Group #50304087 — subgroups

Subgroups — C₇×D₅×D₇×C₁₃⋊C₃ #50304087

Order 38220.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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	C₇×C₁₃⋊C₃×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₅×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×D₇×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₅×C₁₃×D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×C₇²×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×D₇×C₁₃⋊C₃	—	5	1	no	maximal, Hall
7	C₇×C₁₃×D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₅×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₇×C₁₃×D₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₇×D₅×C₁₃⋊C₃	—	7	1	no	maximal
11	D₅×D₇×C₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₇²×C₁₃⋊C₃	—	5	1	no	—
13	C₇×D₇×C₁₃⋊C₃	—	5	1	no	—
14	C₇×D₇×C₁₃⋊C₃	D₅	1	1	yes	characteristic, direct product factor
15	C₅×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×D₅×D₇	—	13	1	no	maximal, Hall
17	C₁₃⋊C₃×D₃₅	C₂×C₇	1	1	yes	characteristic, complemented
18	C₇×D₅×C₁₃⋊C₃	—	2	3	no	—
19	C₇×D₅×C₁₃⋊C₃	—	7	1	no	—
20	C₇×D₅×C₁₃⋊C₃	D₇	1	1	yes	characteristic, direct product factor
21	C₇×D₅×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
22	C₅×D₇×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
23	C₂×C₅×C₇×C₁₃⋊C₃	—	7	1	no	—
24	C₂×C₇×C₁₃×D₇	—	5	1	no	Hall
25	C₇²×C₁₃⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×D₅×C₁₃	—	7	1	no	—
27	D₅×C₁₃×D₇	C₃×C₇	1	1	yes	characteristic, complemented
28	C₃×C₇×D₃₅	—	13	1	no	—
29	C₃×C₇²×D₅	—	13	1	no	—
30	C₃×C₅×C₇×D₇	—	13	1	no	—
31	C₅×C₇×C₁₃⋊C₃	—	2	3	no	—
32	C₅×C₇×C₁₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented
33	C₅×C₇×C₁₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented
34	C₂×C₇²×C₁₃	—	5	1	no	—
35	C₇×C₁₃×D₇	—	5	1	no	—
36	C₇×C₁₃×D₇	C₃×D₅	1	1	yes	characteristic, complemented
37	C₂²×C₇×C₁₃⋊C₃	—	35	1	no	—
38	C₂×D₇×C₁₃⋊C₃	—	5	1	no	—
39	C₇×D₅×D₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅×C₇×C₁₃	—	7	1	no	—
41	C₁₃×D₃₅	C₂×C₃×C₇	1	1	yes	characteristic, complemented
42	C₇×D₅×C₁₃	—	2	3	no	—
43	C₇×D₅×C₁₃	—	7	1	no	—
44	C₇×D₅×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
45	C₇×D₅×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
46	C₅×C₁₃×D₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
47	C₂×D₅×C₁₃⋊C₃	—	7	1	no	Hall
48	C₃×C₅×C₇²	—	13	1	no	Hall
49	C₇²×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₇×D₇	—	65	1	no	Hall
51	C₂×C₇×C₁₃⋊C₃	—	5	1	no	—
52	C₂×C₇×C₁₃⋊C₃	—	5	1	no	—
53	C₂×C₇×C₁₃⋊C₃	—	7	1	no	—
54	C₂×C₇×C₁₃⋊C₃	—	10	3	no	—
55	C₂×C₇×C₁₃⋊C₃	—	35	1	no	—
56	D₇×C₁₃⋊C₃	—	5	1	no	—
57	D₇×C₁₃⋊C₃	C₇×D₅	1	1	yes	characteristic, direct product factor
58	C₇×D₃₅	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
59	C₇²×D₅	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
60	C₅×C₇×D₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
61	C₅×C₇×C₁₃	—	2	3	no	—
62	C₅×C₇×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
63	C₅×C₇×C₁₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
64	C₂×C₃×C₇×D₅	—	91	1	no	—
65	C₃×D₅×D₇	—	13	1	no	—
66	C₂×C₅×C₁₃⋊C₃	—	7	1	no	—
67	D₅×C₁₃⋊C₃	—	7	1	no	—
68	D₅×C₁₃⋊C₃	C₇×D₇	1	1	yes	characteristic, direct product factor
69	C₂²×C₇×C₁₃	—	35	1	no	—
70	C₂×C₁₃×D₇	—	5	1	no	—
71	C₂×C₃×C₇²	—	65	1	no	—
72	C₃×C₇×D₇	—	13	1	no	—
73	C₃×C₇×D₇	—	65	1	no	—
74	C₇×C₁₃⋊C₃	—	2	3	no	—
75	C₇×C₁₃⋊C₃	D₅×D₇	1	1	yes	characteristic, direct product factor
76	C₇×C₁₃⋊C₃	C₂×C₇×D₅	1	1	yes	characteristic, complemented
77	C₂×D₅×C₁₃	—	7	1	no	Hall
78	C₅×C₇²	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
79	C₂×C₃×C₅×C₇	—	91	1	no	—
80	C₃×D₃₅	—	13	1	no	—
81	C₃×C₇×D₅	—	13	1	no	—
82	C₃×C₇×D₅	—	13	1	no	—
83	C₃×C₇×D₅	—	26	3	no	—
84	C₃×C₇×D₅	—	91	1	no	—
85	C₃×C₅×D₇	—	13	1	no	—
86	C₂×C₇×D₇	—	5	1	no	Hall
87	C₅×C₁₃⋊C₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
88	C₂×C₇×C₁₃	—	5	1	no	—
89	C₂×C₇×C₁₃	—	5	1	no	—
90	C₂×C₇×C₁₃	—	7	1	no	—
91	C₂×C₇×C₁₃	—	10	3	no	—
92	C₂×C₇×C₁₃	—	35	1	no	—
93	C₁₃×D₇	—	5	1	no	—
94	C₁₃×D₇	C₃×C₇×D₅	1	1	yes	characteristic, complemented
95	C₂²×C₁₃⋊C₃	—	35	1	no	Hall
96	C₃×C₇²	—	13	1	no	Hall
97	C₂×C₇×D₅	—	7	1	no	—
98	D₅×D₇	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
99	C₂×C₅×C₁₃	—	7	1	no	—
100	D₅×C₁₃	—	7	1	no	—
101	D₅×C₁₃	C₃×C₇×D₇	1	1	yes	characteristic, complemented
102	C₃×C₅×C₇	—	13	1	no	—
103	C₃×C₅×C₇	—	13	1	no	—
104	C₃×C₅×C₇	—	26	3	no	—
105	C₂×C₇²	—	5	1	no	—
106	C₇×D₇	—	5	1	no	—
107	C₇×D₇	D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
108	C₇×C₁₃	—	2	3	no	—
109	C₇×C₁₃	C₃×D₅×D₇	1	1	yes	characteristic, complemented
110	C₇×C₁₃	C₂×C₃×C₇×D₅	1	1	yes	characteristic, complemented
111	C₂²×C₃×C₇	—	455	1	no	—
112	C₂×C₃×D₇	—	65	1	no	—
113	C₂×C₁₃⋊C₃	—	5	1	no	—
114	C₂×C₁₃⋊C₃	—	7	1	no	—
115	C₂×C₁₃⋊C₃	—	35	1	no	—
116	C₂×C₅×C₇	—	7	1	no	—
117	D₃₅	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
118	C₅×D₇	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
119	C₇×D₅	—	2	3	no	—
120	C₇×D₅	—	7	1	no	—
121	C₇×D₅	D₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
122	C₇×D₅	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
123	C₅×C₁₃	C₂×C₃×C₇×D₇	1	1	yes	characteristic, complemented, Hall
124	C₂×C₃×D₅	—	91	1	no	Hall
125	C₂²×C₁₃	—	35	1	no	Hall
126	C₇²	C₂×D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₃×C₇	—	65	1	no	—
128	C₂×C₃×C₇	—	65	1	no	—
129	C₂×C₃×C₇	—	91	1	no	—
130	C₂×C₃×C₇	—	130	3	no	—
131	C₂×C₃×C₇	—	455	1	no	—
132	C₃×D₇	—	13	1	no	—
133	C₃×D₇	—	65	1	no	—
134	C₁₃⋊C₃	C₇×D₅×D₇	1	1	yes	characteristic, direct product factor, Hall
135	C₅×C₇	—	2	3	no	—
136	C₅×C₇	C₂×D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
137	C₅×C₇	C₂²×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
138	C₂×C₃×C₅	—	91	1	no	—
139	C₃×D₅	—	13	1	no	—
140	C₃×D₅	—	91	1	no	—
141	C₂²×C₇	—	35	1	no	—
142	C₂×D₇	—	5	1	no	—
143	C₂×C₁₃	—	5	1	no	—
144	C₂×C₁₃	—	7	1	no	—
145	C₂×C₁₃	—	35	1	no	—
146	C₃×C₇	—	13	1	no	—
147	C₃×C₇	—	13	1	no	—
148	C₃×C₇	—	26	3	no	—
149	C₂×D₅	—	7	1	no	Hall
150	C₃×C₅	—	13	1	no	Hall
151	C₂×C₇	—	5	1	no	—
152	C₂×C₇	—	5	1	no	—
153	C₂×C₇	—	7	1	no	—
154	C₂×C₇	—	10	3	no	—
155	C₂×C₇	—	35	1	no	—
156	D₇	—	5	1	no	—
157	D₇	C₇×D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
158	C₁₃	C₃×C₇×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
159	C₂²×C₃	—	455	1	no	Hall
160	C₂×C₅	—	7	1	no	—
161	D₅	—	7	1	no	—
162	D₅	C₇×D₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
163	C₇	—	2	3	no	—
164	C₇	D₅×D₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
165	C₇	C₂×C₇×D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
166	C₂×C₃	—	65	1	no	—
167	C₂×C₃	—	91	1	no	—
168	C₂×C₃	—	455	1	no	—
169	C₅	C₂×C₇×D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
170	C₂²	—	35	1	no	Sylow
171	C₃	—	13	1	no	Sylow
172	C₂	—	5	1	no	—
173	C₂	—	7	1	no	—
174	C₂	—	35	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇×C₁₃⋊C₃×D₃₅

C₂

yes

maximal, characteristic, complemented

C₇²×D₅×C₁₃⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅×C₇×D₇×C₁₃⋊C₃

C₂

yes

maximal, characteristic, complemented

C₇×D₅×C₁₃×D₇

C₃

yes

maximal, characteristic, complemented, Hall

C₅×C₇²×C₁₃⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₂×C₇×D₇×C₁₃⋊C₃

—

maximal, Hall

C₇×C₁₃×D₃₅

C₂×C₃

yes

characteristic, complemented

C₇²×D₅×C₁₃

C₂×C₃

yes

characteristic, complemented

C₅×C₇×C₁₃×D₇

C₂×C₃

yes

characteristic, complemented

C₂×C₇×D₅×C₁₃⋊C₃

—

maximal

D₅×D₇×C₁₃⋊C₃

C₇

yes

maximal, characteristic, direct product factor

C₂×C₇²×C₁₃⋊C₃

—

C₇×D₇×C₁₃⋊C₃

—

C₇×D₇×C₁₃⋊C₃

D₅

yes

characteristic, direct product factor

C₅×C₇²×C₁₃

C₂²×C₃

yes

characteristic, complemented, Hall

C₃×C₇×D₅×D₇

—

maximal, Hall

C₁₃⋊C₃×D₃₅

C₂×C₇

yes

characteristic, complemented

C₇×D₅×C₁₃⋊C₃

—

C₇×D₅×C₁₃⋊C₃

—

C₇×D₅×C₁₃⋊C₃

D₇

yes

characteristic, direct product factor

C₇×D₅×C₁₃⋊C₃

C₂×C₇

yes

characteristic, complemented

C₅×D₇×C₁₃⋊C₃

C₂×C₇

yes

characteristic, complemented

C₂×C₅×C₇×C₁₃⋊C₃

—

C₂×C₇×C₁₃×D₇

—

Hall

C₇²×C₁₃⋊C₃

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₇×D₅×C₁₃

—

D₅×C₁₃×D₇

C₃×C₇

yes

characteristic, complemented

C₃×C₇×D₃₅

—

C₃×C₇²×D₅

—

C₃×C₅×C₇×D₇

—

C₅×C₇×C₁₃⋊C₃

—

C₅×C₇×C₁₃⋊C₃

C₂×D₇

yes

characteristic, complemented

C₅×C₇×C₁₃⋊C₃

C₂²×C₇

yes

characteristic, complemented

C₂×C₇²×C₁₃

—

C₇×C₁₃×D₇

—

C₇×C₁₃×D₇

C₃×D₅

yes

characteristic, complemented

C₂²×C₇×C₁₃⋊C₃

—

C₂×D₇×C₁₃⋊C₃

—

C₇×D₅×D₇

C₁₃⋊C₃

yes

characteristic, direct product factor, Hall

C₂×C₅×C₇×C₁₃

—

C₁₃×D₃₅

C₂×C₃×C₇

yes

characteristic, complemented

C₇×D₅×C₁₃

—

C₇×D₅×C₁₃

—

C₇×D₅×C₁₃

C₃×D₇

yes

characteristic, complemented

C₇×D₅×C₁₃

C₂×C₃×C₇

yes

characteristic, complemented

C₅×C₁₃×D₇

C₂×C₃×C₇

yes

characteristic, complemented

C₂×D₅×C₁₃⋊C₃

—

Hall

C₃×C₅×C₇²

—

Hall

C₇²×C₁₃

C₂×C₃×D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₇×D₇

—

Hall

C₂×C₇×C₁₃⋊C₃

—

C₂×C₇×C₁₃⋊C₃

—

C₂×C₇×C₁₃⋊C₃

—

C₂×C₇×C₁₃⋊C₃

—

C₂×C₇×C₁₃⋊C₃

—

D₇×C₁₃⋊C₃

—

D₇×C₁₃⋊C₃

C₇×D₅

yes

characteristic, direct product factor

C₇×D₃₅

C₂×C₁₃⋊C₃

yes

characteristic, complemented

C₇²×D₅

C₂×C₁₃⋊C₃

yes

characteristic, complemented

C₅×C₇×D₇

C₂×C₁₃⋊C₃

yes

characteristic, complemented

C₅×C₇×C₁₃

—

C₅×C₇×C₁₃

C₂×C₃×D₇

yes

characteristic, complemented

C₅×C₇×C₁₃

C₂²×C₃×C₇

yes

characteristic, complemented

C₂×C₃×C₇×D₅

—

C₃×D₅×D₇

—

C₂×C₅×C₁₃⋊C₃

—

D₅×C₁₃⋊C₃

—

D₅×C₁₃⋊C₃

C₇×D₇

yes

characteristic, direct product factor

C₂²×C₇×C₁₃

—

C₂×C₁₃×D₇

—

C₂×C₃×C₇²

—

C₃×C₇×D₇

—

C₃×C₇×D₇

—

C₇×C₁₃⋊C₃

—

C₇×C₁₃⋊C₃

D₅×D₇

yes

characteristic, direct product factor

C₇×C₁₃⋊C₃

C₂×C₇×D₅

yes

characteristic, complemented

C₂×D₅×C₁₃

—

Hall

C₅×C₇²

C₂²×C₁₃⋊C₃

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₇

—

C₃×D₃₅

—

C₃×C₇×D₅

—

C₃×C₇×D₅

—

C₃×C₇×D₅

—

C₃×C₇×D₅

—

C₃×C₅×D₇

—

C₂×C₇×D₇

—

Hall

C₅×C₁₃⋊C₃

C₂×C₇×D₇

yes

characteristic, complemented, Hall

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

C₃×C₇×D₅

yes

characteristic, complemented

C₂²×C₁₃⋊C₃

—

Hall

C₃×C₇²

—

Hall

C₂×C₇×D₅

—

D₅×D₇

C₇×C₁₃⋊C₃

yes

characteristic, direct product factor

C₂×C₅×C₁₃

—

100

D₅×C₁₃

—

101

D₅×C₁₃

C₃×C₇×D₇

yes

characteristic, complemented

102

C₃×C₅×C₇

—

103

C₃×C₅×C₇

—

104

C₃×C₅×C₇

—

105

C₂×C₇²

—

106

C₇×D₇

—

107

C₇×D₇

D₅×C₁₃⋊C₃

yes

characteristic, direct product factor

108

C₇×C₁₃

—

109

C₇×C₁₃

C₃×D₅×D₇

yes

characteristic, complemented

110

C₇×C₁₃

C₂×C₃×C₇×D₅

yes

characteristic, complemented

111

C₂²×C₃×C₇

—

455

—

112

C₂×C₃×D₇

—

113

C₂×C₁₃⋊C₃

—

114

C₂×C₁₃⋊C₃

—

115

C₂×C₁₃⋊C₃

—

116

C₂×C₅×C₇

—

117

D₃₅

C₂×C₇×C₁₃⋊C₃

yes

characteristic, complemented

118

C₅×D₇

C₂×C₇×C₁₃⋊C₃

yes

characteristic, complemented

119

C₇×D₅

—

120

C₇×D₅

—

121

C₇×D₅

D₇×C₁₃⋊C₃

yes

characteristic, direct product factor

122

C₇×D₅

C₂×C₇×C₁₃⋊C₃

yes

characteristic, complemented

123

C₅×C₁₃

C₂×C₃×C₇×D₇

yes

characteristic, complemented, Hall

124

C₂×C₃×D₅

—

Hall

125

C₂²×C₁₃

—

Hall

126

C₇²

C₂×D₅×C₁₃⋊C₃

yes

characteristic, complemented, Sylow

127

C₂×C₃×C₇

—

128

C₂×C₃×C₇

—

129

C₂×C₃×C₇

—

130

C₂×C₃×C₇

—

130

—

131

C₂×C₃×C₇

—

455

—

132

C₃×D₇

—

133

C₃×D₇

—

134

C₁₃⋊C₃

C₇×D₅×D₇

yes

characteristic, direct product factor, Hall

135

C₅×C₇

—

136

C₅×C₇

C₂×D₇×C₁₃⋊C₃

yes

characteristic, complemented

137

C₅×C₇

C₂²×C₇×C₁₃⋊C₃

yes

characteristic, complemented

138

C₂×C₃×C₅

—

139

C₃×D₅

—

140

C₃×D₅

—

141

C₂²×C₇

—

142

C₂×D₇

—

143

C₂×C₁₃

—

144

C₂×C₁₃

—

145

C₂×C₁₃

—

146

C₃×C₇

—

147

C₃×C₇

—

148

C₃×C₇

—

149

C₂×D₅

—

Hall

150

C₃×C₅

—

Hall

151

C₂×C₇

—

152

C₂×C₇

—

153

C₂×C₇

—

154

C₂×C₇

—

155

C₂×C₇

—

156

D₇

—

157

D₇

C₇×D₅×C₁₃⋊C₃

yes

characteristic, direct product factor

158

C₁₃

C₃×C₇×D₅×D₇

yes

characteristic, complemented, Sylow

159

C₂²×C₃

—

455

Hall

160

C₂×C₅

—

161

D₅

—

162

D₅

C₇×D₇×C₁₃⋊C₃

yes

characteristic, direct product factor

163

C₇

—

164

C₇

D₅×D₇×C₁₃⋊C₃

yes

characteristic, direct product factor

165

C₇

C₂×C₇×D₅×C₁₃⋊C₃

yes

characteristic, complemented

166

C₂×C₃

—

167

C₂×C₃

—

168

C₂×C₃

—

455

—

169

C₅

C₂×C₇×D₇×C₁₃⋊C₃

yes

characteristic, complemented, Sylow

170

C₂²

—

Sylow

171

C₃

—

Sylow

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₇	D₅×D₇×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₅×C₇×C₁₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₇

subgroup

G/H

center, hypercenter

C₇

D₅×D₇×C₁₃⋊C₃

commutator, cosocle, hypocenter

C₅×C₇×C₁₃

C₂²×C₃×C₇

Frattini

C₁

Fitting, socle

C₅×C₇²×C₁₃

C₂²×C₃

LCS

G ▷ C₅×C₇×C₁₃

UCS

C₁ ◁ C₇

N	H ≅ G/N	type
1. C₇×C₁₃⋊C₃×D₃₅	C₂	semidirect
2. C₇²×D₅×C₁₃⋊C₃	C₂	semidirect
3. C₅×C₇×D₇×C₁₃⋊C₃	C₂	semidirect
4. C₇×D₅×C₁₃×D₇	C₃	semidirect
5. C₅×C₇²×C₁₃⋊C₃	C₂²	semidirect
7. C₇×C₁₃×D₃₅	C₂×C₃	semidirect
8. C₇²×D₅×C₁₃	C₂×C₃	semidirect
9. C₅×C₇×C₁₃×D₇	C₂×C₃	semidirect
11. D₅×D₇×C₁₃⋊C₃	C₇	direct (N × H)
14. C₇×D₇×C₁₃⋊C₃	D₅	direct (N × H)
15. C₅×C₇²×C₁₃	C₂²×C₃	semidirect
17. C₁₃⋊C₃×D₃₅	C₂×C₇	semidirect
20. C₇×D₅×C₁₃⋊C₃	D₇	direct (N × H)
21. C₇×D₅×C₁₃⋊C₃	C₂×C₇	semidirect
22. C₅×D₇×C₁₃⋊C₃	C₂×C₇	semidirect
25. C₇²×C₁₃⋊C₃	C₂×D₅	semidirect
27. D₅×C₁₃×D₇	C₃×C₇	semidirect
32. C₅×C₇×C₁₃⋊C₃	C₂×D₇	semidirect
33. C₅×C₇×C₁₃⋊C₃	C₂²×C₇	semidirect
36. C₇×C₁₃×D₇	C₃×D₅	semidirect
39. C₇×D₅×D₇	C₁₃⋊C₃	direct (N × H)
41. C₁₃×D₃₅	C₂×C₃×C₇	semidirect
44. C₇×D₅×C₁₃	C₃×D₇	semidirect
45. C₇×D₅×C₁₃	C₂×C₃×C₇	semidirect
46. C₅×C₁₃×D₇	C₂×C₃×C₇	semidirect
49. C₇²×C₁₃	C₂×C₃×D₅	semidirect
57. D₇×C₁₃⋊C₃	C₇×D₅	direct (N × H)
58. C₇×D₃₅	C₂×C₁₃⋊C₃	semidirect
59. C₇²×D₅	C₂×C₁₃⋊C₃	semidirect
60. C₅×C₇×D₇	C₂×C₁₃⋊C₃	semidirect
62. C₅×C₇×C₁₃	C₂×C₃×D₇	semidirect
63. C₅×C₇×C₁₃	C₂²×C₃×C₇	semidirect
68. D₅×C₁₃⋊C₃	C₇×D₇	direct (N × H)
75. C₇×C₁₃⋊C₃	D₅×D₇	direct (N × H)
76. C₇×C₁₃⋊C₃	C₂×C₇×D₅	semidirect
78. C₅×C₇²	C₂²×C₁₃⋊C₃	semidirect
87. C₅×C₁₃⋊C₃	C₂×C₇×D₇	semidirect
94. C₁₃×D₇	C₃×C₇×D₅	semidirect
98. D₅×D₇	C₇×C₁₃⋊C₃	direct (N × H)
101. D₅×C₁₃	C₃×C₇×D₇	semidirect
107. C₇×D₇	D₅×C₁₃⋊C₃	direct (N × H)
109. C₇×C₁₃	C₃×D₅×D₇	semidirect
110. C₇×C₁₃	C₂×C₃×C₇×D₅	semidirect
117. D₃₅	C₂×C₇×C₁₃⋊C₃	semidirect
118. C₅×D₇	C₂×C₇×C₁₃⋊C₃	semidirect
121. C₇×D₅	D₇×C₁₃⋊C₃	direct (N × H)
122. C₇×D₅	C₂×C₇×C₁₃⋊C₃	semidirect
123. C₅×C₁₃	C₂×C₃×C₇×D₇	semidirect
126. C₇²	C₂×D₅×C₁₃⋊C₃	semidirect
134. C₁₃⋊C₃	C₇×D₅×D₇	direct (N × H)
136. C₅×C₇	C₂×D₇×C₁₃⋊C₃	semidirect
137. C₅×C₇	C₂²×C₇×C₁₃⋊C₃	semidirect
157. D₇	C₇×D₅×C₁₃⋊C₃	direct (N × H)
158. C₁₃	C₃×C₇×D₅×D₇	semidirect
162. D₅	C₇×D₇×C₁₃⋊C₃	direct (N × H)
164. C₇	D₅×D₇×C₁₃⋊C₃	direct (N × H)
165. C₇	C₂×C₇×D₅×C₁₃⋊C₃	semidirect
169. C₅	C₂×C₇×D₇×C₁₃⋊C₃	semidirect

H ≅ G/N

type

1. C₇×C₁₃⋊C₃×D₃₅

C₂

semidirect

2. C₇²×D₅×C₁₃⋊C₃

C₂

semidirect

3. C₅×C₇×D₇×C₁₃⋊C₃

C₂

semidirect

4. C₇×D₅×C₁₃×D₇

C₃

semidirect

5. C₅×C₇²×C₁₃⋊C₃

C₂²

semidirect

7. C₇×C₁₃×D₃₅

C₂×C₃

semidirect

8. C₇²×D₅×C₁₃

C₂×C₃

semidirect

9. C₅×C₇×C₁₃×D₇

C₂×C₃

semidirect

11. D₅×D₇×C₁₃⋊C₃

C₇

direct (N × H)

14. C₇×D₇×C₁₃⋊C₃

D₅

direct (N × H)

15. C₅×C₇²×C₁₃

C₂²×C₃

semidirect

17. C₁₃⋊C₃×D₃₅

C₂×C₇

semidirect

20. C₇×D₅×C₁₃⋊C₃

D₇

direct (N × H)

21. C₇×D₅×C₁₃⋊C₃

C₂×C₇

semidirect

22. C₅×D₇×C₁₃⋊C₃

C₂×C₇

semidirect

25. C₇²×C₁₃⋊C₃

C₂×D₅

semidirect

27. D₅×C₁₃×D₇

C₃×C₇

semidirect

32. C₅×C₇×C₁₃⋊C₃

C₂×D₇

semidirect

33. C₅×C₇×C₁₃⋊C₃

C₂²×C₇

semidirect

36. C₇×C₁₃×D₇

C₃×D₅

semidirect

39. C₇×D₅×D₇

C₁₃⋊C₃

direct (N × H)

41. C₁₃×D₃₅

C₂×C₃×C₇

semidirect

44. C₇×D₅×C₁₃

C₃×D₇

semidirect

45. C₇×D₅×C₁₃

C₂×C₃×C₇

semidirect

46. C₅×C₁₃×D₇

C₂×C₃×C₇

semidirect

49. C₇²×C₁₃

C₂×C₃×D₅

semidirect

57. D₇×C₁₃⋊C₃

C₇×D₅

direct (N × H)

58. C₇×D₃₅

C₂×C₁₃⋊C₃

semidirect

59. C₇²×D₅

C₂×C₁₃⋊C₃

semidirect

60. C₅×C₇×D₇

C₂×C₁₃⋊C₃

semidirect

62. C₅×C₇×C₁₃

C₂×C₃×D₇

semidirect

63. C₅×C₇×C₁₃

C₂²×C₃×C₇

semidirect

68. D₅×C₁₃⋊C₃

C₇×D₇

direct (N × H)

75. C₇×C₁₃⋊C₃

D₅×D₇

direct (N × H)

76. C₇×C₁₃⋊C₃

C₂×C₇×D₅

semidirect

78. C₅×C₇²

C₂²×C₁₃⋊C₃

semidirect

87. C₅×C₁₃⋊C₃

C₂×C₇×D₇

semidirect

94. C₁₃×D₇

C₃×C₇×D₅

semidirect

98. D₅×D₇

C₇×C₁₃⋊C₃

direct (N × H)

101. D₅×C₁₃

C₃×C₇×D₇

semidirect

107. C₇×D₇

D₅×C₁₃⋊C₃

direct (N × H)

109. C₇×C₁₃

C₃×D₅×D₇

semidirect

110. C₇×C₁₃

C₂×C₃×C₇×D₅

semidirect

117. D₃₅

C₂×C₇×C₁₃⋊C₃

semidirect

118. C₅×D₇

C₂×C₇×C₁₃⋊C₃

semidirect

121. C₇×D₅

D₇×C₁₃⋊C₃

direct (N × H)

122. C₇×D₅

C₂×C₇×C₁₃⋊C₃

semidirect

123. C₅×C₁₃

C₂×C₃×C₇×D₇

semidirect

126. C₇²

C₂×D₅×C₁₃⋊C₃

semidirect

134. C₁₃⋊C₃

C₇×D₅×D₇

direct (N × H)

136. C₅×C₇

C₂×D₇×C₁₃⋊C₃

semidirect

137. C₅×C₇

C₂²×C₇×C₁₃⋊C₃

semidirect

157. D₇

C₇×D₅×C₁₃⋊C₃

direct (N × H)

158. C₁₃

C₃×C₇×D₅×D₇

semidirect

162. D₅

C₇×D₇×C₁₃⋊C₃

direct (N × H)

164. C₇

D₅×D₇×C₁₃⋊C₃

direct (N × H)

165. C₇

C₂×C₇×D₅×C₁₃⋊C₃

semidirect

169. C₅

C₂×C₇×D₇×C₁₃⋊C₃

semidirect

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

subgroup	index
C₇×C₁₃⋊C₃×D₃₅	2
C₇²×D₅×C₁₃⋊C₃	2
C₅×C₇×D₇×C₁₃⋊C₃	2
C₇×D₅×C₁₃×D₇	3
C₂×C₇×D₇×C₁₃⋊C₃	5
C₂×C₇×D₅×C₁₃⋊C₃	7
D₅×D₇×C₁₃⋊C₃	7
C₃×C₇×D₅×D₇	13

subgroup

index

C₇×C₁₃⋊C₃×D₃₅

C₇²×D₅×C₁₃⋊C₃

C₅×C₇×D₇×C₁₃⋊C₃

C₇×D₅×C₁₃×D₇

C₂×C₇×D₇×C₁₃⋊C₃

C₂×C₇×D₅×C₁₃⋊C₃

D₅×D₇×C₁₃⋊C₃

C₃×C₇×D₅×D₇

Subgroups — C₇×D₅×D₇×C₁₃⋊C₃ #50304087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C7×D5×D7×C13⋊C3 #50304087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₅×D₇×C₁₃⋊C₃ #50304087