Subgroups — C₂²×C₄²×C₁₆×C₁₉ #72197136

Order 19456.

18282 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₁₆×C₁₉	C₂	1	6	yes	maximal
3	C₂×C₄²×C₁₆×C₁₉	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄²×C₁₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂⁴×C₁₆×C₁₉	C₂²	1	4	yes	—
6	C₂³×C₄×C₈×C₁₉	C₄	1	3	yes	—
7	C₂³×C₄×C₈×C₁₉	C₂²	1	3	yes	—
8	C₂²×C₄³×C₁₉	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₁₆×C₁₉	C₄	1	96	yes	direct product factor
10	C₂²×C₄×C₁₆×C₁₉	C₂²	1	72	yes	—
11	C₂×C₄²×C₈×C₁₉	C₄	1	12	yes	—
12	C₂×C₄²×C₈×C₁₉	C₂²	1	12	yes	—
13	C₄²×C₁₆×C₁₉	C₂²	1	64	yes	direct product factor
14	C₂⁴×C₈×C₁₉	C₂×C₄	1	3	yes	—
15	C₂⁴×C₈×C₁₉	C₂³	1	1	yes	characteristic
16	C₂³×C₄²×C₁₉	C₈	1	4	yes	—
17	C₂³×C₄²×C₁₉	C₂×C₄	1	3	yes	—
18	C₂³×C₁₆×C₁₉	C₂×C₄	1	96	yes	—
19	C₂³×C₁₆×C₁₉	C₂³	1	24	yes	—
20	C₂²×C₄×C₈×C₁₉	C₈	1	48	yes	—
21	C₂²×C₄×C₈×C₁₉	C₂×C₄	1	18	yes	—
22	C₂²×C₄×C₈×C₁₉	C₂×C₄	1	36	yes	—
23	C₂²×C₄×C₈×C₁₉	C₂×C₄	1	48	yes	—
24	C₂²×C₄×C₈×C₁₉	C₂³	1	18	yes	—
25	C₂×C₄³×C₁₉	C₈	1	12	yes	—
26	C₂×C₄³×C₁₉	C₂×C₄	1	12	yes	—
27	C₂×C₄×C₁₆×C₁₉	C₂×C₄	1	576	yes	direct product factor
28	C₂×C₄×C₁₆×C₁₉	C₂³	1	96	yes	—
29	C₄²×C₈×C₁₉	C₂×C₄	1	48	yes	—
30	C₄²×C₈×C₁₉	C₂³	1	16	yes	—
31	C₂⁴×C₄×C₁₉	C₂×C₈	1	6	yes	—
32	C₂⁴×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂³×C₈×C₁₉	C₄²	1	24	yes	—
34	C₂³×C₈×C₁₉	C₂×C₈	1	48	yes	—
35	C₂³×C₈×C₁₉	C₂²×C₄	1	3	yes	—
36	C₂³×C₈×C₁₉	C₂²×C₄	1	18	yes	—
37	C₂³×C₈×C₁₉	C₂²×C₄	1	24	yes	—
38	C₂³×C₈×C₁₉	C₂⁴	1	3	yes	—
39	C₂²×C₄²×C₁₉	C₁₆	1	64	yes	direct product factor
40	C₂²×C₄²×C₁₉	C₄²	1	24	yes	—
41	C₂²×C₄²×C₁₉	C₂×C₈	1	18	yes	—
42	C₂²×C₄²×C₁₉	C₂×C₈	1	24	yes	—
43	C₂²×C₄²×C₁₉	C₂×C₈	1	48	yes	—
44	C₂²×C₄²×C₁₉	C₂²×C₄	1	18	yes	—
45	C₂²×C₁₆×C₁₉	C₄²	1	256	yes	direct product factor
46	C₂²×C₁₆×C₁₉	C₂²×C₄	1	288	yes	—
47	C₂²×C₁₆×C₁₉	C₂⁴	1	16	yes	—
48	C₂×C₄×C₈×C₁₉	C₄²	1	144	yes	—
49	C₂×C₄×C₈×C₁₉	C₂×C₈	1	288	yes	—
50	C₂×C₄×C₈×C₁₉	C₂²×C₄	1	36	yes	—
51	C₂×C₄×C₈×C₁₉	C₂²×C₄	1	48	yes	—
52	C₂×C₄×C₈×C₁₉	C₂²×C₄	1	144	yes	—
53	C₂×C₄×C₈×C₁₉	C₂⁴	1	12	yes	—
54	C₄³×C₁₉	C₂×C₈	1	48	yes	—
55	C₄³×C₁₉	C₂²×C₄	1	16	yes	—
56	C₄×C₁₆×C₁₉	C₂²×C₄	1	384	yes	direct product factor
57	C₂⁵×C₁₉	C₂²×C₈	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	C₄×C₈	1	48	yes	—
59	C₂³×C₄×C₁₉	C₂×C₁₆	1	96	yes	—
60	C₂³×C₄×C₁₉	C₂×C₄²	1	12	yes	—
61	C₂³×C₄×C₁₉	C₂²×C₈	1	3	yes	—
62	C₂³×C₄×C₁₉	C₂²×C₈	1	12	yes	—
63	C₂³×C₄×C₁₉	C₂²×C₈	1	36	yes	—
64	C₂³×C₄×C₁₉	C₂³×C₄	1	3	yes	—
65	C₂²×C₈×C₁₉	C₄×C₈	1	192	yes	—
66	C₂²×C₈×C₁₉	C₂×C₄²	1	36	yes	—
67	C₂²×C₈×C₁₉	C₂×C₄²	1	64	yes	—
68	C₂²×C₈×C₁₉	C₂×C₄²	1	72	yes	—
69	C₂²×C₈×C₁₉	C₂²×C₈	1	144	yes	—
70	C₂²×C₈×C₁₉	C₂³×C₄	1	3	yes	—
71	C₂²×C₈×C₁₉	C₂³×C₄	1	12	yes	—
72	C₂²×C₈×C₁₉	C₂³×C₄	1	36	yes	—
73	C₂²×C₈×C₁₉	C₂⁵	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	C₄×C₈	1	144	yes	—
75	C₂×C₄²×C₁₉	C₂×C₁₆	1	384	yes	direct product factor
76	C₂×C₄²×C₁₉	C₂×C₄²	1	72	yes	—
77	C₂×C₄²×C₁₉	C₂²×C₈	1	36	yes	—
78	C₂×C₄²×C₁₉	C₂²×C₈	1	64	yes	—
79	C₂×C₄²×C₁₉	C₂²×C₈	1	72	yes	—
80	C₂×C₄²×C₁₉	C₂³×C₄	1	12	yes	—
81	C₂×C₁₆×C₁₉	C₂×C₄²	1	384	yes	direct product factor
82	C₂×C₁₆×C₁₉	C₂³×C₄	1	96	yes	—
83	C₄×C₈×C₁₉	C₂×C₄²	1	144	yes	—
84	C₄×C₈×C₁₉	C₂²×C₈	1	192	yes	—
85	C₄×C₈×C₁₉	C₂³×C₄	1	48	yes	—
86	C₂³×C₄×C₁₆	C₂×C₁₉	1	6	yes	—
87	C₂²×C₄²×C₈	C₂×C₁₉	1	1	yes	characteristic
88	C₂×C₄²×C₁₆	C₂×C₁₉	1	24	yes	direct product factor
89	C₂⁴×C₁₉	C₂×C₄×C₈	1	12	yes	—
90	C₂⁴×C₁₉	C₂²×C₁₆	1	16	yes	—
91	C₂⁴×C₁₉	C₂³×C₈	1	3	yes	—
92	C₂²×C₄×C₁₉	C₄×C₁₆	1	384	yes	direct product factor
93	C₂²×C₄×C₁₉	C₄³	1	16	yes	—
94	C₂²×C₄×C₁₉	C₂×C₄×C₈	1	36	yes	—
95	C₂²×C₄×C₁₉	C₂×C₄×C₈	1	48	yes	—
96	C₂²×C₄×C₁₉	C₂×C₄×C₈	1	144	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₁₆	1	288	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄²	1	18	yes	—
99	C₂²×C₄×C₁₉	C₂³×C₈	1	3	yes	—
100	C₂²×C₄×C₁₉	C₂³×C₈	1	18	yes	—
101	C₂²×C₄×C₁₉	C₂³×C₈	1	24	yes	—
102	C₂²×C₄×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₉	C₄³	1	48	yes	—
104	C₂×C₈×C₁₉	C₂×C₄×C₈	1	288	yes	—
105	C₂×C₈×C₁₉	C₂²×C₄²	1	18	yes	—
106	C₂×C₈×C₁₉	C₂²×C₄²	1	24	yes	—
107	C₂×C₈×C₁₉	C₂²×C₄²	1	48	yes	—
108	C₂×C₈×C₁₉	C₂³×C₈	1	48	yes	—
109	C₂×C₈×C₁₉	C₂⁴×C₄	1	6	yes	—
110	C₄²×C₁₉	C₂×C₄×C₈	1	144	yes	—
111	C₄²×C₁₉	C₂²×C₁₆	1	256	yes	direct product factor
112	C₄²×C₁₉	C₂²×C₄²	1	24	yes	—
113	C₄²×C₁₉	C₂³×C₈	1	24	yes	—
114	C₁₆×C₁₉	C₂²×C₄²	1	64	yes	direct product factor
115	C₂⁴×C₁₆	C₂²×C₁₉	1	4	yes	—
116	C₂³×C₄×C₈	C₄×C₁₉	1	3	yes	—
117	C₂³×C₄×C₈	C₂²×C₁₉	1	3	yes	—
118	C₂²×C₄³	C₄×C₁₉	1	1	yes	characteristic
119	C₂²×C₄×C₁₆	C₄×C₁₉	1	96	yes	direct product factor
120	C₂²×C₄×C₁₆	C₂²×C₁₉	1	72	yes	—
121	C₂×C₄²×C₈	C₄×C₁₉	1	12	yes	—
122	C₂×C₄²×C₈	C₂²×C₁₉	1	12	yes	—
123	C₄²×C₁₆	C₂²×C₁₉	1	64	yes	direct product factor
124	C₂³×C₁₉	C₄²×C₈	1	16	yes	—
125	C₂³×C₁₉	C₂×C₄×C₁₆	1	96	yes	—
126	C₂³×C₁₉	C₂²×C₄×C₈	1	18	yes	—
127	C₂³×C₁₉	C₂³×C₁₆	1	24	yes	—
128	C₂³×C₁₉	C₂⁴×C₈	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₄²×C₈	1	48	yes	—
130	C₂×C₄×C₁₉	C₂×C₄×C₁₆	1	576	yes	direct product factor
131	C₂×C₄×C₁₉	C₂×C₄³	1	12	yes	—
132	C₂×C₄×C₁₉	C₂²×C₄×C₈	1	18	yes	—
133	C₂×C₄×C₁₉	C₂²×C₄×C₈	1	36	yes	—
134	C₂×C₄×C₁₉	C₂²×C₄×C₈	1	48	yes	—
135	C₂×C₄×C₁₉	C₂³×C₁₆	1	96	yes	—
136	C₂×C₄×C₁₉	C₂³×C₄²	1	3	yes	—
137	C₂×C₄×C₁₉	C₂⁴×C₈	1	3	yes	—
138	C₈×C₁₉	C₂×C₄³	1	12	yes	—
139	C₈×C₁₉	C₂²×C₄×C₈	1	48	yes	—
140	C₈×C₁₉	C₂³×C₄²	1	4	yes	—
141	C₂⁴×C₈	C₂×C₄×C₁₉	1	3	yes	—
142	C₂⁴×C₈	C₂³×C₁₉	1	1	yes	characteristic
143	C₂³×C₄²	C₈×C₁₉	1	4	yes	—
144	C₂³×C₄²	C₂×C₄×C₁₉	1	3	yes	—
145	C₂³×C₁₆	C₂×C₄×C₁₉	1	96	yes	—
146	C₂³×C₁₆	C₂³×C₁₉	1	24	yes	—
147	C₂²×C₄×C₈	C₈×C₁₉	1	48	yes	—
148	C₂²×C₄×C₈	C₂×C₄×C₁₉	1	18	yes	—
149	C₂²×C₄×C₈	C₂×C₄×C₁₉	1	36	yes	—
150	C₂²×C₄×C₈	C₂×C₄×C₁₉	1	48	yes	—
151	C₂²×C₄×C₈	C₂³×C₁₉	1	18	yes	—
152	C₂×C₄³	C₈×C₁₉	1	12	yes	—
153	C₂×C₄³	C₂×C₄×C₁₉	1	12	yes	—
154	C₂×C₄×C₁₆	C₂×C₄×C₁₉	1	576	yes	direct product factor
155	C₂×C₄×C₁₆	C₂³×C₁₉	1	96	yes	—
156	C₄²×C₈	C₂×C₄×C₁₉	1	48	yes	—
157	C₄²×C₈	C₂³×C₁₉	1	16	yes	—
158	C₂²×C₁₉	C₄²×C₁₆	1	64	yes	direct product factor
159	C₂²×C₁₉	C₂×C₄²×C₈	1	12	yes	—
160	C₂²×C₁₉	C₂²×C₄×C₁₆	1	72	yes	—
161	C₂²×C₁₉	C₂³×C₄×C₈	1	3	yes	—
162	C₂²×C₁₉	C₂⁴×C₁₆	1	4	yes	—
163	C₄×C₁₉	C₂×C₄²×C₈	1	12	yes	—
164	C₄×C₁₉	C₂²×C₄×C₁₆	1	96	yes	direct product factor
165	C₄×C₁₉	C₂²×C₄³	1	1	yes	characteristic
166	C₄×C₁₉	C₂³×C₄×C₈	1	3	yes	—
167	C₂⁴×C₄	C₂×C₈×C₁₉	1	6	yes	—
168	C₂⁴×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
169	C₂³×C₈	C₄²×C₁₉	1	24	yes	—
170	C₂³×C₈	C₂×C₈×C₁₉	1	48	yes	—
171	C₂³×C₈	C₂²×C₄×C₁₉	1	3	yes	—
172	C₂³×C₈	C₂²×C₄×C₁₉	1	18	yes	—
173	C₂³×C₈	C₂²×C₄×C₁₉	1	24	yes	—
174	C₂³×C₈	C₂⁴×C₁₉	1	3	yes	—
175	C₂²×C₄²	C₁₆×C₁₉	1	64	yes	direct product factor
176	C₂²×C₄²	C₄²×C₁₉	1	24	yes	—
177	C₂²×C₄²	C₂×C₈×C₁₉	1	18	yes	—
178	C₂²×C₄²	C₂×C₈×C₁₉	1	24	yes	—
179	C₂²×C₄²	C₂×C₈×C₁₉	1	48	yes	—
180	C₂²×C₄²	C₂²×C₄×C₁₉	1	18	yes	—
181	C₂²×C₁₆	C₄²×C₁₉	1	256	yes	direct product factor
182	C₂²×C₁₆	C₂²×C₄×C₁₉	1	288	yes	—
183	C₂²×C₁₆	C₂⁴×C₁₉	1	16	yes	—
184	C₂×C₄×C₈	C₄²×C₁₉	1	144	yes	—
185	C₂×C₄×C₈	C₂×C₈×C₁₉	1	288	yes	—
186	C₂×C₄×C₈	C₂²×C₄×C₁₉	1	36	yes	—
187	C₂×C₄×C₈	C₂²×C₄×C₁₉	1	48	yes	—
188	C₂×C₄×C₈	C₂²×C₄×C₁₉	1	144	yes	—
189	C₂×C₄×C₈	C₂⁴×C₁₉	1	12	yes	—
190	C₄³	C₂×C₈×C₁₉	1	48	yes	—
191	C₄³	C₂²×C₄×C₁₉	1	16	yes	—
192	C₄×C₁₆	C₂²×C₄×C₁₉	1	384	yes	direct product factor
193	C₂×C₁₉	C₂×C₄²×C₁₆	1	24	yes	direct product factor
194	C₂×C₁₉	C₂²×C₄²×C₈	1	1	yes	characteristic
195	C₂×C₁₉	C₂³×C₄×C₁₆	1	6	yes	—
196	C₂⁵	C₂²×C₈×C₁₉	1	1	yes	characteristic
197	C₂³×C₄	C₄×C₈×C₁₉	1	48	yes	—
198	C₂³×C₄	C₂×C₁₆×C₁₉	1	96	yes	—
199	C₂³×C₄	C₂×C₄²×C₁₉	1	12	yes	—
200	C₂³×C₄	C₂²×C₈×C₁₉	1	3	yes	—
201	C₂³×C₄	C₂²×C₈×C₁₉	1	12	yes	—
202	C₂³×C₄	C₂²×C₈×C₁₉	1	36	yes	—
203	C₂³×C₄	C₂³×C₄×C₁₉	1	3	yes	—
204	C₂²×C₈	C₄×C₈×C₁₉	1	192	yes	—
205	C₂²×C₈	C₂×C₄²×C₁₉	1	36	yes	—
206	C₂²×C₈	C₂×C₄²×C₁₉	1	64	yes	—
207	C₂²×C₈	C₂×C₄²×C₁₉	1	72	yes	—
208	C₂²×C₈	C₂²×C₈×C₁₉	1	144	yes	—
209	C₂²×C₈	C₂³×C₄×C₁₉	1	3	yes	—
210	C₂²×C₈	C₂³×C₄×C₁₉	1	12	yes	—
211	C₂²×C₈	C₂³×C₄×C₁₉	1	36	yes	—
212	C₂²×C₈	C₂⁵×C₁₉	1	1	yes	characteristic
213	C₂×C₄²	C₄×C₈×C₁₉	1	144	yes	—
214	C₂×C₄²	C₂×C₁₆×C₁₉	1	384	yes	direct product factor
215	C₂×C₄²	C₂×C₄²×C₁₉	1	72	yes	—
216	C₂×C₄²	C₂²×C₈×C₁₉	1	36	yes	—
217	C₂×C₄²	C₂²×C₈×C₁₉	1	64	yes	—
218	C₂×C₄²	C₂²×C₈×C₁₉	1	72	yes	—
219	C₂×C₄²	C₂³×C₄×C₁₉	1	12	yes	—
220	C₂×C₁₆	C₂×C₄²×C₁₉	1	384	yes	direct product factor
221	C₂×C₁₆	C₂³×C₄×C₁₉	1	96	yes	—
222	C₄×C₈	C₂×C₄²×C₁₉	1	144	yes	—
223	C₄×C₈	C₂²×C₈×C₁₉	1	192	yes	—
224	C₄×C₈	C₂³×C₄×C₁₉	1	48	yes	—
225	C₁₉	C₂²×C₄²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
226	C₂⁴	C₂×C₄×C₈×C₁₉	1	12	yes	—
227	C₂⁴	C₂²×C₁₆×C₁₉	1	16	yes	—
228	C₂⁴	C₂³×C₈×C₁₉	1	3	yes	—
229	C₂²×C₄	C₄×C₁₆×C₁₉	1	384	yes	direct product factor
230	C₂²×C₄	C₄³×C₁₉	1	16	yes	—
231	C₂²×C₄	C₂×C₄×C₈×C₁₉	1	36	yes	—
232	C₂²×C₄	C₂×C₄×C₈×C₁₉	1	48	yes	—
233	C₂²×C₄	C₂×C₄×C₈×C₁₉	1	144	yes	—
234	C₂²×C₄	C₂²×C₁₆×C₁₉	1	288	yes	—
235	C₂²×C₄	C₂²×C₄²×C₁₉	1	18	yes	—
236	C₂²×C₄	C₂³×C₈×C₁₉	1	3	yes	—
237	C₂²×C₄	C₂³×C₈×C₁₉	1	18	yes	—
238	C₂²×C₄	C₂³×C₈×C₁₉	1	24	yes	—
239	C₂²×C₄	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
240	C₂×C₈	C₄³×C₁₉	1	48	yes	—
241	C₂×C₈	C₂×C₄×C₈×C₁₉	1	288	yes	—
242	C₂×C₈	C₂²×C₄²×C₁₉	1	18	yes	—
243	C₂×C₈	C₂²×C₄²×C₁₉	1	24	yes	—
244	C₂×C₈	C₂²×C₄²×C₁₉	1	48	yes	—
245	C₂×C₈	C₂³×C₈×C₁₉	1	48	yes	—
246	C₂×C₈	C₂⁴×C₄×C₁₉	1	6	yes	—
247	C₄²	C₂×C₄×C₈×C₁₉	1	144	yes	—
248	C₄²	C₂²×C₁₆×C₁₉	1	256	yes	direct product factor
249	C₄²	C₂²×C₄²×C₁₉	1	24	yes	—
250	C₄²	C₂³×C₈×C₁₉	1	24	yes	—
251	C₁₆	C₂²×C₄²×C₁₉	1	64	yes	direct product factor
252	C₂³	C₄²×C₈×C₁₉	1	16	yes	—
253	C₂³	C₂×C₄×C₁₆×C₁₉	1	96	yes	—
254	C₂³	C₂²×C₄×C₈×C₁₉	1	18	yes	—
255	C₂³	C₂³×C₁₆×C₁₉	1	24	yes	—
256	C₂³	C₂⁴×C₈×C₁₉	1	1	yes	characteristic
257	C₂×C₄	C₄²×C₈×C₁₉	1	48	yes	—
258	C₂×C₄	C₂×C₄×C₁₆×C₁₉	1	576	yes	direct product factor
259	C₂×C₄	C₂×C₄³×C₁₉	1	12	yes	—
260	C₂×C₄	C₂²×C₄×C₈×C₁₉	1	18	yes	—
261	C₂×C₄	C₂²×C₄×C₈×C₁₉	1	36	yes	—
262	C₂×C₄	C₂²×C₄×C₈×C₁₉	1	48	yes	—
263	C₂×C₄	C₂³×C₁₆×C₁₉	1	96	yes	—
264	C₂×C₄	C₂³×C₄²×C₁₉	1	3	yes	—
265	C₂×C₄	C₂⁴×C₈×C₁₉	1	3	yes	—
266	C₈	C₂×C₄³×C₁₉	1	12	yes	—
267	C₈	C₂²×C₄×C₈×C₁₉	1	48	yes	—
268	C₈	C₂³×C₄²×C₁₉	1	4	yes	—
269	C₂²	C₄²×C₁₆×C₁₉	1	64	yes	direct product factor
270	C₂²	C₂×C₄²×C₈×C₁₉	1	12	yes	—
271	C₂²	C₂²×C₄×C₁₆×C₁₉	1	72	yes	—
272	C₂²	C₂³×C₄×C₈×C₁₉	1	3	yes	—
273	C₂²	C₂⁴×C₁₆×C₁₉	1	4	yes	—
274	C₄	C₂×C₄²×C₈×C₁₉	1	12	yes	—
275	C₄	C₂²×C₄×C₁₆×C₁₉	1	96	yes	direct product factor
276	C₄	C₂²×C₄³×C₁₉	1	1	yes	characteristic
277	C₄	C₂³×C₄×C₈×C₁₉	1	3	yes	—
278	C₂	C₂×C₄²×C₁₆×C₁₉	1	24	yes	direct product factor
279	C₂	C₂³×C₄×C₁₆×C₁₉	1	6	yes	—
280	C₂	C₂²×C₄²×C₈×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₈	C₂⁵×C₁₉
socle, prime radical	C₂⁵×C₁₉	C₂²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄²×C₁₆×C₁₉	C₂	direct (N × H)
4. C₂²×C₄²×C₁₆	C₁₉	direct (N × H)
9. C₂²×C₄×C₁₆×C₁₉	C₄	direct (N × H)
13. C₄²×C₁₆×C₁₉	C₂²	direct (N × H)
27. C₂×C₄×C₁₆×C₁₉	C₂×C₄	direct (N × H)
39. C₂²×C₄²×C₁₉	C₁₆	direct (N × H)
45. C₂²×C₁₆×C₁₉	C₄²	direct (N × H)
56. C₄×C₁₆×C₁₉	C₂²×C₄	direct (N × H)
75. C₂×C₄²×C₁₉	C₂×C₁₆	direct (N × H)
81. C₂×C₁₆×C₁₉	C₂×C₄²	direct (N × H)
88. C₂×C₄²×C₁₆	C₂×C₁₉	direct (N × H)
92. C₂²×C₄×C₁₉	C₄×C₁₆	direct (N × H)
111. C₄²×C₁₉	C₂²×C₁₆	direct (N × H)
114. C₁₆×C₁₉	C₂²×C₄²	direct (N × H)
119. C₂²×C₄×C₁₆	C₄×C₁₉	direct (N × H)
123. C₄²×C₁₆	C₂²×C₁₉	direct (N × H)
130. C₂×C₄×C₁₉	C₂×C₄×C₁₆	direct (N × H)
154. C₂×C₄×C₁₆	C₂×C₄×C₁₉	direct (N × H)
158. C₂²×C₁₉	C₄²×C₁₆	direct (N × H)
164. C₄×C₁₉	C₂²×C₄×C₁₆	direct (N × H)
175. C₂²×C₄²	C₁₆×C₁₉	direct (N × H)
181. C₂²×C₁₆	C₄²×C₁₉	direct (N × H)
192. C₄×C₁₆	C₂²×C₄×C₁₉	direct (N × H)
193. C₂×C₁₉	C₂×C₄²×C₁₆	direct (N × H)
214. C₂×C₄²	C₂×C₁₆×C₁₉	direct (N × H)
220. C₂×C₁₆	C₂×C₄²×C₁₉	direct (N × H)
225. C₁₉	C₂²×C₄²×C₁₆	direct (N × H)
229. C₂²×C₄	C₄×C₁₆×C₁₉	direct (N × H)
248. C₄²	C₂²×C₁₆×C₁₉	direct (N × H)
251. C₁₆	C₂²×C₄²×C₁₉	direct (N × H)
258. C₂×C₄	C₂×C₄×C₁₆×C₁₉	direct (N × H)
269. C₂²	C₄²×C₁₆×C₁₉	direct (N × H)
275. C₄	C₂²×C₄×C₁₆×C₁₉	direct (N × H)
278. C₂	C₂×C₄²×C₁₆×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×C₄²×C₈×C₁₉	2
C₂³×C₄×C₁₆×C₁₉	2
C₂×C₄²×C₁₆×C₁₉	2
C₂²×C₄²×C₁₆	19

Subgroups — C22×C42×C16×C19 #72197136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄²×C₁₆×C₁₉ #72197136