Group #37561636 — subgroups

Subgroups — C₂×C₃×C₅×D₃×C₇×C₁₉ #37561636

Order 23940.

176 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 112 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×D₃×C₇×C₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₇×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂²×C₃×C₅×C₇×C₁₉	—	3	1	no	maximal
5	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃×C₇×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₃×C₇×C₁₉	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅×C₇×C₁₉	—	2	1	no	—
9	C₂×C₃×C₅×C₇×C₁₉	—	3	2	no	—
10	C₂×C₃×C₅×C₇×C₁₉	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×D₃×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₅×C₇×C₁₉	—	3	1	no	Hall
14	C₃×D₃×C₇×C₁₉	C₂×C₅	1	2	yes	direct product factor
15	C₂×C₃²×C₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
16	C₃×C₅×C₇×C₁₉	—	2	1	no	—
17	C₃×C₅×C₇×C₁₉	C₂×D₃	1	1	yes	characteristic, direct product factor
18	C₃×C₅×C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₅×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
20	C₃×C₅×D₃×C₁₉	C₂×C₇	1	2	yes	direct product factor
21	C₂²×C₃×C₇×C₁₉	—	3	1	no	—
22	C₂×D₃×C₇×C₁₉	C₃×C₅	1	1	yes	characteristic, direct product factor
23	C₂×C₅×C₇×C₁₉	—	3	2	no	—
24	C₂×C₅×C₇×C₁₉	C₃×D₃	1	1	yes	characteristic, direct product factor
25	C₂×C₃×C₅×D₃×C₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₃²×C₇×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₅×C₁₉	—	3	1	no	—
28	C₂×C₅×D₃×C₁₉	C₃×C₇	1	1	yes	characteristic, direct product factor
29	C₃²×C₅×C₁₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇×C₁₉	—	2	1	no	—
31	C₂×C₃×C₇×C₁₉	—	3	2	no	—
32	C₂×C₃×C₇×C₁₉	C₅×D₃	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₇×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
34	D₃×C₇×C₁₉	C₂×C₃×C₅	1	2	yes	direct product factor
35	C₂×C₃×D₃×C₁₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
36	C₅×C₇×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₃²×C₅×C₇	C₂×C₁₉	1	1	yes	characteristic, complemented
38	C₃×C₅×D₃×C₇	C₂×C₁₉	1	2	yes	direct product factor
39	C₂×C₃×C₅×C₁₉	—	2	1	no	—
40	C₂×C₃×C₅×C₁₉	—	3	2	no	—
41	C₂×C₃×C₅×C₁₉	D₃×C₇	1	1	yes	characteristic, direct product factor
42	C₂×C₃×C₅×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
43	C₅×D₃×C₁₉	C₂×C₃×C₇	1	2	yes	direct product factor
44	C₂²×C₇×C₁₉	—	3	1	no	Hall
45	C₂²×C₃×C₅×C₇	—	3	1	no	—
46	C₂×C₅×D₃×C₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor
47	C₃×C₇×C₁₉	—	2	1	no	—
48	C₃×C₇×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor
49	C₃×C₇×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
50	C₂²×C₅×C₁₉	—	3	1	no	Hall
51	C₂×C₃²×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
52	C₃×D₃×C₁₉	C₂×C₅×C₇	1	2	yes	direct product factor
53	C₃²×C₅×C₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
54	C₃×C₅×C₁₉	—	2	1	no	—
55	C₃×C₅×C₁₉	C₂×D₃×C₇	1	1	yes	characteristic, direct product factor
56	C₃×C₅×C₁₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
57	C₂×C₇×C₁₉	—	3	2	no	—
58	C₂×C₇×C₁₉	C₃×C₅×D₃	1	1	yes	characteristic, direct product factor
59	C₂×C₃×D₃×C₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
60	C₂²×C₃×C₁₉	—	3	1	no	—
61	C₂×D₃×C₁₉	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor
62	C₂×C₃×C₅×C₇	—	2	1	no	—
63	C₂×C₃×C₅×C₇	—	3	2	no	—
64	C₂×C₃×C₅×C₇	D₃×C₁₉	1	1	yes	characteristic, direct product factor
65	C₂×C₃×C₅×C₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
66	C₅×D₃×C₇	C₂×C₃×C₁₉	1	2	yes	direct product factor
67	C₂×C₅×C₁₉	—	3	2	no	—
68	C₂×C₅×C₁₉	C₃×D₃×C₇	1	1	yes	characteristic, direct product factor
69	C₂×C₃×C₅×D₃	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
70	C₃²×C₁₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
71	C₂²×C₅×C₇	—	3	1	no	Hall
72	C₇×C₁₉	C₂×C₃×C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
73	C₂×C₃²×C₇	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
74	C₃×D₃×C₇	C₂×C₅×C₁₉	1	2	yes	direct product factor
75	C₂×C₃×C₁₉	—	2	1	no	—
76	C₂×C₃×C₁₉	—	3	2	no	—
77	C₂×C₃×C₁₉	C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
78	C₂×C₃×C₁₉	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
79	D₃×C₁₉	C₂×C₃×C₅×C₇	1	2	yes	direct product factor
80	C₃×C₅×C₇	—	2	1	no	—
81	C₃×C₅×C₇	C₂×D₃×C₁₉	1	1	yes	characteristic, direct product factor
82	C₃×C₅×C₇	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented
83	C₅×C₁₉	C₂×C₃×D₃×C₇	1	1	yes	characteristic, direct product factor, Hall
84	C₂×C₃²×C₅	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
85	C₃×C₅×D₃	C₂×C₇×C₁₉	1	2	yes	direct product factor
86	C₂²×C₃×C₇	—	3	1	no	—
87	C₂×D₃×C₇	C₃×C₅×C₁₉	1	1	yes	characteristic, direct product factor
88	C₂²×C₁₉	—	3	1	no	Hall
89	C₂×C₅×C₇	—	3	2	no	—
90	C₂×C₅×C₇	C₃×D₃×C₁₉	1	1	yes	characteristic, direct product factor
91	C₃²×C₇	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
92	C₂²×C₃×C₅	—	3	1	no	—
93	C₂×C₅×D₃	C₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
94	C₃×C₁₉	—	2	1	no	—
95	C₃×C₁₉	C₂×C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
96	C₃×C₁₉	C₂²×C₃×C₅×C₇	1	1	yes	characteristic, complemented
97	C₃²×C₅	C₂²×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
98	C₂×C₃×C₇	—	2	1	no	—
99	C₂×C₃×C₇	—	3	2	no	—
100	C₂×C₃×C₇	C₅×D₃×C₁₉	1	1	yes	characteristic, direct product factor
101	C₂×C₃×C₇	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
102	D₃×C₇	C₂×C₃×C₅×C₁₉	1	2	yes	direct product factor
103	C₂×C₁₉	—	3	2	no	—
104	C₂×C₁₉	C₃×C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
105	C₂×C₃×D₃	C₅×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
106	C₅×C₇	C₂×C₃×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
107	C₂×C₃×C₅	—	2	1	no	—
108	C₂×C₃×C₅	—	3	2	no	—
109	C₂×C₃×C₅	D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
110	C₂×C₃×C₅	C₂×C₃×C₇×C₁₉	1	1	yes	characteristic, complemented
111	C₅×D₃	C₂×C₃×C₇×C₁₉	1	2	yes	direct product factor
112	C₂²×C₇	—	3	1	no	Hall
113	C₃×C₇	—	2	1	no	—
114	C₃×C₇	C₂×C₅×D₃×C₁₉	1	1	yes	characteristic, direct product factor
115	C₃×C₇	C₂²×C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
116	C₂²×C₅	—	3	1	no	Hall
117	C₁₉	C₂×C₃×C₅×D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
118	C₂×C₃²	C₂×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented
119	C₃×D₃	C₂×C₅×C₇×C₁₉	1	2	yes	direct product factor
120	C₃×C₅	—	2	1	no	—
121	C₃×C₅	C₂×D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
122	C₃×C₅	C₂²×C₃×C₇×C₁₉	1	1	yes	characteristic, complemented
123	C₂×C₇	—	3	2	no	—
124	C₂×C₇	C₃×C₅×D₃×C₁₉	1	1	yes	characteristic, direct product factor
125	C₂²×C₃	—	3	1	no	—
126	C₂×D₃	C₃×C₅×C₇×C₁₉	1	1	yes	characteristic, direct product factor
127	C₂×C₅	—	3	2	no	—
128	C₂×C₅	C₃×D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
129	C₃²	C₂²×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
130	C₇	C₂×C₃×C₅×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₃	—	2	1	no	—
132	C₂×C₃	—	3	2	no	—
133	C₂×C₃	C₂×C₃×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented
134	C₂×C₃	C₅×D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
135	D₃	C₂×C₃×C₅×C₇×C₁₉	1	2	yes	direct product factor
136	C₅	C₂×C₃×D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²	—	3	1	no	Sylow
138	C₃	—	2	1	no	—
139	C₃	C₂²×C₃×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented
140	C₃	C₂×C₅×D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
141	C₂	—	3	2	no	—
142	C₂	C₃×C₅×D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×D₃×C₇×C₁₉

C₂

yes

maximal, direct product factor

C₂×C₃²×C₅×C₇×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₅×D₃×C₇×C₁₉

C₃

yes

maximal, characteristic, direct product factor

C₂²×C₃×C₅×C₇×C₁₉

—

maximal

C₃²×C₅×C₇×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₃×D₃×C₇×C₁₉

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×D₃×C₇×C₁₉

C₂×C₃

yes

direct product factor

C₂×C₃×C₅×C₇×C₁₉

—

C₂×C₃×C₅×C₇×C₁₉

—

C₂×C₃×C₅×C₇×C₁₉

D₃

yes

characteristic, direct product factor

C₂×C₃×C₅×C₇×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂×C₃×C₅×D₃×C₁₉

C₇

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₅×C₇×C₁₉

—

Hall

C₃×D₃×C₇×C₁₉

C₂×C₅

yes

direct product factor

C₂×C₃²×C₇×C₁₉

C₂×C₅

yes

characteristic, complemented

C₃×C₅×C₇×C₁₉

—

C₃×C₅×C₇×C₁₉

C₂×D₃

yes

characteristic, direct product factor

C₃×C₅×C₇×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₂×C₃²×C₅×C₁₉

C₂×C₇

yes

characteristic, complemented

C₃×C₅×D₃×C₁₉

C₂×C₇

yes

direct product factor

C₂²×C₃×C₇×C₁₉

—

C₂×D₃×C₇×C₁₉

C₃×C₅

yes

characteristic, direct product factor

C₂×C₅×C₇×C₁₉

—

C₂×C₅×C₇×C₁₉

C₃×D₃

yes

characteristic, direct product factor

C₂×C₃×C₅×D₃×C₇

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₇×C₁₉

C₂²×C₅

yes

characteristic, complemented, Hall

C₂²×C₃×C₅×C₁₉

—

C₂×C₅×D₃×C₁₉

C₃×C₇

yes

characteristic, direct product factor

C₃²×C₅×C₁₉

C₂²×C₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

C₅×D₃

yes

characteristic, direct product factor

C₂×C₃×C₇×C₁₉

C₂×C₃×C₅

yes

characteristic, complemented

D₃×C₇×C₁₉

C₂×C₃×C₅

yes

direct product factor

C₂×C₃×D₃×C₁₉

C₅×C₇

yes

characteristic, direct product factor, Hall

C₅×C₇×C₁₉

C₂×C₃×D₃

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₅×C₇

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅×D₃×C₇

C₂×C₁₉

yes

direct product factor

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

D₃×C₇

yes

characteristic, direct product factor

C₂×C₃×C₅×C₁₉

C₂×C₃×C₇

yes

characteristic, complemented

C₅×D₃×C₁₉

C₂×C₃×C₇

yes

direct product factor

C₂²×C₇×C₁₉

—

Hall

C₂²×C₃×C₅×C₇

—

C₂×C₅×D₃×C₇

C₃×C₁₉

yes

characteristic, direct product factor

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

C₂×C₅×D₃

yes

characteristic, direct product factor

C₃×C₇×C₁₉

C₂²×C₃×C₅

yes

characteristic, complemented

C₂²×C₅×C₁₉

—

Hall

C₂×C₃²×C₁₉

C₂×C₅×C₇

yes

characteristic, complemented

C₃×D₃×C₁₉

C₂×C₅×C₇

yes

direct product factor

C₃²×C₅×C₇

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×D₃×C₇

yes

characteristic, direct product factor

C₃×C₅×C₁₉

C₂²×C₃×C₇

yes

characteristic, complemented

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

C₃×C₅×D₃

yes

characteristic, direct product factor

C₂×C₃×D₃×C₇

C₅×C₁₉

yes

characteristic, direct product factor, Hall

C₂²×C₃×C₁₉

—

C₂×D₃×C₁₉

C₃×C₅×C₇

yes

characteristic, direct product factor

C₂×C₃×C₅×C₇

—

C₂×C₃×C₅×C₇

—

C₂×C₃×C₅×C₇

D₃×C₁₉

yes

characteristic, direct product factor

C₂×C₃×C₅×C₇

C₂×C₃×C₁₉

yes

characteristic, complemented

C₅×D₃×C₇

C₂×C₃×C₁₉

yes

direct product factor

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃×D₃×C₇

yes

characteristic, direct product factor

C₂×C₃×C₅×D₃

C₇×C₁₉

yes

characteristic, direct product factor, Hall

C₃²×C₁₉

C₂²×C₅×C₇

yes

characteristic, complemented, Hall

C₂²×C₅×C₇

—

Hall

C₇×C₁₉

C₂×C₃×C₅×D₃

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₇

C₂×C₅×C₁₉

yes

characteristic, complemented

C₃×D₃×C₇

C₂×C₅×C₁₉

yes

direct product factor

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₅×D₃×C₇

yes

characteristic, direct product factor

C₂×C₃×C₁₉

C₂×C₃×C₅×C₇

yes

characteristic, complemented

D₃×C₁₉

C₂×C₃×C₅×C₇

yes

direct product factor

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂×D₃×C₁₉

yes

characteristic, direct product factor

C₃×C₅×C₇

C₂²×C₃×C₁₉

yes

characteristic, complemented

C₅×C₁₉

C₂×C₃×D₃×C₇

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₅

C₂×C₇×C₁₉

yes

characteristic, complemented

C₃×C₅×D₃

C₂×C₇×C₁₉

yes

direct product factor

C₂²×C₃×C₇

—

C₂×D₃×C₇

C₃×C₅×C₁₉

yes

characteristic, direct product factor

C₂²×C₁₉

—

Hall

C₂×C₅×C₇

—

C₂×C₅×C₇

C₃×D₃×C₁₉

yes

characteristic, direct product factor

C₃²×C₇

C₂²×C₅×C₁₉

yes

characteristic, complemented, Hall

C₂²×C₃×C₅

—

C₂×C₅×D₃

C₃×C₇×C₁₉

yes

characteristic, direct product factor

C₃×C₁₉

—

C₃×C₁₉

C₂×C₅×D₃×C₇

yes

characteristic, direct product factor

C₃×C₁₉

C₂²×C₃×C₅×C₇

yes

characteristic, complemented

C₃²×C₅

C₂²×C₇×C₁₉

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

C₂×C₃×C₇

—

100

C₂×C₃×C₇

C₅×D₃×C₁₉

yes

characteristic, direct product factor

101

C₂×C₃×C₇

C₂×C₃×C₅×C₁₉

yes

characteristic, complemented

102

D₃×C₇

C₂×C₃×C₅×C₁₉

yes

direct product factor

103

C₂×C₁₉

—

104

C₂×C₁₉

C₃×C₅×D₃×C₇

yes

characteristic, direct product factor

105

C₂×C₃×D₃

C₅×C₇×C₁₉

yes

characteristic, direct product factor, Hall

106

C₅×C₇

C₂×C₃×D₃×C₁₉

yes

characteristic, direct product factor, Hall

107

C₂×C₃×C₅

—

108

C₂×C₃×C₅

—

109

C₂×C₃×C₅

D₃×C₇×C₁₉

yes

characteristic, direct product factor

110

C₂×C₃×C₅

C₂×C₃×C₇×C₁₉

yes

characteristic, complemented

111

C₅×D₃

C₂×C₃×C₇×C₁₉

yes

direct product factor

112

C₂²×C₇

—

Hall

113

C₃×C₇

—

114

C₃×C₇

C₂×C₅×D₃×C₁₉

yes

characteristic, direct product factor

115

C₃×C₇

C₂²×C₃×C₅×C₁₉

yes

characteristic, complemented

116

C₂²×C₅

—

Hall

117

C₁₉

C₂×C₃×C₅×D₃×C₇

yes

characteristic, direct product factor, Sylow

118

C₂×C₃²

C₂×C₅×C₇×C₁₉

yes

characteristic, complemented

119

C₃×D₃

C₂×C₅×C₇×C₁₉

yes

direct product factor

120

C₃×C₅

—

121

C₃×C₅

C₂×D₃×C₇×C₁₉

yes

characteristic, direct product factor

122

C₃×C₅

C₂²×C₃×C₇×C₁₉

yes

characteristic, complemented

123

C₂×C₇

—

124

C₂×C₇

C₃×C₅×D₃×C₁₉

yes

characteristic, direct product factor

125

C₂²×C₃

—

126

C₂×D₃

C₃×C₅×C₇×C₁₉

yes

characteristic, direct product factor

127

C₂×C₅

—

128

C₂×C₅

C₃×D₃×C₇×C₁₉

yes

characteristic, direct product factor

129

C₃²

C₂²×C₅×C₇×C₁₉

yes

characteristic, complemented, Sylow

130

C₇

C₂×C₃×C₅×D₃×C₁₉

yes

characteristic, direct product factor, Sylow

131

C₂×C₃

—

132

C₂×C₃

—

133

C₂×C₃

C₂×C₃×C₅×C₇×C₁₉

yes

characteristic, complemented

134

C₂×C₃

C₅×D₃×C₇×C₁₉

yes

characteristic, direct product factor

135

D₃

C₂×C₃×C₅×C₇×C₁₉

yes

direct product factor

136

C₅

C₂×C₃×D₃×C₇×C₁₉

yes

characteristic, direct product factor, Sylow

137

C₂²

—

Sylow

138

C₃

—

139

C₃

C₂²×C₃×C₅×C₇×C₁₉

yes

characteristic, complemented

140

C₃

C₂×C₅×D₃×C₇×C₁₉

yes

characteristic, direct product factor

141

C₂

—

142

C₂

C₃×C₅×D₃×C₇×C₁₉

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₇×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₅×C₇×C₁₉

subgroup

G/H

center, hypercenter

C₂×C₃×C₅×C₇×C₁₉

D₃

commutator, cosocle, hypocenter

C₃

C₂²×C₃×C₅×C₇×C₁₉

Frattini

C₁

Fitting, socle

C₂×C₃²×C₅×C₇×C₁₉

C₂

LCS

G ▷ C₃

UCS

C₁ ◁ C₂×C₃×C₅×C₇×C₁₉

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₇×C₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₉	C₂	semidirect
3. C₂×C₅×D₃×C₇×C₁₉	C₃	direct (N × H)
5. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
6. C₂×C₃×D₃×C₇×C₁₉	C₅	direct (N × H)
7. C₅×D₃×C₇×C₁₉	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₇×C₁₉	D₃	direct (N × H)
11. C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	semidirect
12. C₂×C₃×C₅×D₃×C₁₉	C₇	direct (N × H)
14. C₃×D₃×C₇×C₁₉	C₂×C₅	direct (N × H)
15. C₂×C₃²×C₇×C₁₉	C₂×C₅	semidirect
17. C₃×C₅×C₇×C₁₉	C₂×D₃	direct (N × H)
18. C₃×C₅×C₇×C₁₉	C₂²×C₃	semidirect
19. C₂×C₃²×C₅×C₁₉	C₂×C₇	semidirect
20. C₃×C₅×D₃×C₁₉	C₂×C₇	direct (N × H)
22. C₂×D₃×C₇×C₁₉	C₃×C₅	direct (N × H)
24. C₂×C₅×C₇×C₁₉	C₃×D₃	direct (N × H)
25. C₂×C₃×C₅×D₃×C₇	C₁₉	direct (N × H)
26. C₃²×C₇×C₁₉	C₂²×C₅	semidirect
28. C₂×C₅×D₃×C₁₉	C₃×C₇	direct (N × H)
29. C₃²×C₅×C₁₉	C₂²×C₇	semidirect
32. C₂×C₃×C₇×C₁₉	C₅×D₃	direct (N × H)
33. C₂×C₃×C₇×C₁₉	C₂×C₃×C₅	semidirect
34. D₃×C₇×C₁₉	C₂×C₃×C₅	direct (N × H)
35. C₂×C₃×D₃×C₁₉	C₅×C₇	direct (N × H)
36. C₅×C₇×C₁₉	C₂×C₃×D₃	direct (N × H)
37. C₂×C₃²×C₅×C₇	C₂×C₁₉	semidirect
38. C₃×C₅×D₃×C₇	C₂×C₁₉	direct (N × H)
41. C₂×C₃×C₅×C₁₉	D₃×C₇	direct (N × H)
42. C₂×C₃×C₅×C₁₉	C₂×C₃×C₇	semidirect
43. C₅×D₃×C₁₉	C₂×C₃×C₇	direct (N × H)
46. C₂×C₅×D₃×C₇	C₃×C₁₉	direct (N × H)
48. C₃×C₇×C₁₉	C₂×C₅×D₃	direct (N × H)
49. C₃×C₇×C₁₉	C₂²×C₃×C₅	semidirect
51. C₂×C₃²×C₁₉	C₂×C₅×C₇	semidirect
52. C₃×D₃×C₁₉	C₂×C₅×C₇	direct (N × H)
53. C₃²×C₅×C₇	C₂²×C₁₉	semidirect
55. C₃×C₅×C₁₉	C₂×D₃×C₇	direct (N × H)
56. C₃×C₅×C₁₉	C₂²×C₃×C₇	semidirect
58. C₂×C₇×C₁₉	C₃×C₅×D₃	direct (N × H)
59. C₂×C₃×D₃×C₇	C₅×C₁₉	direct (N × H)
61. C₂×D₃×C₁₉	C₃×C₅×C₇	direct (N × H)
64. C₂×C₃×C₅×C₇	D₃×C₁₉	direct (N × H)
65. C₂×C₃×C₅×C₇	C₂×C₃×C₁₉	semidirect
66. C₅×D₃×C₇	C₂×C₃×C₁₉	direct (N × H)
68. C₂×C₅×C₁₉	C₃×D₃×C₇	direct (N × H)
69. C₂×C₃×C₅×D₃	C₇×C₁₉	direct (N × H)
70. C₃²×C₁₉	C₂²×C₅×C₇	semidirect
72. C₇×C₁₉	C₂×C₃×C₅×D₃	direct (N × H)
73. C₂×C₃²×C₇	C₂×C₅×C₁₉	semidirect
74. C₃×D₃×C₇	C₂×C₅×C₁₉	direct (N × H)
77. C₂×C₃×C₁₉	C₅×D₃×C₇	direct (N × H)
78. C₂×C₃×C₁₉	C₂×C₃×C₅×C₇	semidirect
79. D₃×C₁₉	C₂×C₃×C₅×C₇	direct (N × H)
81. C₃×C₅×C₇	C₂×D₃×C₁₉	direct (N × H)
82. C₃×C₅×C₇	C₂²×C₃×C₁₉	semidirect
83. C₅×C₁₉	C₂×C₃×D₃×C₇	direct (N × H)
84. C₂×C₃²×C₅	C₂×C₇×C₁₉	semidirect
85. C₃×C₅×D₃	C₂×C₇×C₁₉	direct (N × H)
87. C₂×D₃×C₇	C₃×C₅×C₁₉	direct (N × H)
90. C₂×C₅×C₇	C₃×D₃×C₁₉	direct (N × H)
91. C₃²×C₇	C₂²×C₅×C₁₉	semidirect
93. C₂×C₅×D₃	C₃×C₇×C₁₉	direct (N × H)
95. C₃×C₁₉	C₂×C₅×D₃×C₇	direct (N × H)
96. C₃×C₁₉	C₂²×C₃×C₅×C₇	semidirect
97. C₃²×C₅	C₂²×C₇×C₁₉	semidirect
100. C₂×C₃×C₇	C₅×D₃×C₁₉	direct (N × H)
101. C₂×C₃×C₇	C₂×C₃×C₅×C₁₉	semidirect
102. D₃×C₇	C₂×C₃×C₅×C₁₉	direct (N × H)
104. C₂×C₁₉	C₃×C₅×D₃×C₇	direct (N × H)
105. C₂×C₃×D₃	C₅×C₇×C₁₉	direct (N × H)
106. C₅×C₇	C₂×C₃×D₃×C₁₉	direct (N × H)
109. C₂×C₃×C₅	D₃×C₇×C₁₉	direct (N × H)
110. C₂×C₃×C₅	C₂×C₃×C₇×C₁₉	semidirect
111. C₅×D₃	C₂×C₃×C₇×C₁₉	direct (N × H)
114. C₃×C₇	C₂×C₅×D₃×C₁₉	direct (N × H)
115. C₃×C₇	C₂²×C₃×C₅×C₁₉	semidirect
117. C₁₉	C₂×C₃×C₅×D₃×C₇	direct (N × H)
118. C₂×C₃²	C₂×C₅×C₇×C₁₉	semidirect
119. C₃×D₃	C₂×C₅×C₇×C₁₉	direct (N × H)
121. C₃×C₅	C₂×D₃×C₇×C₁₉	direct (N × H)
122. C₃×C₅	C₂²×C₃×C₇×C₁₉	semidirect
124. C₂×C₇	C₃×C₅×D₃×C₁₉	direct (N × H)
126. C₂×D₃	C₃×C₅×C₇×C₁₉	direct (N × H)
128. C₂×C₅	C₃×D₃×C₇×C₁₉	direct (N × H)
129. C₃²	C₂²×C₅×C₇×C₁₉	semidirect
130. C₇	C₂×C₃×C₅×D₃×C₁₉	direct (N × H)
133. C₂×C₃	C₂×C₃×C₅×C₇×C₁₉	semidirect
134. C₂×C₃	C₅×D₃×C₇×C₁₉	direct (N × H)
135. D₃	C₂×C₃×C₅×C₇×C₁₉	direct (N × H)
136. C₅	C₂×C₃×D₃×C₇×C₁₉	direct (N × H)
139. C₃	C₂²×C₃×C₅×C₇×C₁₉	semidirect
140. C₃	C₂×C₅×D₃×C₇×C₁₉	direct (N × H)
142. C₂	C₃×C₅×D₃×C₇×C₁₉	direct (N × H)

H ≅ G/N

type

1. C₃×C₅×D₃×C₇×C₁₉

C₂

direct (N × H)

2. C₂×C₃²×C₅×C₇×C₁₉

C₂

semidirect

3. C₂×C₅×D₃×C₇×C₁₉

C₃

direct (N × H)

5. C₃²×C₅×C₇×C₁₉

C₂²

semidirect

6. C₂×C₃×D₃×C₇×C₁₉

C₅

direct (N × H)

7. C₅×D₃×C₇×C₁₉

C₂×C₃

direct (N × H)

10. C₂×C₃×C₅×C₇×C₁₉

D₃

direct (N × H)

11. C₂×C₃×C₅×C₇×C₁₉

C₂×C₃

semidirect

12. C₂×C₃×C₅×D₃×C₁₉

C₇

direct (N × H)

14. C₃×D₃×C₇×C₁₉

C₂×C₅

direct (N × H)

15. C₂×C₃²×C₇×C₁₉

C₂×C₅

semidirect

17. C₃×C₅×C₇×C₁₉

C₂×D₃

direct (N × H)

18. C₃×C₅×C₇×C₁₉

C₂²×C₃

semidirect

19. C₂×C₃²×C₅×C₁₉

C₂×C₇

semidirect

20. C₃×C₅×D₃×C₁₉

C₂×C₇

direct (N × H)

22. C₂×D₃×C₇×C₁₉

C₃×C₅

direct (N × H)

24. C₂×C₅×C₇×C₁₉

C₃×D₃

direct (N × H)

25. C₂×C₃×C₅×D₃×C₇

C₁₉

direct (N × H)

26. C₃²×C₇×C₁₉

C₂²×C₅

semidirect

28. C₂×C₅×D₃×C₁₉

C₃×C₇

direct (N × H)

29. C₃²×C₅×C₁₉

C₂²×C₇

semidirect

32. C₂×C₃×C₇×C₁₉

C₅×D₃

direct (N × H)

33. C₂×C₃×C₇×C₁₉

C₂×C₃×C₅

semidirect

34. D₃×C₇×C₁₉

C₂×C₃×C₅

direct (N × H)

35. C₂×C₃×D₃×C₁₉

C₅×C₇

direct (N × H)

36. C₅×C₇×C₁₉

C₂×C₃×D₃

direct (N × H)

37. C₂×C₃²×C₅×C₇

C₂×C₁₉

semidirect

38. C₃×C₅×D₃×C₇

C₂×C₁₉

direct (N × H)

41. C₂×C₃×C₅×C₁₉

D₃×C₇

direct (N × H)

42. C₂×C₃×C₅×C₁₉

C₂×C₃×C₇

semidirect

43. C₅×D₃×C₁₉

C₂×C₃×C₇

direct (N × H)

46. C₂×C₅×D₃×C₇

C₃×C₁₉

direct (N × H)

48. C₃×C₇×C₁₉

C₂×C₅×D₃

direct (N × H)

49. C₃×C₇×C₁₉

C₂²×C₃×C₅

semidirect

51. C₂×C₃²×C₁₉

C₂×C₅×C₇

semidirect

52. C₃×D₃×C₁₉

C₂×C₅×C₇

direct (N × H)

53. C₃²×C₅×C₇

C₂²×C₁₉

semidirect

55. C₃×C₅×C₁₉

C₂×D₃×C₇

direct (N × H)

56. C₃×C₅×C₁₉

C₂²×C₃×C₇

semidirect

58. C₂×C₇×C₁₉

C₃×C₅×D₃

direct (N × H)

59. C₂×C₃×D₃×C₇

C₅×C₁₉

direct (N × H)

61. C₂×D₃×C₁₉

C₃×C₅×C₇

direct (N × H)

64. C₂×C₃×C₅×C₇

D₃×C₁₉

direct (N × H)

65. C₂×C₃×C₅×C₇

C₂×C₃×C₁₉

semidirect

66. C₅×D₃×C₇

C₂×C₃×C₁₉

direct (N × H)

68. C₂×C₅×C₁₉

C₃×D₃×C₇

direct (N × H)

69. C₂×C₃×C₅×D₃

C₇×C₁₉

direct (N × H)

70. C₃²×C₁₉

C₂²×C₅×C₇

semidirect

72. C₇×C₁₉

C₂×C₃×C₅×D₃

direct (N × H)

73. C₂×C₃²×C₇

C₂×C₅×C₁₉

semidirect

74. C₃×D₃×C₇

C₂×C₅×C₁₉

direct (N × H)

77. C₂×C₃×C₁₉

C₅×D₃×C₇

direct (N × H)

78. C₂×C₃×C₁₉

C₂×C₃×C₅×C₇

semidirect

79. D₃×C₁₉

C₂×C₃×C₅×C₇

direct (N × H)

81. C₃×C₅×C₇

C₂×D₃×C₁₉

direct (N × H)

82. C₃×C₅×C₇

C₂²×C₃×C₁₉

semidirect

83. C₅×C₁₉

C₂×C₃×D₃×C₇

direct (N × H)

84. C₂×C₃²×C₅

C₂×C₇×C₁₉

semidirect

85. C₃×C₅×D₃

C₂×C₇×C₁₉

direct (N × H)

87. C₂×D₃×C₇

C₃×C₅×C₁₉

direct (N × H)

90. C₂×C₅×C₇

C₃×D₃×C₁₉

direct (N × H)

91. C₃²×C₇

C₂²×C₅×C₁₉

semidirect

93. C₂×C₅×D₃

C₃×C₇×C₁₉

direct (N × H)

95. C₃×C₁₉

C₂×C₅×D₃×C₇

direct (N × H)

96. C₃×C₁₉

C₂²×C₃×C₅×C₇

semidirect

97. C₃²×C₅

C₂²×C₇×C₁₉

semidirect

100. C₂×C₃×C₇

C₅×D₃×C₁₉

direct (N × H)

101. C₂×C₃×C₇

C₂×C₃×C₅×C₁₉

semidirect

102. D₃×C₇

C₂×C₃×C₅×C₁₉

direct (N × H)

104. C₂×C₁₉

C₃×C₅×D₃×C₇

direct (N × H)

105. C₂×C₃×D₃

C₅×C₇×C₁₉

direct (N × H)

106. C₅×C₇

C₂×C₃×D₃×C₁₉

direct (N × H)

109. C₂×C₃×C₅

D₃×C₇×C₁₉

direct (N × H)

110. C₂×C₃×C₅

C₂×C₃×C₇×C₁₉

semidirect

111. C₅×D₃

C₂×C₃×C₇×C₁₉

direct (N × H)

114. C₃×C₇

C₂×C₅×D₃×C₁₉

direct (N × H)

115. C₃×C₇

C₂²×C₃×C₅×C₁₉

semidirect

117. C₁₉

C₂×C₃×C₅×D₃×C₇

direct (N × H)

118. C₂×C₃²

C₂×C₅×C₇×C₁₉

semidirect

119. C₃×D₃

C₂×C₅×C₇×C₁₉

direct (N × H)

121. C₃×C₅

C₂×D₃×C₇×C₁₉

direct (N × H)

122. C₃×C₅

C₂²×C₃×C₇×C₁₉

semidirect

124. C₂×C₇

C₃×C₅×D₃×C₁₉

direct (N × H)

126. C₂×D₃

C₃×C₅×C₇×C₁₉

direct (N × H)

128. C₂×C₅

C₃×D₃×C₇×C₁₉

direct (N × H)

129. C₃²

C₂²×C₅×C₇×C₁₉

semidirect

130. C₇

C₂×C₃×C₅×D₃×C₁₉

direct (N × H)

133. C₂×C₃

C₂×C₃×C₅×C₇×C₁₉

semidirect

134. C₂×C₃

C₅×D₃×C₇×C₁₉

direct (N × H)

135. D₃

C₂×C₃×C₅×C₇×C₁₉

direct (N × H)

136. C₅

C₂×C₃×D₃×C₇×C₁₉

direct (N × H)

139. C₃

C₂²×C₃×C₅×C₇×C₁₉

semidirect

140. C₃

C₂×C₅×D₃×C₇×C₁₉

direct (N × H)

142. C₂

C₃×C₅×D₃×C₇×C₁₉

direct (N × H)

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

subgroup	index
C₃×C₅×D₃×C₇×C₁₉	2
C₂×C₃²×C₅×C₇×C₁₉	2
C₂×C₅×D₃×C₇×C₁₉	3
C₂²×C₃×C₅×C₇×C₁₉	3
C₂×C₃×D₃×C₇×C₁₉	5
C₂×C₃×C₅×D₃×C₁₉	7
C₂×C₃×C₅×D₃×C₇	19

subgroup

index

C₃×C₅×D₃×C₇×C₁₉

C₂×C₃²×C₅×C₇×C₁₉

C₂×C₅×D₃×C₇×C₁₉

C₂²×C₃×C₅×C₇×C₁₉

C₂×C₃×D₃×C₇×C₁₉

C₂×C₃×C₅×D₃×C₁₉

C₂×C₃×C₅×D₃×C₇

Subgroups — C₂×C₃×C₅×D₃×C₇×C₁₉ #37561636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C5×D3×C7×C19 #37561636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×D₃×C₇×C₁₉ #37561636