Subgroups — C₂²×C₄×C₅×C₁₆×C₁₉ #72201615

Order 24320.

2044 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×C₁₆×C₁₉	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×C₁₆×C₁₉	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₄²×C₅×C₁₉	C₄	1	1	yes	characteristic
5	C₂³×C₅×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₂³×C₅×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈×C₁₉	C₄	1	6	yes	—
8	C₂×C₄×C₅×C₈×C₁₉	C₂²	1	6	yes	—
9	C₂²×C₅×C₁₆×C₁₉	C₄	1	16	yes	direct product factor
10	C₂²×C₅×C₁₆×C₁₉	C₂²	1	12	yes	—
11	C₄×C₅×C₁₆×C₁₉	C₂²	1	16	yes	direct product factor
12	C₂³×C₄×C₅×C₁₉	C₈	1	2	yes	—
13	C₂³×C₄×C₅×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄²×C₅×C₁₉	C₈	1	6	yes	—
15	C₂×C₄²×C₅×C₁₉	C₂×C₄	1	6	yes	—
16	C₂²×C₅×C₈×C₁₉	C₈	1	8	yes	—
17	C₂²×C₅×C₈×C₁₉	C₂×C₄	1	3	yes	—
18	C₂²×C₅×C₈×C₁₉	C₂×C₄	1	6	yes	—
19	C₂²×C₅×C₈×C₁₉	C₂×C₄	1	8	yes	—
20	C₂²×C₅×C₈×C₁₉	C₂³	1	3	yes	—
21	C₄×C₅×C₈×C₁₉	C₂×C₄	1	12	yes	—
22	C₄×C₅×C₈×C₁₉	C₂³	1	4	yes	—
23	C₂×C₅×C₁₆×C₁₉	C₂×C₄	1	48	yes	direct product factor
24	C₂×C₅×C₁₆×C₁₉	C₂³	1	8	yes	—
25	C₂²×C₄×C₁₆×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂³×C₁₆×C₁₉	C₂×C₅	1	2	yes	—
27	C₂²×C₄×C₈×C₁₉	C₂×C₅	1	1	yes	characteristic
28	C₂×C₄×C₁₆×C₁₉	C₂×C₅	1	12	yes	direct product factor
29	C₂⁴×C₅×C₁₉	C₂×C₈	1	1	yes	characteristic
30	C₂²×C₄×C₅×C₁₉	C₁₆	1	16	yes	direct product factor
31	C₂²×C₄×C₅×C₁₉	C₄²	1	4	yes	—
32	C₂²×C₄×C₅×C₁₉	C₂×C₈	1	3	yes	—
33	C₂²×C₄×C₅×C₁₉	C₂×C₈	1	4	yes	—
34	C₂²×C₄×C₅×C₁₉	C₂×C₈	1	12	yes	—
35	C₂²×C₄×C₅×C₁₉	C₂²×C₄	1	3	yes	—
36	C₂×C₅×C₈×C₁₉	C₄²	1	12	yes	—
37	C₂×C₅×C₈×C₁₉	C₂×C₈	1	24	yes	—
38	C₂×C₅×C₈×C₁₉	C₂²×C₄	1	3	yes	—
39	C₂×C₅×C₈×C₁₉	C₂²×C₄	1	4	yes	—
40	C₂×C₅×C₈×C₁₉	C₂²×C₄	1	12	yes	—
41	C₂×C₅×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
42	C₄²×C₅×C₁₉	C₂×C₈	1	12	yes	—
43	C₄²×C₅×C₁₉	C₂²×C₄	1	4	yes	—
44	C₅×C₁₆×C₁₉	C₂²×C₄	1	16	yes	direct product factor
45	C₂²×C₄×C₅×C₁₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂³×C₈×C₁₉	C₄×C₅	1	1	yes	characteristic
47	C₂³×C₈×C₁₉	C₂²×C₅	1	1	yes	characteristic
48	C₂²×C₄²×C₁₉	C₄×C₅	1	1	yes	characteristic
49	C₂²×C₁₆×C₁₉	C₄×C₅	1	16	yes	direct product factor
50	C₂²×C₁₆×C₁₉	C₂²×C₅	1	12	yes	—
51	C₂×C₄×C₈×C₁₉	C₄×C₅	1	6	yes	—
52	C₂×C₄×C₈×C₁₉	C₂²×C₅	1	6	yes	—
53	C₄×C₁₆×C₁₉	C₂²×C₅	1	16	yes	direct product factor
54	C₂³×C₅×C₁₉	C₄×C₈	1	4	yes	—
55	C₂³×C₅×C₁₉	C₂×C₁₆	1	8	yes	—
56	C₂³×C₅×C₁₉	C₂²×C₈	1	3	yes	—
57	C₂×C₄×C₅×C₁₉	C₄×C₈	1	12	yes	—
58	C₂×C₄×C₅×C₁₉	C₂×C₁₆	1	48	yes	direct product factor
59	C₂×C₄×C₅×C₁₉	C₂×C₄²	1	6	yes	—
60	C₂×C₄×C₅×C₁₉	C₂²×C₈	1	3	yes	—
61	C₂×C₄×C₅×C₁₉	C₂²×C₈	1	6	yes	—
62	C₂×C₄×C₅×C₁₉	C₂²×C₈	1	8	yes	—
63	C₂×C₄×C₅×C₁₉	C₂³×C₄	1	1	yes	characteristic
64	C₅×C₈×C₁₉	C₂×C₄²	1	6	yes	—
65	C₅×C₈×C₁₉	C₂²×C₈	1	8	yes	—
66	C₅×C₈×C₁₉	C₂³×C₄	1	2	yes	—
67	C₂³×C₅×C₁₆	C₂×C₁₉	1	2	yes	—
68	C₂²×C₄×C₅×C₈	C₂×C₁₉	1	1	yes	characteristic
69	C₂×C₄×C₅×C₁₆	C₂×C₁₉	1	12	yes	direct product factor
70	C₂³×C₄×C₁₉	C₅×C₈	1	2	yes	—
71	C₂³×C₄×C₁₉	C₂×C₄×C₅	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₅×C₈	1	8	yes	—
73	C₂²×C₈×C₁₉	C₂×C₄×C₅	1	3	yes	—
74	C₂²×C₈×C₁₉	C₂×C₄×C₅	1	6	yes	—
75	C₂²×C₈×C₁₉	C₂×C₄×C₅	1	8	yes	—
76	C₂²×C₈×C₁₉	C₂³×C₅	1	3	yes	—
77	C₂×C₄²×C₁₉	C₅×C₈	1	6	yes	—
78	C₂×C₄²×C₁₉	C₂×C₄×C₅	1	6	yes	—
79	C₂×C₁₆×C₁₉	C₂×C₄×C₅	1	48	yes	direct product factor
80	C₂×C₁₆×C₁₉	C₂³×C₅	1	8	yes	—
81	C₄×C₈×C₁₉	C₂×C₄×C₅	1	12	yes	—
82	C₄×C₈×C₁₉	C₂³×C₅	1	4	yes	—
83	C₂²×C₅×C₁₉	C₄×C₁₆	1	16	yes	direct product factor
84	C₂²×C₅×C₁₉	C₂×C₄×C₈	1	6	yes	—
85	C₂²×C₅×C₁₉	C₂²×C₁₆	1	12	yes	—
86	C₂²×C₅×C₁₉	C₂³×C₈	1	1	yes	characteristic
87	C₄×C₅×C₁₉	C₂×C₄×C₈	1	6	yes	—
88	C₄×C₅×C₁₉	C₂²×C₁₆	1	16	yes	direct product factor
89	C₄×C₅×C₁₉	C₂²×C₄²	1	1	yes	characteristic
90	C₄×C₅×C₁₉	C₂³×C₈	1	1	yes	characteristic
91	C₂³×C₅×C₈	C₄×C₁₉	1	1	yes	characteristic
92	C₂³×C₅×C₈	C₂²×C₁₉	1	1	yes	characteristic
93	C₂²×C₄²×C₅	C₄×C₁₉	1	1	yes	characteristic
94	C₂²×C₅×C₁₆	C₄×C₁₉	1	16	yes	direct product factor
95	C₂²×C₅×C₁₆	C₂²×C₁₉	1	12	yes	—
96	C₂×C₄×C₅×C₈	C₄×C₁₉	1	6	yes	—
97	C₂×C₄×C₅×C₈	C₂²×C₁₉	1	6	yes	—
98	C₄×C₅×C₁₆	C₂²×C₁₉	1	16	yes	direct product factor
99	C₂⁴×C₁₉	C₂×C₅×C₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₅×C₁₆	1	16	yes	direct product factor
101	C₂²×C₄×C₁₉	C₄²×C₅	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂×C₅×C₈	1	3	yes	—
103	C₂²×C₄×C₁₉	C₂×C₅×C₈	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂×C₅×C₈	1	12	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄×C₅	1	3	yes	—
106	C₂×C₈×C₁₉	C₄²×C₅	1	12	yes	—
107	C₂×C₈×C₁₉	C₂×C₅×C₈	1	24	yes	—
108	C₂×C₈×C₁₉	C₂²×C₄×C₅	1	3	yes	—
109	C₂×C₈×C₁₉	C₂²×C₄×C₅	1	4	yes	—
110	C₂×C₈×C₁₉	C₂²×C₄×C₅	1	12	yes	—
111	C₂×C₈×C₁₉	C₂⁴×C₅	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×C₅×C₈	1	12	yes	—
113	C₄²×C₁₉	C₂²×C₄×C₅	1	4	yes	—
114	C₁₆×C₁₉	C₂²×C₄×C₅	1	16	yes	direct product factor
115	C₂²×C₄×C₁₆	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
116	C₂×C₅×C₁₉	C₂×C₄×C₁₆	1	12	yes	direct product factor
117	C₂×C₅×C₁₉	C₂²×C₄×C₈	1	1	yes	characteristic
118	C₂×C₅×C₁₉	C₂³×C₁₆	1	2	yes	—
119	C₂³×C₄×C₅	C₈×C₁₉	1	2	yes	—
120	C₂³×C₄×C₅	C₂×C₄×C₁₉	1	1	yes	characteristic
121	C₂²×C₅×C₈	C₈×C₁₉	1	8	yes	—
122	C₂²×C₅×C₈	C₂×C₄×C₁₉	1	3	yes	—
123	C₂²×C₅×C₈	C₂×C₄×C₁₉	1	6	yes	—
124	C₂²×C₅×C₈	C₂×C₄×C₁₉	1	8	yes	—
125	C₂²×C₅×C₈	C₂³×C₁₉	1	3	yes	—
126	C₂×C₄²×C₅	C₈×C₁₉	1	6	yes	—
127	C₂×C₄²×C₅	C₂×C₄×C₁₉	1	6	yes	—
128	C₂×C₅×C₁₆	C₂×C₄×C₁₉	1	48	yes	direct product factor
129	C₂×C₅×C₁₆	C₂³×C₁₉	1	8	yes	—
130	C₄×C₅×C₈	C₂×C₄×C₁₉	1	12	yes	—
131	C₄×C₅×C₈	C₂³×C₁₉	1	4	yes	—
132	C₂³×C₁₉	C₄×C₅×C₈	1	4	yes	—
133	C₂³×C₁₉	C₂×C₅×C₁₆	1	8	yes	—
134	C₂³×C₁₉	C₂²×C₅×C₈	1	3	yes	—
135	C₂×C₄×C₁₉	C₄×C₅×C₈	1	12	yes	—
136	C₂×C₄×C₁₉	C₂×C₅×C₁₆	1	48	yes	direct product factor
137	C₂×C₄×C₁₉	C₂×C₄²×C₅	1	6	yes	—
138	C₂×C₄×C₁₉	C₂²×C₅×C₈	1	3	yes	—
139	C₂×C₄×C₁₉	C₂²×C₅×C₈	1	6	yes	—
140	C₂×C₄×C₁₉	C₂²×C₅×C₈	1	8	yes	—
141	C₂×C₄×C₁₉	C₂³×C₄×C₅	1	1	yes	characteristic
142	C₈×C₁₉	C₂×C₄²×C₅	1	6	yes	—
143	C₈×C₁₉	C₂²×C₅×C₈	1	8	yes	—
144	C₈×C₁₉	C₂³×C₄×C₅	1	2	yes	—
145	C₂³×C₁₆	C₂×C₅×C₁₉	1	2	yes	—
146	C₂²×C₄×C₈	C₂×C₅×C₁₉	1	1	yes	characteristic
147	C₂×C₄×C₁₆	C₂×C₅×C₁₉	1	12	yes	direct product factor
148	C₅×C₁₉	C₂²×C₄×C₁₆	1	1	yes	characteristic, direct product factor, Hall
149	C₂⁴×C₅	C₂×C₈×C₁₉	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₁₆×C₁₉	1	16	yes	direct product factor
151	C₂²×C₄×C₅	C₄²×C₁₉	1	4	yes	—
152	C₂²×C₄×C₅	C₂×C₈×C₁₉	1	3	yes	—
153	C₂²×C₄×C₅	C₂×C₈×C₁₉	1	4	yes	—
154	C₂²×C₄×C₅	C₂×C₈×C₁₉	1	12	yes	—
155	C₂²×C₄×C₅	C₂²×C₄×C₁₉	1	3	yes	—
156	C₂×C₅×C₈	C₄²×C₁₉	1	12	yes	—
157	C₂×C₅×C₈	C₂×C₈×C₁₉	1	24	yes	—
158	C₂×C₅×C₈	C₂²×C₄×C₁₉	1	3	yes	—
159	C₂×C₅×C₈	C₂²×C₄×C₁₉	1	4	yes	—
160	C₂×C₅×C₈	C₂²×C₄×C₁₉	1	12	yes	—
161	C₂×C₅×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
162	C₄²×C₅	C₂×C₈×C₁₉	1	12	yes	—
163	C₄²×C₅	C₂²×C₄×C₁₉	1	4	yes	—
164	C₅×C₁₆	C₂²×C₄×C₁₉	1	16	yes	direct product factor
165	C₂²×C₁₉	C₄×C₅×C₁₆	1	16	yes	direct product factor
166	C₂²×C₁₉	C₂×C₄×C₅×C₈	1	6	yes	—
167	C₂²×C₁₉	C₂²×C₅×C₁₆	1	12	yes	—
168	C₂²×C₁₉	C₂³×C₅×C₈	1	1	yes	characteristic
169	C₄×C₁₉	C₂×C₄×C₅×C₈	1	6	yes	—
170	C₄×C₁₉	C₂²×C₅×C₁₆	1	16	yes	direct product factor
171	C₄×C₁₉	C₂²×C₄²×C₅	1	1	yes	characteristic
172	C₄×C₁₉	C₂³×C₅×C₈	1	1	yes	characteristic
173	C₂³×C₈	C₄×C₅×C₁₉	1	1	yes	characteristic
174	C₂³×C₈	C₂²×C₅×C₁₉	1	1	yes	characteristic
175	C₂²×C₄²	C₄×C₅×C₁₉	1	1	yes	characteristic
176	C₂²×C₁₆	C₄×C₅×C₁₉	1	16	yes	direct product factor
177	C₂²×C₁₆	C₂²×C₅×C₁₉	1	12	yes	—
178	C₂×C₄×C₈	C₄×C₅×C₁₉	1	6	yes	—
179	C₂×C₄×C₈	C₂²×C₅×C₁₉	1	6	yes	—
180	C₄×C₁₆	C₂²×C₅×C₁₉	1	16	yes	direct product factor
181	C₂³×C₅	C₄×C₈×C₁₉	1	4	yes	—
182	C₂³×C₅	C₂×C₁₆×C₁₉	1	8	yes	—
183	C₂³×C₅	C₂²×C₈×C₁₉	1	3	yes	—
184	C₂×C₄×C₅	C₄×C₈×C₁₉	1	12	yes	—
185	C₂×C₄×C₅	C₂×C₁₆×C₁₉	1	48	yes	direct product factor
186	C₂×C₄×C₅	C₂×C₄²×C₁₉	1	6	yes	—
187	C₂×C₄×C₅	C₂²×C₈×C₁₉	1	3	yes	—
188	C₂×C₄×C₅	C₂²×C₈×C₁₉	1	6	yes	—
189	C₂×C₄×C₅	C₂²×C₈×C₁₉	1	8	yes	—
190	C₂×C₄×C₅	C₂³×C₄×C₁₉	1	1	yes	characteristic
191	C₅×C₈	C₂×C₄²×C₁₉	1	6	yes	—
192	C₅×C₈	C₂²×C₈×C₁₉	1	8	yes	—
193	C₅×C₈	C₂³×C₄×C₁₉	1	2	yes	—
194	C₂×C₁₉	C₂×C₄×C₅×C₁₆	1	12	yes	direct product factor
195	C₂×C₁₉	C₂²×C₄×C₅×C₈	1	1	yes	characteristic
196	C₂×C₁₉	C₂³×C₅×C₁₆	1	2	yes	—
197	C₂³×C₄	C₅×C₈×C₁₉	1	2	yes	—
198	C₂³×C₄	C₂×C₄×C₅×C₁₉	1	1	yes	characteristic
199	C₂²×C₈	C₅×C₈×C₁₉	1	8	yes	—
200	C₂²×C₈	C₂×C₄×C₅×C₁₉	1	3	yes	—
201	C₂²×C₈	C₂×C₄×C₅×C₁₉	1	6	yes	—
202	C₂²×C₈	C₂×C₄×C₅×C₁₉	1	8	yes	—
203	C₂²×C₈	C₂³×C₅×C₁₉	1	3	yes	—
204	C₂×C₄²	C₅×C₈×C₁₉	1	6	yes	—
205	C₂×C₄²	C₂×C₄×C₅×C₁₉	1	6	yes	—
206	C₂×C₁₆	C₂×C₄×C₅×C₁₉	1	48	yes	direct product factor
207	C₂×C₁₆	C₂³×C₅×C₁₉	1	8	yes	—
208	C₄×C₈	C₂×C₄×C₅×C₁₉	1	12	yes	—
209	C₄×C₈	C₂³×C₅×C₁₉	1	4	yes	—
210	C₂²×C₅	C₄×C₁₆×C₁₉	1	16	yes	direct product factor
211	C₂²×C₅	C₂×C₄×C₈×C₁₉	1	6	yes	—
212	C₂²×C₅	C₂²×C₁₆×C₁₉	1	12	yes	—
213	C₂²×C₅	C₂³×C₈×C₁₉	1	1	yes	characteristic
214	C₄×C₅	C₂×C₄×C₈×C₁₉	1	6	yes	—
215	C₄×C₅	C₂²×C₁₆×C₁₉	1	16	yes	direct product factor
216	C₄×C₅	C₂²×C₄²×C₁₉	1	1	yes	characteristic
217	C₄×C₅	C₂³×C₈×C₁₉	1	1	yes	characteristic
218	C₁₉	C₂²×C₄×C₅×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
219	C₂⁴	C₂×C₅×C₈×C₁₉	1	1	yes	characteristic
220	C₂²×C₄	C₅×C₁₆×C₁₉	1	16	yes	direct product factor
221	C₂²×C₄	C₄²×C₅×C₁₉	1	4	yes	—
222	C₂²×C₄	C₂×C₅×C₈×C₁₉	1	3	yes	—
223	C₂²×C₄	C₂×C₅×C₈×C₁₉	1	4	yes	—
224	C₂²×C₄	C₂×C₅×C₈×C₁₉	1	12	yes	—
225	C₂²×C₄	C₂²×C₄×C₅×C₁₉	1	3	yes	—
226	C₂×C₈	C₄²×C₅×C₁₉	1	12	yes	—
227	C₂×C₈	C₂×C₅×C₈×C₁₉	1	24	yes	—
228	C₂×C₈	C₂²×C₄×C₅×C₁₉	1	3	yes	—
229	C₂×C₈	C₂²×C₄×C₅×C₁₉	1	4	yes	—
230	C₂×C₈	C₂²×C₄×C₅×C₁₉	1	12	yes	—
231	C₂×C₈	C₂⁴×C₅×C₁₉	1	1	yes	characteristic
232	C₄²	C₂×C₅×C₈×C₁₉	1	12	yes	—
233	C₄²	C₂²×C₄×C₅×C₁₉	1	4	yes	—
234	C₁₆	C₂²×C₄×C₅×C₁₉	1	16	yes	direct product factor
235	C₂×C₅	C₂×C₄×C₁₆×C₁₉	1	12	yes	direct product factor
236	C₂×C₅	C₂²×C₄×C₈×C₁₉	1	1	yes	characteristic
237	C₂×C₅	C₂³×C₁₆×C₁₉	1	2	yes	—
238	C₂³	C₂×C₅×C₁₆×C₁₉	1	8	yes	—
239	C₂³	C₄×C₅×C₈×C₁₉	1	4	yes	—
240	C₂³	C₂²×C₅×C₈×C₁₉	1	3	yes	—
241	C₂×C₄	C₂×C₅×C₁₆×C₁₉	1	48	yes	direct product factor
242	C₂×C₄	C₄×C₅×C₈×C₁₉	1	12	yes	—
243	C₂×C₄	C₂²×C₅×C₈×C₁₉	1	3	yes	—
244	C₂×C₄	C₂²×C₅×C₈×C₁₉	1	6	yes	—
245	C₂×C₄	C₂²×C₅×C₈×C₁₉	1	8	yes	—
246	C₂×C₄	C₂×C₄²×C₅×C₁₉	1	6	yes	—
247	C₂×C₄	C₂³×C₄×C₅×C₁₉	1	1	yes	characteristic
248	C₈	C₂²×C₅×C₈×C₁₉	1	8	yes	—
249	C₈	C₂×C₄²×C₅×C₁₉	1	6	yes	—
250	C₈	C₂³×C₄×C₅×C₁₉	1	2	yes	—
251	C₅	C₂²×C₄×C₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²	C₄×C₅×C₁₆×C₁₉	1	16	yes	direct product factor
253	C₂²	C₂²×C₅×C₁₆×C₁₉	1	12	yes	—
254	C₂²	C₂×C₄×C₅×C₈×C₁₉	1	6	yes	—
255	C₂²	C₂³×C₅×C₈×C₁₉	1	1	yes	characteristic
256	C₄	C₂²×C₅×C₁₆×C₁₉	1	16	yes	direct product factor
257	C₄	C₂×C₄×C₅×C₈×C₁₉	1	6	yes	—
258	C₄	C₂³×C₅×C₈×C₁₉	1	1	yes	characteristic
259	C₄	C₂²×C₄²×C₅×C₁₉	1	1	yes	characteristic
260	C₂	C₂×C₄×C₅×C₁₆×C₁₉	1	12	yes	direct product factor
261	C₂	C₂³×C₅×C₁₆×C₁₉	1	2	yes	—
262	C₂	C₂²×C₄×C₅×C₈×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂⁴×C₅×C₁₉
socle, prime radical	C₂⁴×C₅×C₁₉	C₂×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×C₄×C₅×C₁₆×C₁₉	C₂	direct (N × H)
9. C₂²×C₅×C₁₆×C₁₉	C₄	direct (N × H)
11. C₄×C₅×C₁₆×C₁₉	C₂²	direct (N × H)
23. C₂×C₅×C₁₆×C₁₉	C₂×C₄	direct (N × H)
25. C₂²×C₄×C₁₆×C₁₉	C₅	direct (N × H)
28. C₂×C₄×C₁₆×C₁₉	C₂×C₅	direct (N × H)
30. C₂²×C₄×C₅×C₁₉	C₁₆	direct (N × H)
44. C₅×C₁₆×C₁₉	C₂²×C₄	direct (N × H)
45. C₂²×C₄×C₅×C₁₆	C₁₉	direct (N × H)
49. C₂²×C₁₆×C₁₉	C₄×C₅	direct (N × H)
53. C₄×C₁₆×C₁₉	C₂²×C₅	direct (N × H)
58. C₂×C₄×C₅×C₁₉	C₂×C₁₆	direct (N × H)
69. C₂×C₄×C₅×C₁₆	C₂×C₁₉	direct (N × H)
79. C₂×C₁₆×C₁₉	C₂×C₄×C₅	direct (N × H)
83. C₂²×C₅×C₁₉	C₄×C₁₆	direct (N × H)
88. C₄×C₅×C₁₉	C₂²×C₁₆	direct (N × H)
94. C₂²×C₅×C₁₆	C₄×C₁₉	direct (N × H)
98. C₄×C₅×C₁₆	C₂²×C₁₉	direct (N × H)
100. C₂²×C₄×C₁₉	C₅×C₁₆	direct (N × H)
114. C₁₆×C₁₉	C₂²×C₄×C₅	direct (N × H)
115. C₂²×C₄×C₁₆	C₅×C₁₉	direct (N × H)
116. C₂×C₅×C₁₉	C₂×C₄×C₁₆	direct (N × H)
128. C₂×C₅×C₁₆	C₂×C₄×C₁₉	direct (N × H)
136. C₂×C₄×C₁₉	C₂×C₅×C₁₆	direct (N × H)
147. C₂×C₄×C₁₆	C₂×C₅×C₁₉	direct (N × H)
148. C₅×C₁₉	C₂²×C₄×C₁₆	direct (N × H)
150. C₂²×C₄×C₅	C₁₆×C₁₉	direct (N × H)
164. C₅×C₁₆	C₂²×C₄×C₁₉	direct (N × H)
165. C₂²×C₁₉	C₄×C₅×C₁₆	direct (N × H)
170. C₄×C₁₉	C₂²×C₅×C₁₆	direct (N × H)
176. C₂²×C₁₆	C₄×C₅×C₁₉	direct (N × H)
180. C₄×C₁₆	C₂²×C₅×C₁₉	direct (N × H)
185. C₂×C₄×C₅	C₂×C₁₆×C₁₉	direct (N × H)
194. C₂×C₁₉	C₂×C₄×C₅×C₁₆	direct (N × H)
206. C₂×C₁₆	C₂×C₄×C₅×C₁₉	direct (N × H)
210. C₂²×C₅	C₄×C₁₆×C₁₉	direct (N × H)
215. C₄×C₅	C₂²×C₁₆×C₁₉	direct (N × H)
218. C₁₉	C₂²×C₄×C₅×C₁₆	direct (N × H)
220. C₂²×C₄	C₅×C₁₆×C₁₉	direct (N × H)
234. C₁₆	C₂²×C₄×C₅×C₁₉	direct (N × H)
235. C₂×C₅	C₂×C₄×C₁₆×C₁₉	direct (N × H)
241. C₂×C₄	C₂×C₅×C₁₆×C₁₉	direct (N × H)
251. C₅	C₂²×C₄×C₁₆×C₁₉	direct (N × H)
252. C₂²	C₄×C₅×C₁₆×C₁₉	direct (N × H)
256. C₄	C₂²×C₅×C₁₆×C₁₉	direct (N × H)
260. C₂	C₂×C₄×C₅×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×C₄×C₅×C₈×C₁₉	2
C₂³×C₅×C₁₆×C₁₉	2
C₂×C₄×C₅×C₁₆×C₁₉	2
C₂²×C₄×C₁₆×C₁₉	5
C₂²×C₄×C₅×C₁₆	19

Subgroups — C22×C4×C5×C16×C19 #72201615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₅×C₁₆×C₁₉ #72201615