Group #30685974 — subgroups

Subgroups — C₂×C₃×C₅×C₁₉×D₁₅ #30685974

Order 17100.

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

normal subgroups only

This group has 224 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	C₃×C₅×C₁₉×D₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₉×D₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₅×D₅×C₁₉	—	3	1	no	maximal
5	C₃²×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×D₃×C₁₉	—	5	1	no	maximal
7	C₂×C₃×C₁₉×D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×C₁₉×D₁₅	C₂×C₃	1	2	yes	direct product factor
9	C₃×C₅×D₅×C₁₉	—	3	2	no	—
10	C₂×C₃×C₅²×C₁₉	—	2	1	no	—
11	C₂×C₃×C₅²×C₁₉	D₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₅×D₅×C₁₉	—	3	1	no	Hall
14	C₂×C₃²×C₅×C₁₉	—	2	2	no	—
15	C₂×C₃²×C₅×C₁₉	D₅	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₅×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×C₁₉×D₁₅	C₂×C₅	1	2	yes	direct product factor
18	C₃×C₅×D₃×C₁₉	—	5	2	no	—
19	C₃×C₅²×C₁₉	—	2	1	no	—
20	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₅×C₁₉	—	15	1	no	—
23	C₂×C₁₉×D₁₅	C₃×C₅	1	1	yes	characteristic, direct product factor
24	C₂×C₅×D₃×C₁₉	—	5	1	no	—
25	C₂×C₃×D₅×C₁₉	—	3	1	no	—
26	C₂×C₅²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
27	C₅×D₅×C₁₉	—	3	2	no	—
28	C₂×C₃×C₅×D₁₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₃²×C₅×C₁₉	—	2	2	no	—
30	C₃²×C₅×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
31	C₃²×C₅×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
32	C₂×C₃×D₃×C₁₉	—	5	1	no	Hall
33	C₂×C₃×C₅×C₁₉	—	2	4	no	—
34	C₂×C₃×C₅×C₁₉	—	2	2	no	—
35	C₂×C₃×C₅×C₁₉	—	2	2	no	—
36	C₂×C₃×C₅×C₁₉	—	2	1	no	—
37	C₂×C₃×C₅×C₁₉	—	2	1	no	—
38	C₂×C₃×C₅×C₁₉	—	15	2	no	—
39	C₂×C₃×C₅×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
41	C₂×C₃×C₅×C₁₉	D₁₅	1	1	yes	characteristic, direct product factor
42	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
43	C₁₉×D₁₅	C₂×C₃×C₅	1	2	yes	direct product factor
44	C₅×D₃×C₁₉	—	5	2	no	—
45	C₃×D₅×C₁₉	—	3	2	no	—
46	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃²×C₅²	C₂×C₁₉	1	1	yes	characteristic, complemented
48	C₃×C₅×D₁₅	C₂×C₁₉	1	2	yes	direct product factor
49	C₂²×C₅×C₁₉	—	15	1	no	—
50	C₂×D₅×C₁₉	—	3	1	no	—
51	C₂×C₃²×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented
52	C₃×D₃×C₁₉	—	5	2	no	—
53	C₂×C₅×D₁₅	C₃×C₁₉	1	1	yes	characteristic, direct product factor
54	C₂×C₃×C₅×D₅	—	3	1	no	—
55	C₃×C₅×C₁₉	—	2	4	no	—
56	C₃×C₅×C₁₉	—	2	2	no	—
57	C₃×C₅×C₁₉	—	2	2	no	—
58	C₃×C₅×C₁₉	—	2	1	no	—
59	C₃×C₅×C₁₉	—	2	1	no	—
60	C₃×C₅×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
61	C₃×C₅×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented
62	C₃×C₅×C₁₉	C₂×D₁₅	1	1	yes	characteristic, direct product factor
63	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
64	C₂²×C₃×C₁₉	—	15	1	no	—
65	C₂×D₃×C₁₉	—	5	1	no	—
66	C₃²×C₅²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
67	C₂×C₅×C₁₉	—	2	2	no	—
68	C₂×C₅×C₁₉	—	15	2	no	—
69	C₂×C₅×C₁₉	C₃×C₅×D₃	1	1	yes	characteristic, complemented
70	C₂×C₅×C₁₉	C₃×D₁₅	1	1	yes	characteristic, direct product factor
71	D₅×C₁₉	—	3	2	no	—
72	C₂×C₃×D₁₅	C₅×C₁₉	1	1	yes	characteristic, direct product factor
73	C₂×C₃×C₅×D₃	—	5	1	no	—
74	C₃²×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
75	C₂×C₃×C₅²	—	2	1	no	—
76	C₂×C₃×C₅²	D₃×C₁₉	1	1	yes	characteristic, complemented
77	C₂×C₃×C₅²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
78	C₅×D₁₅	C₂×C₃×C₁₉	1	2	yes	direct product factor
79	C₃×C₅×D₅	—	3	2	no	—
80	C₂×C₃×C₁₉	—	2	1	no	—
81	C₂×C₃×C₁₉	—	15	2	no	—
82	C₂×C₃×C₁₉	C₃×C₅×D₅	1	1	yes	characteristic, complemented
83	C₂×C₃×C₁₉	C₅×D₁₅	1	1	yes	characteristic, direct product factor
84	D₃×C₁₉	—	5	2	no	—
85	C₂×C₅×D₅	—	3	1	no	Hall
86	C₅×C₁₉	—	2	2	no	—
87	C₅×C₁₉	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented
88	C₅×C₁₉	C₂×C₃×D₁₅	1	1	yes	characteristic, direct product factor
89	C₂×C₃²×C₅	—	2	2	no	—
90	C₂×C₃²×C₅	D₅×C₁₉	1	1	yes	characteristic, complemented
91	C₂×C₃²×C₅	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
92	C₃×D₁₅	C₂×C₅×C₁₉	1	2	yes	direct product factor
93	C₃×C₅×D₃	—	5	2	no	—
94	C₂²×C₁₉	—	15	1	no	Hall
95	C₃×C₅²	—	2	1	no	—
96	C₃×C₅²	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented
97	C₃×C₅²	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented
98	C₂²×C₃×C₅	—	15	1	no	—
99	C₂×D₁₅	C₃×C₅×C₁₉	1	1	yes	characteristic, direct product factor
100	C₂×C₅×D₃	—	5	1	no	—
101	C₂×C₃×D₅	—	3	1	no	—
102	C₃×C₁₉	—	2	1	no	—
103	C₃×C₁₉	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented
104	C₃×C₁₉	C₂×C₅×D₁₅	1	1	yes	characteristic, direct product factor
105	C₂×C₅²	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented
106	C₅×D₅	—	3	2	no	—
107	C₃²×C₅	—	2	2	no	—
108	C₃²×C₅	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented
109	C₃²×C₅	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented
110	C₂×C₁₉	—	15	2	no	—
111	C₂×C₁₉	C₃×C₅×D₁₅	1	1	yes	characteristic, direct product factor
112	C₂×C₃×D₃	—	5	1	no	Hall
113	C₂×C₃×C₅	—	2	4	no	—
114	C₂×C₃×C₅	—	2	1	no	—
115	C₂×C₃×C₅	—	2	1	no	—
116	C₂×C₃×C₅	—	2	2	no	—
117	C₂×C₃×C₅	—	2	2	no	—
118	C₂×C₃×C₅	—	15	2	no	—
119	C₂×C₃×C₅	C₃×D₅×C₁₉	1	1	yes	characteristic, complemented
120	C₂×C₃×C₅	C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
121	C₂×C₃×C₅	C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
122	C₂×C₃×C₅	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
123	D₁₅	C₂×C₃×C₅×C₁₉	1	2	yes	direct product factor
124	C₃×D₅	—	3	2	no	—
125	C₅×D₃	—	5	2	no	—
126	C₅²	C₂×C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
127	C₂²×C₅	—	15	1	no	—
128	C₂×D₅	—	3	1	no	—
129	C₁₉	C₂×C₃×C₅×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂×C₃²	C₅×D₅×C₁₉	1	1	yes	characteristic, complemented
131	C₃×D₃	—	5	2	no	—
132	C₃×C₅	—	2	4	no	—
133	C₃×C₅	—	2	1	no	—
134	C₃×C₅	—	2	1	no	—
135	C₃×C₅	—	2	2	no	—
136	C₃×C₅	—	2	2	no	—
137	C₃×C₅	C₂×C₃×D₅×C₁₉	1	1	yes	characteristic, complemented
138	C₃×C₅	C₂×C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
139	C₃×C₅	C₂×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
140	C₃×C₅	C₂²×C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
141	C₂²×C₃	—	15	1	no	—
142	C₂×D₃	—	5	1	no	—
143	C₂×C₅	—	2	2	no	—
144	C₂×C₅	—	15	2	no	—
145	C₂×C₅	C₃×C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
146	C₂×C₅	C₃×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
147	D₅	—	3	2	no	—
148	C₃²	C₂×C₅×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
149	C₂×C₃	—	2	1	no	—
150	C₂×C₃	—	15	2	no	—
151	C₂×C₃	C₃×C₅×D₅×C₁₉	1	1	yes	characteristic, complemented
152	C₂×C₃	C₅×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
153	D₃	—	5	2	no	—
154	C₅	—	2	2	no	—
155	C₅	C₂×C₃×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
156	C₅	C₂×C₃×C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
157	C₂²	—	15	1	no	Sylow
158	C₃	—	2	1	no	—
159	C₃	C₂×C₃×C₅×D₅×C₁₉	1	1	yes	characteristic, complemented
160	C₃	C₂×C₅×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
161	C₂	—	15	2	no	—
162	C₂	C₃×C₅×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₁₉×D₁₅

C₂

yes

maximal, direct product factor

C₂×C₃²×C₅²×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₅×C₁₉×D₁₅

C₃

yes

maximal, characteristic, direct product factor

C₂×C₃×C₅×D₅×C₁₉

—

maximal

C₃²×C₅²×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×D₃×C₁₉

—

maximal

C₂×C₃×C₁₉×D₁₅

C₅

yes

maximal, characteristic, direct product factor

C₅×C₁₉×D₁₅

C₂×C₃

yes

direct product factor

C₃×C₅×D₅×C₁₉

—

C₂×C₃×C₅²×C₁₉

—

C₂×C₃×C₅²×C₁₉

D₃

yes

characteristic, complemented

C₂×C₃×C₅²×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂×C₅×D₅×C₁₉

—

Hall

C₂×C₃²×C₅×C₁₉

—

C₂×C₃²×C₅×C₁₉

D₅

yes

characteristic, complemented

C₂×C₃²×C₅×C₁₉

C₂×C₅

yes

characteristic, complemented

C₃×C₁₉×D₁₅

C₂×C₅

yes

direct product factor

C₃×C₅×D₃×C₁₉

—

C₃×C₅²×C₁₉

—

C₃×C₅²×C₁₉

C₂×D₃

yes

characteristic, complemented

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₂²×C₃×C₅×C₁₉

—

C₂×C₁₉×D₁₅

C₃×C₅

yes

characteristic, direct product factor

C₂×C₅×D₃×C₁₉

—

C₂×C₃×D₅×C₁₉

—

C₂×C₅²×C₁₉

C₃×D₃

yes

characteristic, complemented

C₅×D₅×C₁₉

—

C₂×C₃×C₅×D₁₅

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₅×C₁₉

—

C₃²×C₅×C₁₉

C₂×D₅

yes

characteristic, complemented

C₃²×C₅×C₁₉

C₂²×C₅

yes

characteristic, complemented

C₂×C₃×D₃×C₁₉

—

Hall

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

C₅×D₃

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉

C₃×D₅

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉

D₁₅

yes

characteristic, direct product factor

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

characteristic, complemented

C₁₉×D₁₅

C₂×C₃×C₅

yes

direct product factor

C₅×D₃×C₁₉

—

C₃×D₅×C₁₉

—

C₅²×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅²

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅×D₁₅

C₂×C₁₉

yes

direct product factor

C₂²×C₅×C₁₉

—

C₂×D₅×C₁₉

—

C₂×C₃²×C₁₉

C₅×D₅

yes

characteristic, complemented

C₃×D₃×C₁₉

—

C₂×C₅×D₁₅

C₃×C₁₉

yes

characteristic, direct product factor

C₂×C₃×C₅×D₅

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₃×D₅

yes

characteristic, complemented

C₃×C₅×C₁₉

C₂×C₅×D₃

yes

characteristic, complemented

C₃×C₅×C₁₉

C₂×D₁₅

yes

characteristic, direct product factor

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

characteristic, complemented

C₂²×C₃×C₁₉

—

C₂×D₃×C₁₉

—

C₃²×C₅²

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃×C₅×D₃

yes

characteristic, complemented

C₂×C₅×C₁₉

C₃×D₁₅

yes

characteristic, direct product factor

D₅×C₁₉

—

C₂×C₃×D₁₅

C₅×C₁₉

yes

characteristic, direct product factor

C₂×C₃×C₅×D₃

—

C₃²×C₁₉

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₂×C₃×C₅²

D₃×C₁₉

yes

characteristic, complemented

C₂×C₃×C₅²

C₂×C₃×C₁₉

yes

characteristic, complemented

C₅×D₁₅

C₂×C₃×C₁₉

yes

direct product factor

C₃×C₅×D₅

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₃×C₅×D₅

yes

characteristic, complemented

C₂×C₃×C₁₉

C₅×D₁₅

yes

characteristic, direct product factor

D₃×C₁₉

—

C₂×C₅×D₅

—

Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₃×C₅×D₃

yes

characteristic, complemented

C₅×C₁₉

C₂×C₃×D₁₅

yes

characteristic, direct product factor

C₂×C₃²×C₅

—

C₂×C₃²×C₅

D₅×C₁₉

yes

characteristic, complemented

C₂×C₃²×C₅

C₂×C₅×C₁₉

yes

characteristic, complemented

C₃×D₁₅

C₂×C₅×C₁₉

yes

direct product factor

C₃×C₅×D₃

—

C₂²×C₁₉

—

Hall

C₃×C₅²

—

C₃×C₅²

C₂×D₃×C₁₉

yes

characteristic, complemented

C₃×C₅²

C₂²×C₃×C₁₉

yes

characteristic, complemented

C₂²×C₃×C₅

—

C₂×D₁₅

C₃×C₅×C₁₉

yes

characteristic, direct product factor

100

C₂×C₅×D₃

—

101

C₂×C₃×D₅

—

102

C₃×C₁₉

—

103

C₃×C₁₉

C₂×C₃×C₅×D₅

yes

characteristic, complemented

104

C₃×C₁₉

C₂×C₅×D₁₅

yes

characteristic, direct product factor

105

C₂×C₅²

C₃×D₃×C₁₉

yes

characteristic, complemented

106

C₅×D₅

—

107

C₃²×C₅

—

108

C₃²×C₅

C₂×D₅×C₁₉

yes

characteristic, complemented

109

C₃²×C₅

C₂²×C₅×C₁₉

yes

characteristic, complemented

110

C₂×C₁₉

—

111

C₂×C₁₉

C₃×C₅×D₁₅

yes

characteristic, direct product factor

112

C₂×C₃×D₃

—

Hall

113

C₂×C₃×C₅

—

114

C₂×C₃×C₅

—

115

C₂×C₃×C₅

—

116

C₂×C₃×C₅

—

117

C₂×C₃×C₅

—

118

C₂×C₃×C₅

—

119

C₂×C₃×C₅

C₃×D₅×C₁₉

yes

characteristic, complemented

120

C₂×C₃×C₅

C₅×D₃×C₁₉

yes

characteristic, complemented

121

C₂×C₃×C₅

C₁₉×D₁₅

yes

characteristic, direct product factor

122

C₂×C₃×C₅

C₂×C₃×C₅×C₁₉

yes

characteristic, complemented

123

D₁₅

C₂×C₃×C₅×C₁₉

yes

direct product factor

124

C₃×D₅

—

125

C₅×D₃

—

126

C₅²

C₂×C₃×D₃×C₁₉

yes

characteristic, complemented, Sylow

127

C₂²×C₅

—

128

C₂×D₅

—

129

C₁₉

C₂×C₃×C₅×D₁₅

yes

characteristic, direct product factor, Sylow

130

C₂×C₃²

C₅×D₅×C₁₉

yes

characteristic, complemented

131

C₃×D₃

—

132

C₃×C₅

—

133

C₃×C₅

—

134

C₃×C₅

—

135

C₃×C₅

—

136

C₃×C₅

—

137

C₃×C₅

C₂×C₃×D₅×C₁₉

yes

characteristic, complemented

138

C₃×C₅

C₂×C₅×D₃×C₁₉

yes

characteristic, complemented

139

C₃×C₅

C₂×C₁₉×D₁₅

yes

characteristic, direct product factor

140

C₃×C₅

C₂²×C₃×C₅×C₁₉

yes

characteristic, complemented

141

C₂²×C₃

—

142

C₂×D₃

—

143

C₂×C₅

—

144

C₂×C₅

—

145

C₂×C₅

C₃×C₅×D₃×C₁₉

yes

characteristic, complemented

146

C₂×C₅

C₃×C₁₉×D₁₅

yes

characteristic, direct product factor

147

D₅

—

148

C₃²

C₂×C₅×D₅×C₁₉

yes

characteristic, complemented, Sylow

149

C₂×C₃

—

150

C₂×C₃

—

151

C₂×C₃

C₃×C₅×D₅×C₁₉

yes

characteristic, complemented

152

C₂×C₃

C₅×C₁₉×D₁₅

yes

characteristic, direct product factor

153

D₃

—

154

C₅

—

155

C₅

C₂×C₃×C₁₉×D₁₅

yes

characteristic, direct product factor

156

C₅

C₂×C₃×C₅×D₃×C₁₉

yes

characteristic, complemented

157

C₂²

—

Sylow

158

C₃

—

159

C₃

C₂×C₃×C₅×D₅×C₁₉

yes

characteristic, complemented

160

C₃

C₂×C₅×C₁₉×D₁₅

yes

characteristic, direct product factor

161

C₂

—

162

C₂

C₃×C₅×C₁₉×D₁₅

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃×C₅×C₁₉

subgroup

G/H

center, hypercenter

C₂×C₃×C₅×C₁₉

D₁₅

commutator, cosocle, hypocenter

C₃×C₅

C₂²×C₃×C₅×C₁₉

Frattini

C₁

Fitting, socle

C₂×C₃²×C₅²×C₁₉

C₂

LCS

G ▷ C₃×C₅

UCS

C₁ ◁ C₂×C₃×C₅×C₁₉

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×D₁₅	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₁₉	C₂	semidirect
3. C₂×C₅×C₁₉×D₁₅	C₃	direct (N × H)
5. C₃²×C₅²×C₁₉	C₂²	semidirect
7. C₂×C₃×C₁₉×D₁₅	C₅	direct (N × H)
8. C₅×C₁₉×D₁₅	C₂×C₃	direct (N × H)
11. C₂×C₃×C₅²×C₁₉	D₃	semidirect
12. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
15. C₂×C₃²×C₅×C₁₉	D₅	semidirect
16. C₂×C₃²×C₅×C₁₉	C₂×C₅	semidirect
17. C₃×C₁₉×D₁₅	C₂×C₅	direct (N × H)
20. C₃×C₅²×C₁₉	C₂×D₃	semidirect
21. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
23. C₂×C₁₉×D₁₅	C₃×C₅	direct (N × H)
26. C₂×C₅²×C₁₉	C₃×D₃	semidirect
28. C₂×C₃×C₅×D₁₅	C₁₉	direct (N × H)
30. C₃²×C₅×C₁₉	C₂×D₅	semidirect
31. C₃²×C₅×C₁₉	C₂²×C₅	semidirect
39. C₂×C₃×C₅×C₁₉	C₅×D₃	semidirect
40. C₂×C₃×C₅×C₁₉	C₃×D₅	semidirect
41. C₂×C₃×C₅×C₁₉	D₁₅	direct (N × H)
42. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
43. C₁₉×D₁₅	C₂×C₃×C₅	direct (N × H)
46. C₅²×C₁₉	C₂×C₃×D₃	semidirect
47. C₂×C₃²×C₅²	C₂×C₁₉	semidirect
48. C₃×C₅×D₁₅	C₂×C₁₉	direct (N × H)
51. C₂×C₃²×C₁₉	C₅×D₅	semidirect
53. C₂×C₅×D₁₅	C₃×C₁₉	direct (N × H)
60. C₃×C₅×C₁₉	C₂×C₃×D₅	semidirect
61. C₃×C₅×C₁₉	C₂×C₅×D₃	semidirect
62. C₃×C₅×C₁₉	C₂×D₁₅	direct (N × H)
63. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
66. C₃²×C₅²	C₂²×C₁₉	semidirect
69. C₂×C₅×C₁₉	C₃×C₅×D₃	semidirect
70. C₂×C₅×C₁₉	C₃×D₁₅	direct (N × H)
72. C₂×C₃×D₁₅	C₅×C₁₉	direct (N × H)
74. C₃²×C₁₉	C₂×C₅×D₅	semidirect
76. C₂×C₃×C₅²	D₃×C₁₉	semidirect
77. C₂×C₃×C₅²	C₂×C₃×C₁₉	semidirect
78. C₅×D₁₅	C₂×C₃×C₁₉	direct (N × H)
82. C₂×C₃×C₁₉	C₃×C₅×D₅	semidirect
83. C₂×C₃×C₁₉	C₅×D₁₅	direct (N × H)
87. C₅×C₁₉	C₂×C₃×C₅×D₃	semidirect
88. C₅×C₁₉	C₂×C₃×D₁₅	direct (N × H)
90. C₂×C₃²×C₅	D₅×C₁₉	semidirect
91. C₂×C₃²×C₅	C₂×C₅×C₁₉	semidirect
92. C₃×D₁₅	C₂×C₅×C₁₉	direct (N × H)
96. C₃×C₅²	C₂×D₃×C₁₉	semidirect
97. C₃×C₅²	C₂²×C₃×C₁₉	semidirect
99. C₂×D₁₅	C₃×C₅×C₁₉	direct (N × H)
103. C₃×C₁₉	C₂×C₃×C₅×D₅	semidirect
104. C₃×C₁₉	C₂×C₅×D₁₅	direct (N × H)
105. C₂×C₅²	C₃×D₃×C₁₉	semidirect
108. C₃²×C₅	C₂×D₅×C₁₉	semidirect
109. C₃²×C₅	C₂²×C₅×C₁₉	semidirect
111. C₂×C₁₉	C₃×C₅×D₁₅	direct (N × H)
119. C₂×C₃×C₅	C₃×D₅×C₁₉	semidirect
120. C₂×C₃×C₅	C₅×D₃×C₁₉	semidirect
121. C₂×C₃×C₅	C₁₉×D₁₅	direct (N × H)
122. C₂×C₃×C₅	C₂×C₃×C₅×C₁₉	semidirect
123. D₁₅	C₂×C₃×C₅×C₁₉	direct (N × H)
126. C₅²	C₂×C₃×D₃×C₁₉	semidirect
129. C₁₉	C₂×C₃×C₅×D₁₅	direct (N × H)
130. C₂×C₃²	C₅×D₅×C₁₉	semidirect
137. C₃×C₅	C₂×C₃×D₅×C₁₉	semidirect
138. C₃×C₅	C₂×C₅×D₃×C₁₉	semidirect
139. C₃×C₅	C₂×C₁₉×D₁₅	direct (N × H)
140. C₃×C₅	C₂²×C₃×C₅×C₁₉	semidirect
145. C₂×C₅	C₃×C₅×D₃×C₁₉	semidirect
146. C₂×C₅	C₃×C₁₉×D₁₅	direct (N × H)
148. C₃²	C₂×C₅×D₅×C₁₉	semidirect
151. C₂×C₃	C₃×C₅×D₅×C₁₉	semidirect
152. C₂×C₃	C₅×C₁₉×D₁₅	direct (N × H)
155. C₅	C₂×C₃×C₁₉×D₁₅	direct (N × H)
156. C₅	C₂×C₃×C₅×D₃×C₁₉	semidirect
159. C₃	C₂×C₃×C₅×D₅×C₁₉	semidirect
160. C₃	C₂×C₅×C₁₉×D₁₅	direct (N × H)
162. C₂	C₃×C₅×C₁₉×D₁₅	direct (N × H)

H ≅ G/N

type

1. C₃×C₅×C₁₉×D₁₅

C₂

direct (N × H)

2. C₂×C₃²×C₅²×C₁₉

C₂

semidirect

3. C₂×C₅×C₁₉×D₁₅

C₃

direct (N × H)

5. C₃²×C₅²×C₁₉

C₂²

semidirect

7. C₂×C₃×C₁₉×D₁₅

C₅

direct (N × H)

8. C₅×C₁₉×D₁₅

C₂×C₃

direct (N × H)

11. C₂×C₃×C₅²×C₁₉

D₃

semidirect

12. C₂×C₃×C₅²×C₁₉

C₂×C₃

semidirect

15. C₂×C₃²×C₅×C₁₉

D₅

semidirect

16. C₂×C₃²×C₅×C₁₉

C₂×C₅

semidirect

17. C₃×C₁₉×D₁₅

C₂×C₅

direct (N × H)

20. C₃×C₅²×C₁₉

C₂×D₃

semidirect

21. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

23. C₂×C₁₉×D₁₅

C₃×C₅

direct (N × H)

26. C₂×C₅²×C₁₉

C₃×D₃

semidirect

28. C₂×C₃×C₅×D₁₅

C₁₉

direct (N × H)

30. C₃²×C₅×C₁₉

C₂×D₅

semidirect

31. C₃²×C₅×C₁₉

C₂²×C₅

semidirect

39. C₂×C₃×C₅×C₁₉

C₅×D₃

semidirect

40. C₂×C₃×C₅×C₁₉

C₃×D₅

semidirect

41. C₂×C₃×C₅×C₁₉

D₁₅

direct (N × H)

42. C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

semidirect

43. C₁₉×D₁₅

C₂×C₃×C₅

direct (N × H)

46. C₅²×C₁₉

C₂×C₃×D₃

semidirect

47. C₂×C₃²×C₅²

C₂×C₁₉

semidirect

48. C₃×C₅×D₁₅

C₂×C₁₉

direct (N × H)

51. C₂×C₃²×C₁₉

C₅×D₅

semidirect

53. C₂×C₅×D₁₅

C₃×C₁₉

direct (N × H)

60. C₃×C₅×C₁₉

C₂×C₃×D₅

semidirect

61. C₃×C₅×C₁₉

C₂×C₅×D₃

semidirect

62. C₃×C₅×C₁₉

C₂×D₁₅

direct (N × H)

63. C₃×C₅×C₁₉

C₂²×C₃×C₅

semidirect

66. C₃²×C₅²

C₂²×C₁₉

semidirect

69. C₂×C₅×C₁₉

C₃×C₅×D₃

semidirect

70. C₂×C₅×C₁₉

C₃×D₁₅

direct (N × H)

72. C₂×C₃×D₁₅

C₅×C₁₉

direct (N × H)

74. C₃²×C₁₉

C₂×C₅×D₅

semidirect

76. C₂×C₃×C₅²

D₃×C₁₉

semidirect

77. C₂×C₃×C₅²

C₂×C₃×C₁₉

semidirect

78. C₅×D₁₅

C₂×C₃×C₁₉

direct (N × H)

82. C₂×C₃×C₁₉

C₃×C₅×D₅

semidirect

83. C₂×C₃×C₁₉

C₅×D₁₅

direct (N × H)

87. C₅×C₁₉

C₂×C₃×C₅×D₃

semidirect

88. C₅×C₁₉

C₂×C₃×D₁₅

direct (N × H)

90. C₂×C₃²×C₅

D₅×C₁₉

semidirect

91. C₂×C₃²×C₅

C₂×C₅×C₁₉

semidirect

92. C₃×D₁₅

C₂×C₅×C₁₉

direct (N × H)

96. C₃×C₅²

C₂×D₃×C₁₉

semidirect

97. C₃×C₅²

C₂²×C₃×C₁₉

semidirect

99. C₂×D₁₅

C₃×C₅×C₁₉

direct (N × H)

103. C₃×C₁₉

C₂×C₃×C₅×D₅

semidirect

104. C₃×C₁₉

C₂×C₅×D₁₅

direct (N × H)

105. C₂×C₅²

C₃×D₃×C₁₉

semidirect

108. C₃²×C₅

C₂×D₅×C₁₉

semidirect

109. C₃²×C₅

C₂²×C₅×C₁₉

semidirect

111. C₂×C₁₉

C₃×C₅×D₁₅

direct (N × H)

119. C₂×C₃×C₅

C₃×D₅×C₁₉

semidirect

120. C₂×C₃×C₅

C₅×D₃×C₁₉

semidirect

121. C₂×C₃×C₅

C₁₉×D₁₅

direct (N × H)

122. C₂×C₃×C₅

C₂×C₃×C₅×C₁₉

semidirect

123. D₁₅

C₂×C₃×C₅×C₁₉

direct (N × H)

126. C₅²

C₂×C₃×D₃×C₁₉

semidirect

129. C₁₉

C₂×C₃×C₅×D₁₅

direct (N × H)

130. C₂×C₃²

C₅×D₅×C₁₉

semidirect

137. C₃×C₅

C₂×C₃×D₅×C₁₉

semidirect

138. C₃×C₅

C₂×C₅×D₃×C₁₉

semidirect

139. C₃×C₅

C₂×C₁₉×D₁₅

direct (N × H)

140. C₃×C₅

C₂²×C₃×C₅×C₁₉

semidirect

145. C₂×C₅

C₃×C₅×D₃×C₁₉

semidirect

146. C₂×C₅

C₃×C₁₉×D₁₅

direct (N × H)

148. C₃²

C₂×C₅×D₅×C₁₉

semidirect

151. C₂×C₃

C₃×C₅×D₅×C₁₉

semidirect

152. C₂×C₃

C₅×C₁₉×D₁₅

direct (N × H)

155. C₅

C₂×C₃×C₁₉×D₁₅

direct (N × H)

156. C₅

C₂×C₃×C₅×D₃×C₁₉

semidirect

159. C₃

C₂×C₃×C₅×D₅×C₁₉

semidirect

160. C₃

C₂×C₅×C₁₉×D₁₅

direct (N × H)

162. C₂

C₃×C₅×C₁₉×D₁₅

direct (N × H)

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

subgroup	index
C₃×C₅×C₁₉×D₁₅	2
C₂×C₃²×C₅²×C₁₉	2
C₂×C₅×C₁₉×D₁₅	3
C₂×C₃×C₅×D₅×C₁₉	3
C₂×C₃×C₅×D₃×C₁₉	5
C₂×C₃×C₁₉×D₁₅	5
C₂×C₃×C₅×D₁₅	19

subgroup

index

C₃×C₅×C₁₉×D₁₅

C₂×C₃²×C₅²×C₁₉

C₂×C₅×C₁₉×D₁₅

C₂×C₃×C₅×D₅×C₁₉

C₂×C₃×C₅×D₃×C₁₉

C₂×C₃×C₁₉×D₁₅

C₂×C₃×C₅×D₁₅

Subgroups — C₂×C₃×C₅×C₁₉×D₁₅ #30685974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C5×C19×D15 #30685974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₉×D₁₅ #30685974