Subgroups — C₂²×C₃×C₄²×C₈×C₁₉ #72206115

Order 29184.

26376 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄³×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×C₄×C₈×C₁₉	C₂	1	6	yes	maximal
3	C₂×C₃×C₄²×C₈×C₁₉	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄²×C₈×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₄²×C₁₉	C₄	1	4	yes	—
6	C₂³×C₃×C₄²×C₁₉	C₂²	1	3	yes	—
7	C₂⁴×C₃×C₈×C₁₉	C₂²	1	4	yes	—
8	C₂×C₃×C₄³×C₁₉	C₄	1	12	yes	—
9	C₂×C₃×C₄³×C₁₉	C₂²	1	12	yes	—
10	C₂²×C₃×C₄×C₈×C₁₉	C₄	1	96	yes	direct product factor
11	C₂²×C₃×C₄×C₈×C₁₉	C₂²	1	72	yes	—
12	C₃×C₄²×C₈×C₁₉	C₂²	1	64	yes	direct product factor
13	C₂⁴×C₃×C₄×C₁₉	C₂×C₄	1	6	yes	—
14	C₂⁴×C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
15	C₂²×C₃×C₄²×C₁₉	C₈	1	64	yes	direct product factor
16	C₂²×C₃×C₄²×C₁₉	C₂×C₄	1	18	yes	—
17	C₂²×C₃×C₄²×C₁₉	C₂×C₄	1	48	yes	—
18	C₂²×C₃×C₄²×C₁₉	C₂×C₄	1	48	yes	—
19	C₂²×C₃×C₄²×C₁₉	C₂³	1	18	yes	—
20	C₃×C₄³×C₁₉	C₂×C₄	1	48	yes	—
21	C₃×C₄³×C₁₉	C₂³	1	16	yes	—
22	C₂³×C₃×C₈×C₁₉	C₂×C₄	1	96	yes	—
23	C₂³×C₃×C₈×C₁₉	C₂³	1	24	yes	—
24	C₂×C₃×C₄×C₈×C₁₉	C₂×C₄	1	576	yes	direct product factor
25	C₂×C₃×C₄×C₈×C₁₉	C₂³	1	96	yes	—
26	C₂²×C₃×C₄²×C₈	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₄×C₈×C₁₉	C₂×C₃	1	6	yes	—
28	C₂²×C₄³×C₁₉	C₂×C₃	1	1	yes	characteristic
29	C₂×C₄²×C₈×C₁₉	C₂×C₃	1	24	yes	direct product factor
30	C₂⁴×C₈×C₁₉	C₂²×C₃	1	4	yes	—
31	C₂³×C₄²×C₁₉	C₃×C₄	1	4	yes	—
32	C₂³×C₄²×C₁₉	C₂²×C₃	1	3	yes	—
33	C₂²×C₄×C₈×C₁₉	C₃×C₄	1	96	yes	direct product factor
34	C₂²×C₄×C₈×C₁₉	C₂²×C₃	1	72	yes	—
35	C₂×C₄³×C₁₉	C₃×C₄	1	12	yes	—
36	C₂×C₄³×C₁₉	C₂²×C₃	1	12	yes	—
37	C₄²×C₈×C₁₉	C₂²×C₃	1	64	yes	direct product factor
38	C₂⁵×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂³×C₃×C₄×C₁₉	C₄²	1	48	yes	—
40	C₂³×C₃×C₄×C₁₉	C₂×C₈	1	96	yes	—
41	C₂³×C₃×C₄×C₁₉	C₂²×C₄	1	3	yes	—
42	C₂³×C₃×C₄×C₁₉	C₂²×C₄	1	24	yes	—
43	C₂³×C₃×C₄×C₁₉	C₂²×C₄	1	36	yes	—
44	C₂³×C₃×C₄×C₁₉	C₂⁴	1	3	yes	—
45	C₂²×C₃×C₈×C₁₉	C₄²	1	256	yes	direct product factor
46	C₂²×C₃×C₈×C₁₉	C₂²×C₄	1	288	yes	—
47	C₂²×C₃×C₈×C₁₉	C₂⁴	1	16	yes	—
48	C₂×C₃×C₄²×C₁₉	C₄²	1	144	yes	—
49	C₂×C₃×C₄²×C₁₉	C₂×C₈	1	384	yes	direct product factor
50	C₂×C₃×C₄²×C₁₉	C₂²×C₄	1	36	yes	—
51	C₂×C₃×C₄²×C₁₉	C₂²×C₄	1	64	yes	—
52	C₂×C₃×C₄²×C₁₉	C₂²×C₄	1	144	yes	—
53	C₂×C₃×C₄²×C₁₉	C₂⁴	1	12	yes	—
54	C₃×C₄×C₈×C₁₉	C₂²×C₄	1	384	yes	direct product factor
55	C₂⁴×C₄×C₁₉	C₂×C₃×C₄	1	6	yes	—
56	C₂⁴×C₄×C₁₉	C₂³×C₃	1	1	yes	characteristic
57	C₂³×C₈×C₁₉	C₂×C₃×C₄	1	96	yes	—
58	C₂³×C₈×C₁₉	C₂³×C₃	1	24	yes	—
59	C₂²×C₄²×C₁₉	C₃×C₈	1	64	yes	direct product factor
60	C₂²×C₄²×C₁₉	C₂×C₃×C₄	1	18	yes	—
61	C₂²×C₄²×C₁₉	C₂×C₃×C₄	1	48	yes	—
62	C₂²×C₄²×C₁₉	C₂×C₃×C₄	1	48	yes	—
63	C₂²×C₄²×C₁₉	C₂³×C₃	1	18	yes	—
64	C₂×C₄×C₈×C₁₉	C₂×C₃×C₄	1	576	yes	direct product factor
65	C₂×C₄×C₈×C₁₉	C₂³×C₃	1	96	yes	—
66	C₄³×C₁₉	C₂×C₃×C₄	1	48	yes	—
67	C₄³×C₁₉	C₂³×C₃	1	16	yes	—
68	C₂⁴×C₃×C₁₉	C₂×C₄²	1	12	yes	—
69	C₂⁴×C₃×C₁₉	C₂²×C₈	1	16	yes	—
70	C₂⁴×C₃×C₁₉	C₂³×C₄	1	3	yes	—
71	C₂²×C₃×C₄×C₁₉	C₄×C₈	1	384	yes	direct product factor
72	C₂²×C₃×C₄×C₁₉	C₂×C₄²	1	36	yes	—
73	C₂²×C₃×C₄×C₁₉	C₂×C₄²	1	64	yes	—
74	C₂²×C₃×C₄×C₁₉	C₂×C₄²	1	144	yes	—
75	C₂²×C₃×C₄×C₁₉	C₂²×C₈	1	288	yes	—
76	C₂²×C₃×C₄×C₁₉	C₂³×C₄	1	3	yes	—
77	C₂²×C₃×C₄×C₁₉	C₂³×C₄	1	24	yes	—
78	C₂²×C₃×C₄×C₁₉	C₂³×C₄	1	36	yes	—
79	C₂²×C₃×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
80	C₂×C₃×C₈×C₁₉	C₂×C₄²	1	384	yes	direct product factor
81	C₂×C₃×C₈×C₁₉	C₂³×C₄	1	96	yes	—
82	C₃×C₄²×C₁₉	C₂×C₄²	1	144	yes	—
83	C₃×C₄²×C₁₉	C₂²×C₈	1	256	yes	direct product factor
84	C₃×C₄²×C₁₉	C₂³×C₄	1	48	yes	—
85	C₂³×C₃×C₄×C₈	C₂×C₁₉	1	6	yes	—
86	C₂²×C₃×C₄³	C₂×C₁₉	1	1	yes	characteristic
87	C₂×C₃×C₄²×C₈	C₂×C₁₉	1	24	yes	direct product factor
88	C₂⁵×C₁₉	C₂²×C₃×C₄	1	1	yes	characteristic
89	C₂³×C₄×C₁₉	C₃×C₄²	1	48	yes	—
90	C₂³×C₄×C₁₉	C₂×C₃×C₈	1	96	yes	—
91	C₂³×C₄×C₁₉	C₂²×C₃×C₄	1	3	yes	—
92	C₂³×C₄×C₁₉	C₂²×C₃×C₄	1	24	yes	—
93	C₂³×C₄×C₁₉	C₂²×C₃×C₄	1	36	yes	—
94	C₂³×C₄×C₁₉	C₂⁴×C₃	1	3	yes	—
95	C₂²×C₈×C₁₉	C₃×C₄²	1	256	yes	direct product factor
96	C₂²×C₈×C₁₉	C₂²×C₃×C₄	1	288	yes	—
97	C₂²×C₈×C₁₉	C₂⁴×C₃	1	16	yes	—
98	C₂×C₄²×C₁₉	C₃×C₄²	1	144	yes	—
99	C₂×C₄²×C₁₉	C₂×C₃×C₈	1	384	yes	direct product factor
100	C₂×C₄²×C₁₉	C₂²×C₃×C₄	1	36	yes	—
101	C₂×C₄²×C₁₉	C₂²×C₃×C₄	1	64	yes	—
102	C₂×C₄²×C₁₉	C₂²×C₃×C₄	1	144	yes	—
103	C₂×C₄²×C₁₉	C₂⁴×C₃	1	12	yes	—
104	C₄×C₈×C₁₉	C₂²×C₃×C₄	1	384	yes	direct product factor
105	C₂²×C₄²×C₈	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
106	C₂³×C₃×C₁₉	C₄³	1	16	yes	—
107	C₂³×C₃×C₁₉	C₂×C₄×C₈	1	96	yes	—
108	C₂³×C₃×C₁₉	C₂²×C₄²	1	18	yes	—
109	C₂³×C₃×C₁₉	C₂³×C₈	1	24	yes	—
110	C₂³×C₃×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₁₉	C₄³	1	48	yes	—
112	C₂×C₃×C₄×C₁₉	C₂×C₄×C₈	1	576	yes	direct product factor
113	C₂×C₃×C₄×C₁₉	C₂²×C₄²	1	18	yes	—
114	C₂×C₃×C₄×C₁₉	C₂²×C₄²	1	48	yes	—
115	C₂×C₃×C₄×C₁₉	C₂²×C₄²	1	48	yes	—
116	C₂×C₃×C₄×C₁₉	C₂³×C₈	1	96	yes	—
117	C₂×C₃×C₄×C₁₉	C₂⁴×C₄	1	6	yes	—
118	C₃×C₈×C₁₉	C₂²×C₄²	1	64	yes	direct product factor
119	C₂⁴×C₃×C₈	C₂²×C₁₉	1	4	yes	—
120	C₂³×C₃×C₄²	C₄×C₁₉	1	4	yes	—
121	C₂³×C₃×C₄²	C₂²×C₁₉	1	3	yes	—
122	C₂²×C₃×C₄×C₈	C₄×C₁₉	1	96	yes	direct product factor
123	C₂²×C₃×C₄×C₈	C₂²×C₁₉	1	72	yes	—
124	C₂×C₃×C₄³	C₄×C₁₉	1	12	yes	—
125	C₂×C₃×C₄³	C₂²×C₁₉	1	12	yes	—
126	C₃×C₄²×C₈	C₂²×C₁₉	1	64	yes	direct product factor
127	C₂⁴×C₁₉	C₂×C₃×C₄²	1	12	yes	—
128	C₂⁴×C₁₉	C₂²×C₃×C₈	1	16	yes	—
129	C₂⁴×C₁₉	C₂³×C₃×C₄	1	3	yes	—
130	C₂²×C₄×C₁₉	C₃×C₄×C₈	1	384	yes	direct product factor
131	C₂²×C₄×C₁₉	C₂×C₃×C₄²	1	36	yes	—
132	C₂²×C₄×C₁₉	C₂×C₃×C₄²	1	64	yes	—
133	C₂²×C₄×C₁₉	C₂×C₃×C₄²	1	144	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₃×C₈	1	288	yes	—
135	C₂²×C₄×C₁₉	C₂³×C₃×C₄	1	3	yes	—
136	C₂²×C₄×C₁₉	C₂³×C₃×C₄	1	24	yes	—
137	C₂²×C₄×C₁₉	C₂³×C₃×C₄	1	36	yes	—
138	C₂²×C₄×C₁₉	C₂⁵×C₃	1	1	yes	characteristic
139	C₂×C₈×C₁₉	C₂×C₃×C₄²	1	384	yes	direct product factor
140	C₂×C₈×C₁₉	C₂³×C₃×C₄	1	96	yes	—
141	C₄²×C₁₉	C₂×C₃×C₄²	1	144	yes	—
142	C₄²×C₁₉	C₂²×C₃×C₈	1	256	yes	direct product factor
143	C₄²×C₁₉	C₂³×C₃×C₄	1	48	yes	—
144	C₂³×C₄×C₈	C₂×C₃×C₁₉	1	6	yes	—
145	C₂²×C₄³	C₂×C₃×C₁₉	1	1	yes	characteristic
146	C₂×C₄²×C₈	C₂×C₃×C₁₉	1	24	yes	direct product factor
147	C₂²×C₃×C₁₉	C₄²×C₈	1	64	yes	direct product factor
148	C₂²×C₃×C₁₉	C₂×C₄³	1	12	yes	—
149	C₂²×C₃×C₁₉	C₂²×C₄×C₈	1	72	yes	—
150	C₂²×C₃×C₁₉	C₂³×C₄²	1	3	yes	—
151	C₂²×C₃×C₁₉	C₂⁴×C₈	1	4	yes	—
152	C₃×C₄×C₁₉	C₂×C₄³	1	12	yes	—
153	C₃×C₄×C₁₉	C₂²×C₄×C₈	1	96	yes	direct product factor
154	C₃×C₄×C₁₉	C₂³×C₄²	1	4	yes	—
155	C₂⁴×C₃×C₄	C₂×C₄×C₁₉	1	6	yes	—
156	C₂⁴×C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
157	C₂³×C₃×C₈	C₂×C₄×C₁₉	1	96	yes	—
158	C₂³×C₃×C₈	C₂³×C₁₉	1	24	yes	—
159	C₂²×C₃×C₄²	C₈×C₁₉	1	64	yes	direct product factor
160	C₂²×C₃×C₄²	C₂×C₄×C₁₉	1	18	yes	—
161	C₂²×C₃×C₄²	C₂×C₄×C₁₉	1	48	yes	—
162	C₂²×C₃×C₄²	C₂×C₄×C₁₉	1	48	yes	—
163	C₂²×C₃×C₄²	C₂³×C₁₉	1	18	yes	—
164	C₂×C₃×C₄×C₈	C₂×C₄×C₁₉	1	576	yes	direct product factor
165	C₂×C₃×C₄×C₈	C₂³×C₁₉	1	96	yes	—
166	C₃×C₄³	C₂×C₄×C₁₉	1	48	yes	—
167	C₃×C₄³	C₂³×C₁₉	1	16	yes	—
168	C₂³×C₁₉	C₃×C₄³	1	16	yes	—
169	C₂³×C₁₉	C₂×C₃×C₄×C₈	1	96	yes	—
170	C₂³×C₁₉	C₂²×C₃×C₄²	1	18	yes	—
171	C₂³×C₁₉	C₂³×C₃×C₈	1	24	yes	—
172	C₂³×C₁₉	C₂⁴×C₃×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₃×C₄³	1	48	yes	—
174	C₂×C₄×C₁₉	C₂×C₃×C₄×C₈	1	576	yes	direct product factor
175	C₂×C₄×C₁₉	C₂²×C₃×C₄²	1	18	yes	—
176	C₂×C₄×C₁₉	C₂²×C₃×C₄²	1	48	yes	—
177	C₂×C₄×C₁₉	C₂²×C₃×C₄²	1	48	yes	—
178	C₂×C₄×C₁₉	C₂³×C₃×C₈	1	96	yes	—
179	C₂×C₄×C₁₉	C₂⁴×C₃×C₄	1	6	yes	—
180	C₈×C₁₉	C₂²×C₃×C₄²	1	64	yes	direct product factor
181	C₂⁴×C₈	C₂²×C₃×C₁₉	1	4	yes	—
182	C₂³×C₄²	C₃×C₄×C₁₉	1	4	yes	—
183	C₂³×C₄²	C₂²×C₃×C₁₉	1	3	yes	—
184	C₂²×C₄×C₈	C₃×C₄×C₁₉	1	96	yes	direct product factor
185	C₂²×C₄×C₈	C₂²×C₃×C₁₉	1	72	yes	—
186	C₂×C₄³	C₃×C₄×C₁₉	1	12	yes	—
187	C₂×C₄³	C₂²×C₃×C₁₉	1	12	yes	—
188	C₄²×C₈	C₂²×C₃×C₁₉	1	64	yes	direct product factor
189	C₂×C₃×C₁₉	C₂×C₄²×C₈	1	24	yes	direct product factor
190	C₂×C₃×C₁₉	C₂²×C₄³	1	1	yes	characteristic
191	C₂×C₃×C₁₉	C₂³×C₄×C₈	1	6	yes	—
192	C₂⁵×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
193	C₂³×C₃×C₄	C₄²×C₁₉	1	48	yes	—
194	C₂³×C₃×C₄	C₂×C₈×C₁₉	1	96	yes	—
195	C₂³×C₃×C₄	C₂²×C₄×C₁₉	1	3	yes	—
196	C₂³×C₃×C₄	C₂²×C₄×C₁₉	1	24	yes	—
197	C₂³×C₃×C₄	C₂²×C₄×C₁₉	1	36	yes	—
198	C₂³×C₃×C₄	C₂⁴×C₁₉	1	3	yes	—
199	C₂²×C₃×C₈	C₄²×C₁₉	1	256	yes	direct product factor
200	C₂²×C₃×C₈	C₂²×C₄×C₁₉	1	288	yes	—
201	C₂²×C₃×C₈	C₂⁴×C₁₉	1	16	yes	—
202	C₂×C₃×C₄²	C₄²×C₁₉	1	144	yes	—
203	C₂×C₃×C₄²	C₂×C₈×C₁₉	1	384	yes	direct product factor
204	C₂×C₃×C₄²	C₂²×C₄×C₁₉	1	36	yes	—
205	C₂×C₃×C₄²	C₂²×C₄×C₁₉	1	64	yes	—
206	C₂×C₃×C₄²	C₂²×C₄×C₁₉	1	144	yes	—
207	C₂×C₃×C₄²	C₂⁴×C₁₉	1	12	yes	—
208	C₃×C₄×C₈	C₂²×C₄×C₁₉	1	384	yes	direct product factor
209	C₂²×C₁₉	C₃×C₄²×C₈	1	64	yes	direct product factor
210	C₂²×C₁₉	C₂×C₃×C₄³	1	12	yes	—
211	C₂²×C₁₉	C₂²×C₃×C₄×C₈	1	72	yes	—
212	C₂²×C₁₉	C₂³×C₃×C₄²	1	3	yes	—
213	C₂²×C₁₉	C₂⁴×C₃×C₈	1	4	yes	—
214	C₄×C₁₉	C₂×C₃×C₄³	1	12	yes	—
215	C₄×C₁₉	C₂²×C₃×C₄×C₈	1	96	yes	direct product factor
216	C₄×C₁₉	C₂³×C₃×C₄²	1	4	yes	—
217	C₂⁴×C₄	C₂×C₃×C₄×C₁₉	1	6	yes	—
218	C₂⁴×C₄	C₂³×C₃×C₁₉	1	1	yes	characteristic
219	C₂³×C₈	C₂×C₃×C₄×C₁₉	1	96	yes	—
220	C₂³×C₈	C₂³×C₃×C₁₉	1	24	yes	—
221	C₂²×C₄²	C₃×C₈×C₁₉	1	64	yes	direct product factor
222	C₂²×C₄²	C₂×C₃×C₄×C₁₉	1	18	yes	—
223	C₂²×C₄²	C₂×C₃×C₄×C₁₉	1	48	yes	—
224	C₂²×C₄²	C₂×C₃×C₄×C₁₉	1	48	yes	—
225	C₂²×C₄²	C₂³×C₃×C₁₉	1	18	yes	—
226	C₂×C₄×C₈	C₂×C₃×C₄×C₁₉	1	576	yes	direct product factor
227	C₂×C₄×C₈	C₂³×C₃×C₁₉	1	96	yes	—
228	C₄³	C₂×C₃×C₄×C₁₉	1	48	yes	—
229	C₄³	C₂³×C₃×C₁₉	1	16	yes	—
230	C₃×C₁₉	C₂²×C₄²×C₈	1	1	yes	characteristic, direct product factor, Hall
231	C₂⁴×C₃	C₂×C₄²×C₁₉	1	12	yes	—
232	C₂⁴×C₃	C₂²×C₈×C₁₉	1	16	yes	—
233	C₂⁴×C₃	C₂³×C₄×C₁₉	1	3	yes	—
234	C₂²×C₃×C₄	C₄×C₈×C₁₉	1	384	yes	direct product factor
235	C₂²×C₃×C₄	C₂×C₄²×C₁₉	1	36	yes	—
236	C₂²×C₃×C₄	C₂×C₄²×C₁₉	1	64	yes	—
237	C₂²×C₃×C₄	C₂×C₄²×C₁₉	1	144	yes	—
238	C₂²×C₃×C₄	C₂²×C₈×C₁₉	1	288	yes	—
239	C₂²×C₃×C₄	C₂³×C₄×C₁₉	1	3	yes	—
240	C₂²×C₃×C₄	C₂³×C₄×C₁₉	1	24	yes	—
241	C₂²×C₃×C₄	C₂³×C₄×C₁₉	1	36	yes	—
242	C₂²×C₃×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂×C₄²×C₁₉	1	384	yes	direct product factor
244	C₂×C₃×C₈	C₂³×C₄×C₁₉	1	96	yes	—
245	C₃×C₄²	C₂×C₄²×C₁₉	1	144	yes	—
246	C₃×C₄²	C₂²×C₈×C₁₉	1	256	yes	direct product factor
247	C₃×C₄²	C₂³×C₄×C₁₉	1	48	yes	—
248	C₂×C₁₉	C₂×C₃×C₄²×C₈	1	24	yes	direct product factor
249	C₂×C₁₉	C₂²×C₃×C₄³	1	1	yes	characteristic
250	C₂×C₁₉	C₂³×C₃×C₄×C₈	1	6	yes	—
251	C₂⁵	C₂²×C₃×C₄×C₁₉	1	1	yes	characteristic
252	C₂³×C₄	C₃×C₄²×C₁₉	1	48	yes	—
253	C₂³×C₄	C₂×C₃×C₈×C₁₉	1	96	yes	—
254	C₂³×C₄	C₂²×C₃×C₄×C₁₉	1	3	yes	—
255	C₂³×C₄	C₂²×C₃×C₄×C₁₉	1	24	yes	—
256	C₂³×C₄	C₂²×C₃×C₄×C₁₉	1	36	yes	—
257	C₂³×C₄	C₂⁴×C₃×C₁₉	1	3	yes	—
258	C₂²×C₈	C₃×C₄²×C₁₉	1	256	yes	direct product factor
259	C₂²×C₈	C₂²×C₃×C₄×C₁₉	1	288	yes	—
260	C₂²×C₈	C₂⁴×C₃×C₁₉	1	16	yes	—
261	C₂×C₄²	C₃×C₄²×C₁₉	1	144	yes	—
262	C₂×C₄²	C₂×C₃×C₈×C₁₉	1	384	yes	direct product factor
263	C₂×C₄²	C₂²×C₃×C₄×C₁₉	1	36	yes	—
264	C₂×C₄²	C₂²×C₃×C₄×C₁₉	1	64	yes	—
265	C₂×C₄²	C₂²×C₃×C₄×C₁₉	1	144	yes	—
266	C₂×C₄²	C₂⁴×C₃×C₁₉	1	12	yes	—
267	C₄×C₈	C₂²×C₃×C₄×C₁₉	1	384	yes	direct product factor
268	C₂³×C₃	C₄³×C₁₉	1	16	yes	—
269	C₂³×C₃	C₂×C₄×C₈×C₁₉	1	96	yes	—
270	C₂³×C₃	C₂²×C₄²×C₁₉	1	18	yes	—
271	C₂³×C₃	C₂³×C₈×C₁₉	1	24	yes	—
272	C₂³×C₃	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
273	C₂×C₃×C₄	C₄³×C₁₉	1	48	yes	—
274	C₂×C₃×C₄	C₂×C₄×C₈×C₁₉	1	576	yes	direct product factor
275	C₂×C₃×C₄	C₂²×C₄²×C₁₉	1	18	yes	—
276	C₂×C₃×C₄	C₂²×C₄²×C₁₉	1	48	yes	—
277	C₂×C₃×C₄	C₂²×C₄²×C₁₉	1	48	yes	—
278	C₂×C₃×C₄	C₂³×C₈×C₁₉	1	96	yes	—
279	C₂×C₃×C₄	C₂⁴×C₄×C₁₉	1	6	yes	—
280	C₃×C₈	C₂²×C₄²×C₁₉	1	64	yes	direct product factor
281	C₁₉	C₂²×C₃×C₄²×C₈	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	C₂×C₃×C₄²×C₁₉	1	12	yes	—
283	C₂⁴	C₂²×C₃×C₈×C₁₉	1	16	yes	—
284	C₂⁴	C₂³×C₃×C₄×C₁₉	1	3	yes	—
285	C₂²×C₄	C₃×C₄×C₈×C₁₉	1	384	yes	direct product factor
286	C₂²×C₄	C₂×C₃×C₄²×C₁₉	1	36	yes	—
287	C₂²×C₄	C₂×C₃×C₄²×C₁₉	1	64	yes	—
288	C₂²×C₄	C₂×C₃×C₄²×C₁₉	1	144	yes	—
289	C₂²×C₄	C₂²×C₃×C₈×C₁₉	1	288	yes	—
290	C₂²×C₄	C₂³×C₃×C₄×C₁₉	1	3	yes	—
291	C₂²×C₄	C₂³×C₃×C₄×C₁₉	1	24	yes	—
292	C₂²×C₄	C₂³×C₃×C₄×C₁₉	1	36	yes	—
293	C₂²×C₄	C₂⁵×C₃×C₁₉	1	1	yes	characteristic
294	C₂×C₈	C₂×C₃×C₄²×C₁₉	1	384	yes	direct product factor
295	C₂×C₈	C₂³×C₃×C₄×C₁₉	1	96	yes	—
296	C₄²	C₂×C₃×C₄²×C₁₉	1	144	yes	—
297	C₄²	C₂²×C₃×C₈×C₁₉	1	256	yes	direct product factor
298	C₄²	C₂³×C₃×C₄×C₁₉	1	48	yes	—
299	C₂²×C₃	C₄²×C₈×C₁₉	1	64	yes	direct product factor
300	C₂²×C₃	C₂×C₄³×C₁₉	1	12	yes	—
301	C₂²×C₃	C₂²×C₄×C₈×C₁₉	1	72	yes	—
302	C₂²×C₃	C₂³×C₄²×C₁₉	1	3	yes	—
303	C₂²×C₃	C₂⁴×C₈×C₁₉	1	4	yes	—
304	C₃×C₄	C₂×C₄³×C₁₉	1	12	yes	—
305	C₃×C₄	C₂²×C₄×C₈×C₁₉	1	96	yes	direct product factor
306	C₃×C₄	C₂³×C₄²×C₁₉	1	4	yes	—
307	C₂³	C₂×C₃×C₄×C₈×C₁₉	1	96	yes	—
308	C₂³	C₂³×C₃×C₈×C₁₉	1	24	yes	—
309	C₂³	C₃×C₄³×C₁₉	1	16	yes	—
310	C₂³	C₂²×C₃×C₄²×C₁₉	1	18	yes	—
311	C₂³	C₂⁴×C₃×C₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄	C₂×C₃×C₄×C₈×C₁₉	1	576	yes	direct product factor
313	C₂×C₄	C₂³×C₃×C₈×C₁₉	1	96	yes	—
314	C₂×C₄	C₃×C₄³×C₁₉	1	48	yes	—
315	C₂×C₄	C₂²×C₃×C₄²×C₁₉	1	18	yes	—
316	C₂×C₄	C₂²×C₃×C₄²×C₁₉	1	48	yes	—
317	C₂×C₄	C₂²×C₃×C₄²×C₁₉	1	48	yes	—
318	C₂×C₄	C₂⁴×C₃×C₄×C₁₉	1	6	yes	—
319	C₈	C₂²×C₃×C₄²×C₁₉	1	64	yes	direct product factor
320	C₂×C₃	C₂×C₄²×C₈×C₁₉	1	24	yes	direct product factor
321	C₂×C₃	C₂²×C₄³×C₁₉	1	1	yes	characteristic
322	C₂×C₃	C₂³×C₄×C₈×C₁₉	1	6	yes	—
323	C₂²	C₃×C₄²×C₈×C₁₉	1	64	yes	direct product factor
324	C₂²	C₂²×C₃×C₄×C₈×C₁₉	1	72	yes	—
325	C₂²	C₂×C₃×C₄³×C₁₉	1	12	yes	—
326	C₂²	C₂⁴×C₃×C₈×C₁₉	1	4	yes	—
327	C₂²	C₂³×C₃×C₄²×C₁₉	1	3	yes	—
328	C₄	C₂²×C₃×C₄×C₈×C₁₉	1	96	yes	direct product factor
329	C₄	C₂×C₃×C₄³×C₁₉	1	12	yes	—
330	C₄	C₂³×C₃×C₄²×C₁₉	1	4	yes	—
331	C₃	C₂²×C₄²×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
332	C₂	C₂×C₃×C₄²×C₈×C₁₉	1	24	yes	direct product factor
333	C₂	C₂³×C₃×C₄×C₈×C₁₉	1	6	yes	—
334	C₂	C₂²×C₃×C₄³×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂⁵×C₃×C₁₉
socle, prime radical	C₂⁵×C₃×C₁₉	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×C₃×C₄²×C₈×C₁₉	C₂	direct (N × H)
4. C₂²×C₄²×C₈×C₁₉	C₃	direct (N × H)
10. C₂²×C₃×C₄×C₈×C₁₉	C₄	direct (N × H)
12. C₃×C₄²×C₈×C₁₉	C₂²	direct (N × H)
15. C₂²×C₃×C₄²×C₁₉	C₈	direct (N × H)
24. C₂×C₃×C₄×C₈×C₁₉	C₂×C₄	direct (N × H)
26. C₂²×C₃×C₄²×C₈	C₁₉	direct (N × H)
29. C₂×C₄²×C₈×C₁₉	C₂×C₃	direct (N × H)
33. C₂²×C₄×C₈×C₁₉	C₃×C₄	direct (N × H)
37. C₄²×C₈×C₁₉	C₂²×C₃	direct (N × H)
45. C₂²×C₃×C₈×C₁₉	C₄²	direct (N × H)
49. C₂×C₃×C₄²×C₁₉	C₂×C₈	direct (N × H)
54. C₃×C₄×C₈×C₁₉	C₂²×C₄	direct (N × H)
59. C₂²×C₄²×C₁₉	C₃×C₈	direct (N × H)
64. C₂×C₄×C₈×C₁₉	C₂×C₃×C₄	direct (N × H)
71. C₂²×C₃×C₄×C₁₉	C₄×C₈	direct (N × H)
80. C₂×C₃×C₈×C₁₉	C₂×C₄²	direct (N × H)
83. C₃×C₄²×C₁₉	C₂²×C₈	direct (N × H)
87. C₂×C₃×C₄²×C₈	C₂×C₁₉	direct (N × H)
95. C₂²×C₈×C₁₉	C₃×C₄²	direct (N × H)
99. C₂×C₄²×C₁₉	C₂×C₃×C₈	direct (N × H)
104. C₄×C₈×C₁₉	C₂²×C₃×C₄	direct (N × H)
105. C₂²×C₄²×C₈	C₃×C₁₉	direct (N × H)
112. C₂×C₃×C₄×C₁₉	C₂×C₄×C₈	direct (N × H)
118. C₃×C₈×C₁₉	C₂²×C₄²	direct (N × H)
122. C₂²×C₃×C₄×C₈	C₄×C₁₉	direct (N × H)
126. C₃×C₄²×C₈	C₂²×C₁₉	direct (N × H)
130. C₂²×C₄×C₁₉	C₃×C₄×C₈	direct (N × H)
139. C₂×C₈×C₁₉	C₂×C₃×C₄²	direct (N × H)
142. C₄²×C₁₉	C₂²×C₃×C₈	direct (N × H)
146. C₂×C₄²×C₈	C₂×C₃×C₁₉	direct (N × H)
147. C₂²×C₃×C₁₉	C₄²×C₈	direct (N × H)
153. C₃×C₄×C₁₉	C₂²×C₄×C₈	direct (N × H)
159. C₂²×C₃×C₄²	C₈×C₁₉	direct (N × H)
164. C₂×C₃×C₄×C₈	C₂×C₄×C₁₉	direct (N × H)
174. C₂×C₄×C₁₉	C₂×C₃×C₄×C₈	direct (N × H)
180. C₈×C₁₉	C₂²×C₃×C₄²	direct (N × H)
184. C₂²×C₄×C₈	C₃×C₄×C₁₉	direct (N × H)
188. C₄²×C₈	C₂²×C₃×C₁₉	direct (N × H)
189. C₂×C₃×C₁₉	C₂×C₄²×C₈	direct (N × H)
199. C₂²×C₃×C₈	C₄²×C₁₉	direct (N × H)
203. C₂×C₃×C₄²	C₂×C₈×C₁₉	direct (N × H)
208. C₃×C₄×C₈	C₂²×C₄×C₁₉	direct (N × H)
209. C₂²×C₁₉	C₃×C₄²×C₈	direct (N × H)
215. C₄×C₁₉	C₂²×C₃×C₄×C₈	direct (N × H)
221. C₂²×C₄²	C₃×C₈×C₁₉	direct (N × H)
226. C₂×C₄×C₈	C₂×C₃×C₄×C₁₉	direct (N × H)
230. C₃×C₁₉	C₂²×C₄²×C₈	direct (N × H)
234. C₂²×C₃×C₄	C₄×C₈×C₁₉	direct (N × H)
243. C₂×C₃×C₈	C₂×C₄²×C₁₉	direct (N × H)
246. C₃×C₄²	C₂²×C₈×C₁₉	direct (N × H)
248. C₂×C₁₉	C₂×C₃×C₄²×C₈	direct (N × H)
258. C₂²×C₈	C₃×C₄²×C₁₉	direct (N × H)
262. C₂×C₄²	C₂×C₃×C₈×C₁₉	direct (N × H)
267. C₄×C₈	C₂²×C₃×C₄×C₁₉	direct (N × H)
274. C₂×C₃×C₄	C₂×C₄×C₈×C₁₉	direct (N × H)
280. C₃×C₈	C₂²×C₄²×C₁₉	direct (N × H)
281. C₁₉	C₂²×C₃×C₄²×C₈	direct (N × H)
285. C₂²×C₄	C₃×C₄×C₈×C₁₉	direct (N × H)
294. C₂×C₈	C₂×C₃×C₄²×C₁₉	direct (N × H)
297. C₄²	C₂²×C₃×C₈×C₁₉	direct (N × H)
299. C₂²×C₃	C₄²×C₈×C₁₉	direct (N × H)
305. C₃×C₄	C₂²×C₄×C₈×C₁₉	direct (N × H)
312. C₂×C₄	C₂×C₃×C₄×C₈×C₁₉	direct (N × H)
319. C₈	C₂²×C₃×C₄²×C₁₉	direct (N × H)
320. C₂×C₃	C₂×C₄²×C₈×C₁₉	direct (N × H)
323. C₂²	C₃×C₄²×C₈×C₁₉	direct (N × H)
328. C₄	C₂²×C₃×C₄×C₈×C₁₉	direct (N × H)
331. C₃	C₂²×C₄²×C₈×C₁₉	direct (N × H)
332. C₂	C₂×C₃×C₄²×C₈×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄³×C₁₉	2
C₂³×C₃×C₄×C₈×C₁₉	2
C₂×C₃×C₄²×C₈×C₁₉	2
C₂²×C₄²×C₈×C₁₉	3
C₂²×C₃×C₄²×C₈	19

Subgroups — C22×C3×C42×C8×C19 #72206115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄²×C₈×C₁₉ #72206115