yes

complemented

C₂×C₃⋊D₃

—

Hall

C₅×C₇

C₂×C₁₃×C₃⋊D₃

yes

characteristic, complemented, Hall

C₂×C₃×C₅

—

C₅×D₃

—

C₅×D₃

—

C₂×D₇

—

Hall

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

—

C₃×C₇

C₂×C₅×D₃×C₁₃

yes

complemented

C₂²×C₅

—

Hall

C₂×C₃²

—

C₃⋊D₃

—

C₃⋊D₃

C₅×C₁₃×D₇

yes

characteristic, direct product factor

C₃×C₅

D₃×C₁₃×D₇

yes

complemented

100

C₂×C₇

—

101

D₇

—

102

D₇

C₅×C₁₃×C₃⋊D₃

yes

characteristic, direct product factor

103

C₁₃

C₅×D₇×C₃⋊D₃

yes

characteristic, direct product factor, Sylow

104

C₂×D₃

—

105

C₂×C₅

—

106

C₂×C₅

—

107

C₂×C₅

—

108

C₃²

C₂×C₅×C₁₃×D₇

yes

characteristic, complemented, Sylow

109

C₇

C₂×C₅×C₁₃×C₃⋊D₃

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

112

D₃

—

113

C₅

C₁₃×D₇×C₃⋊D₃

yes

characteristic, direct product factor, Sylow

114

C₂²

—

Sylow

115

C₃

C₅×D₃×C₁₃×D₇

yes

complemented

116

C₂

—

117

C₂

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₇×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₃	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₅×C₁₃

subgroup

G/H

center, hypercenter

C₅×C₁₃

D₇×C₃⋊D₃

commutator, cosocle, hypocenter

C₃²×C₇

C₂²×C₅×C₁₃

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₁₃

C₂²

LCS

G ▷ C₃²×C₇

UCS

C₁ ◁ C₅×C₁₃

N	H ≅ G/N	type
1. C₅×C₁₃×C₃⋊D₂₁	C₂	semidirect
2. C₅×C₇×C₁₃×C₃⋊D₃	C₂	semidirect
3. C₃²×C₅×C₁₃×D₇	C₂	semidirect
5. C₃²×C₅×C₇×C₁₃	C₂²	semidirect
6. C₁₃×D₇×C₃⋊D₃	C₅	direct (N × H)
9. C₃×C₅×C₁₃×D₇	D₃	semidirect
12. C₁₃×C₃⋊D₂₁	C₂×C₅	semidirect
13. C₇×C₁₃×C₃⋊D₃	C₂×C₅	semidirect
14. C₃²×C₁₃×D₇	C₂×C₅	semidirect
15. C₃×C₅×C₇×C₁₃	C₂×D₃	semidirect
16. C₅×D₇×C₃⋊D₃	C₁₃	direct (N × H)
19. C₅×C₁₃×C₃⋊D₃	D₇	direct (N × H)
23. C₅×C₁₃×D₇	C₃⋊D₃	direct (N × H)
24. C₃²×C₇×C₁₃	C₂²×C₅	semidirect
26. C₅×C₃⋊D₂₁	C₂×C₁₃	semidirect
27. C₅×C₇×C₃⋊D₃	C₂×C₁₃	semidirect
28. C₃²×C₅×D₇	C₂×C₁₃	semidirect
29. C₃²×C₅×C₁₃	C₂×D₇	semidirect
32. C₃×C₁₃×D₇	C₅×D₃	semidirect
34. C₅×C₇×C₁₃	C₂×C₃⋊D₃	semidirect
40. C₃²×C₅×C₇	C₂²×C₁₃	semidirect
41. C₃×C₇×C₁₃	C₂×C₅×D₃	semidirect
43. D₇×C₃⋊D₃	C₅×C₁₃	direct (N × H)
46. C₁₃×C₃⋊D₃	C₅×D₇	direct (N × H)
49. C₃×C₅×D₇	D₃×C₁₃	semidirect
50. C₃×C₅×C₁₃	D₃×D₇	semidirect
53. C₁₃×D₇	C₅×C₃⋊D₃	direct (N × H)
60. C₃⋊D₂₁	C₂×C₅×C₁₃	semidirect
61. C₇×C₃⋊D₃	C₂×C₅×C₁₃	semidirect
62. C₃²×D₇	C₂×C₅×C₁₃	semidirect
63. C₃²×C₁₃	C₂×C₅×D₇	semidirect
64. C₃×C₅×C₇	C₂×D₃×C₁₃	semidirect
65. C₇×C₁₃	C₂×C₅×C₃⋊D₃	semidirect
68. C₅×C₃⋊D₃	C₁₃×D₇	direct (N × H)
75. C₅×D₇	C₁₃×C₃⋊D₃	direct (N × H)
76. C₅×C₁₃	D₇×C₃⋊D₃	direct (N × H)
77. C₃²×C₇	C₂²×C₅×C₁₃	semidirect
80. C₃²×C₅	C₂×C₁₃×D₇	semidirect
82. C₃×D₇	C₅×D₃×C₁₃	semidirect
84. C₃×C₁₃	C₅×D₃×D₇	semidirect
86. C₅×C₇	C₂×C₁₃×C₃⋊D₃	semidirect
94. C₃×C₇	C₂×C₅×D₃×C₁₃	semidirect
98. C₃⋊D₃	C₅×C₁₃×D₇	direct (N × H)
99. C₃×C₅	D₃×C₁₃×D₇	semidirect
102. D₇	C₅×C₁₃×C₃⋊D₃	direct (N × H)
103. C₁₃	C₅×D₇×C₃⋊D₃	direct (N × H)
108. C₃²	C₂×C₅×C₁₃×D₇	semidirect
109. C₇	C₂×C₅×C₁₃×C₃⋊D₃	semidirect
113. C₅	C₁₃×D₇×C₃⋊D₃	direct (N × H)
115. C₃	C₅×D₃×C₁₃×D₇	semidirect

H ≅ G/N

type

1. C₅×C₁₃×C₃⋊D₂₁

C₂

semidirect

2. C₅×C₇×C₁₃×C₃⋊D₃

C₂

semidirect

3. C₃²×C₅×C₁₃×D₇

C₂

semidirect

5. C₃²×C₅×C₇×C₁₃

C₂²

semidirect

6. C₁₃×D₇×C₃⋊D₃

C₅

direct (N × H)

9. C₃×C₅×C₁₃×D₇

D₃

semidirect

12. C₁₃×C₃⋊D₂₁

C₂×C₅

semidirect

13. C₇×C₁₃×C₃⋊D₃

C₂×C₅

semidirect

14. C₃²×C₁₃×D₇

C₂×C₅

semidirect

15. C₃×C₅×C₇×C₁₃

C₂×D₃

semidirect

16. C₅×D₇×C₃⋊D₃

C₁₃

direct (N × H)

19. C₅×C₁₃×C₃⋊D₃

D₇

direct (N × H)

23. C₅×C₁₃×D₇

C₃⋊D₃

direct (N × H)

24. C₃²×C₇×C₁₃

C₂²×C₅

semidirect

26. C₅×C₃⋊D₂₁

C₂×C₁₃

semidirect

27. C₅×C₇×C₃⋊D₃

C₂×C₁₃

semidirect

28. C₃²×C₅×D₇

C₂×C₁₃

semidirect

29. C₃²×C₅×C₁₃

C₂×D₇

semidirect

32. C₃×C₁₃×D₇

C₅×D₃

semidirect

34. C₅×C₇×C₁₃

C₂×C₃⋊D₃

semidirect

40. C₃²×C₅×C₇

C₂²×C₁₃

semidirect

41. C₃×C₇×C₁₃

C₂×C₅×D₃

semidirect

43. D₇×C₃⋊D₃

C₅×C₁₃

direct (N × H)

46. C₁₃×C₃⋊D₃

C₅×D₇

direct (N × H)

49. C₃×C₅×D₇

D₃×C₁₃

semidirect

50. C₃×C₅×C₁₃

D₃×D₇

semidirect

53. C₁₃×D₇

C₅×C₃⋊D₃

direct (N × H)

60. C₃⋊D₂₁

C₂×C₅×C₁₃

semidirect

61. C₇×C₃⋊D₃

C₂×C₅×C₁₃

semidirect

62. C₃²×D₇

C₂×C₅×C₁₃

semidirect

63. C₃²×C₁₃

C₂×C₅×D₇

semidirect

64. C₃×C₅×C₇

C₂×D₃×C₁₃

semidirect

65. C₇×C₁₃

C₂×C₅×C₃⋊D₃

semidirect

68. C₅×C₃⋊D₃

C₁₃×D₇

direct (N × H)

75. C₅×D₇

C₁₃×C₃⋊D₃

direct (N × H)

76. C₅×C₁₃

D₇×C₃⋊D₃

direct (N × H)

77. C₃²×C₇

C₂²×C₅×C₁₃

semidirect

80. C₃²×C₅

C₂×C₁₃×D₇

semidirect

82. C₃×D₇

C₅×D₃×C₁₃

semidirect

84. C₃×C₁₃

C₅×D₃×D₇

semidirect

86. C₅×C₇

C₂×C₁₃×C₃⋊D₃

semidirect

94. C₃×C₇

C₂×C₅×D₃×C₁₃

semidirect

98. C₃⋊D₃

C₅×C₁₃×D₇

direct (N × H)

99. C₃×C₅

D₃×C₁₃×D₇

semidirect

102. D₇

C₅×C₁₃×C₃⋊D₃

direct (N × H)

103. C₁₃

C₅×D₇×C₃⋊D₃

direct (N × H)

108. C₃²

C₂×C₅×C₁₃×D₇

semidirect

109. C₇

C₂×C₅×C₁₃×C₃⋊D₃

semidirect

113. C₅

C₁₃×D₇×C₃⋊D₃

direct (N × H)

115. C₃

C₅×D₃×C₁₃×D₇

semidirect

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

subgroup	index
C₅×C₁₃×C₃⋊D₂₁	2
C₅×C₇×C₁₃×C₃⋊D₃	2
C₃²×C₅×C₁₃×D₇	2
C₅×D₃×C₁₃×D₇	3
C₁₃×D₇×C₃⋊D₃	5
C₂×C₅×C₁₃×C₃⋊D₃	7
C₅×D₇×C₃⋊D₃	13

subgroup

index

C₅×C₁₃×C₃⋊D₂₁

C₅×C₇×C₁₃×C₃⋊D₃

C₃²×C₅×C₁₃×D₇

C₅×D₃×C₁₃×D₇

C₁₃×D₇×C₃⋊D₃

C₂×C₅×C₁₃×C₃⋊D₃

C₅×D₇×C₃⋊D₃

Subgroups — C₅×C₁₃×D₇×C₃⋊D₃ #30655678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×C13×D7×C3⋊D3 #30655678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×D₇×C₃⋊D₃ #30655678