Subgroups — C₁₉×#22410 #18028369

Order 4864.

1404 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#548	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1967	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1901	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1900	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1785	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#548	—	2	2	no	—
17	C₁₉×#548	—	2	2	no	—
18	C₁₉×#548	—	2	2	no	—
19	C₁₉×#548	—	2	2	no	—
20	C₂×C₁₉×#124	C₄	1	2	yes	—
21	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#121	C₄	1	2	yes	—
25	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
28	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#436	—	2	2	no	—
30	C₁₉×#435	—	2	2	no	—
31	C₁₉×#435	—	2	2	no	—
32	C₈×D₄×C₁₉	—	2	2	no	—
33	C₁₉×#423	C₂²	1	2	yes	—
34	C₁₉×#413	—	2	4	no	—
35	C₂×C₁₉×#101	—	2	4	no	—
36	C₂×C₁₉×#101	C₂²	1	2	yes	—
37	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#101	C₂²	1	2	yes	—
41	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#100	C₂²	1	2	yes	—
43	C₂×C₁₉×#100	C₂²	1	2	yes	—
44	C₁₉×#407	C₂²	1	2	yes	—
45	C₁₉×#407	C₂²	1	2	yes	—
46	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
47	C₁₉×#343	C₂²	1	2	yes	—
48	C₁₉×#343	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	—	2	2	no	—
53	C₂×#41×C₁₉	—	4	2	no	—
54	C₂²×Q₈×C₁₉	—	2	2	no	—
55	C₂²×Q₈×C₁₉	—	2	2	no	—
56	C₂²×Q₈×C₁₉	—	2	2	no	—
57	C₂²×Q₈×C₁₉	—	2	2	no	—
58	C₂²×Q₈×C₁₉	—	4	2	no	—
59	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
64	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
67	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₁₉	—	2	2	no	—
71	C₂×M₁₆×C₁₉	—	2	2	no	—
72	C₂×M₁₆×C₁₉	—	2	4	no	—
73	C₂×M₁₆×C₁₉	—	2	4	no	—
74	C₂×M₁₆×C₁₉	—	4	2	no	—
75	C₂×M₁₆×C₁₉	—	4	2	no	—
76	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
77	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
78	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
79	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₉	—	2	2	no	—
81	C₂²×C₈×C₁₉	—	2	2	no	—
82	C₁₉×#124	—	2	4	no	—
83	C₁₉×#124	—	2	4	no	—
84	C₁₉×#124	—	2	2	no	—
85	C₁₉×#124	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	4	no	—
89	C₁₉×C₂²⋊Q₈	—	2	4	no	—
90	C₁₉×#121	—	2	4	no	—
91	C₁₉×#121	—	2	4	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₄×Q₈×C₁₉	—	2	2	no	—
95	C₄×Q₈×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	D₄	1	2	yes	—
101	C₄×D₄×C₁₉	D₄	1	2	yes	—
102	C₄×D₄×C₁₉	D₄	1	2	yes	—
103	C₄×D₄×C₁₉	D₄	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
110	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
111	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	—	2	2	no	—
117	C₁₉×C₄⋊C₈	—	2	2	no	—
118	C₁₉×#101	—	2	2	no	—
119	C₁₉×#101	—	2	2	no	—
120	C₁₉×#101	—	2	2	no	—
121	C₁₉×#101	—	2	4	no	—
122	C₁₉×#101	—	4	2	no	—
123	C₁₉×#101	D₄	1	4	yes	complemented
124	C₁₉×#100	—	2	4	no	—
125	C₁₉×#100	—	4	2	no	—
126	C₁₉×C₂²⋊C₈	—	2	2	no	—
127	C₁₉×C₂²⋊C₈	—	2	2	no	—
128	C₁₉×C₂²⋊C₈	—	2	2	no	—
129	C₁₉×C₂²⋊C₈	—	2	2	no	—
130	C₁₉×#97	—	2	2	no	—
131	C₄×C₈×C₁₉	—	2	2	no	—
132	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
134	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	#41×C₁₉	—	4	4	no	—
136	#41×C₁₉	—	4	4	no	—
137	#41×C₁₉	—	4	4	no	—
138	#41×C₁₉	—	4	4	no	—
139	C₂×Q₈×C₁₉	—	2	4	no	—
140	C₂×Q₈×C₁₉	—	2	4	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	2	2	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	2	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	4	2	no	—
148	C₂×Q₈×C₁₉	—	4	4	no	—
149	C₂×Q₈×C₁₉	—	4	4	no	—
150	C₂×Q₈×C₁₉	—	4	4	no	—
151	C₂×Q₈×C₁₉	—	4	4	no	—
152	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
153	C₂×Q₈×C₁₉	#41	1	2	yes	—
154	C₂×D₄×C₁₉	—	2	2	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	4	no	—
157	C₂×D₄×C₁₉	—	2	4	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	4	no	—
165	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
166	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	4	no	—
178	C₂²×C₄×C₁₉	—	2	4	no	—
179	C₂²×C₄×C₁₉	—	4	2	no	—
180	C₂²×C₄×C₁₉	—	4	2	no	—
181	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
185	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
193	M₁₆×C₁₉	—	2	2	no	—
194	M₁₆×C₁₉	—	2	2	no	—
195	M₁₆×C₁₉	—	2	2	no	—
196	M₁₆×C₁₉	—	2	2	no	—
197	M₁₆×C₁₉	—	2	2	no	—
198	M₁₆×C₁₉	—	2	2	no	—
199	M₁₆×C₁₉	—	2	2	no	—
200	M₁₆×C₁₉	—	4	4	no	—
201	M₁₆×C₁₉	—	4	4	no	—
202	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
203	C₂×C₈×C₁₉	—	2	2	no	—
204	C₂×C₈×C₁₉	—	2	2	no	—
205	C₂×C₈×C₁₉	—	2	2	no	—
206	C₂×C₈×C₁₉	—	2	2	no	—
207	C₂×C₈×C₁₉	—	4	4	no	—
208	C₂×C₈×C₁₉	—	4	4	no	—
209	C₄⋊C₄×C₁₉	—	2	2	no	—
210	C₄⋊C₄×C₁₉	—	2	2	no	—
211	C₄⋊C₄×C₁₉	—	2	4	no	—
212	C₄⋊C₄×C₁₉	—	2	2	no	—
213	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
214	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
215	C₂²⋊C₄×C₁₉	—	2	4	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	4	no	—
219	C₂²⋊C₄×C₁₉	—	2	4	no	—
220	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
221	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
225	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
226	C₄²×C₁₉	—	2	2	no	—
227	C₄²×C₁₉	—	2	2	no	—
228	C₄²×C₁₉	C₂×D₄	1	2	yes	—
229	C₄²×C₁₉	C₂×D₄	1	2	yes	—
230	#22410	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	2	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	2	no	—
237	C₂³×C₁₉	—	2	2	no	—
238	C₂³×C₁₉	—	2	2	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	4	2	no	—
243	C₂³×C₁₉	—	4	2	no	—
244	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
248	Q₈×C₁₉	—	2	4	no	—
249	Q₈×C₁₉	—	2	4	no	—
250	Q₈×C₁₉	—	4	8	no	—
251	Q₈×C₁₉	—	4	2	no	—
252	Q₈×C₁₉	—	4	2	no	—
253	D₄×C₁₉	—	2	4	no	—
254	D₄×C₁₉	—	4	2	no	—
255	D₄×C₁₉	—	4	8	no	—
256	D₄×C₁₉	—	4	4	no	—
257	D₄×C₁₉	—	4	4	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	4	no	—
281	C₂×C₄×C₁₉	—	4	4	no	—
282	C₂×C₄×C₁₉	—	4	4	no	—
283	C₂×C₄×C₁₉	—	4	4	no	—
284	C₂×C₄×C₁₉	—	4	2	no	—
285	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
292	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
296	C₈×C₁₉	—	2	4	no	—
297	C₈×C₁₉	—	4	2	no	—
298	C₈×C₁₉	—	4	2	no	—
299	C₈×C₁₉	—	4	2	no	—
300	C₂×#548	C₂×C₁₉	1	1	yes	characteristic
301	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
302	C₂×#413	C₂×C₁₉	1	1	yes	characteristic, complemented
303	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1967	C₂×C₁₉	1	2	yes	complemented
305	#1901	C₂×C₁₉	1	2	yes	complemented
306	#1900	C₂×C₁₉	1	2	yes	complemented
307	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1785	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1784	C₂×C₁₉	1	1	yes	characteristic, complemented
310	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	2	2	no	—
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	2	1	no	—
320	C₂²×C₁₉	—	2	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	2	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	2	no	—
329	C₂²×C₁₉	—	8	2	no	—
330	C₂²×C₁₉	#413	1	2	yes	complemented
331	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂²×C₁₉	#518	1	1	yes	characteristic
334	C₄×C₁₉	—	2	1	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	2	no	—
337	C₄×C₁₉	—	2	4	no	—
338	C₄×C₁₉	—	2	2	no	—
339	C₄×C₁₉	—	2	1	no	—
340	C₄×C₁₉	—	2	1	no	—
341	C₄×C₁₉	—	4	2	no	—
342	C₄×C₁₉	—	4	2	no	—
343	C₄×C₁₉	D₄²	1	2	yes	—
344	C₄×C₁₉	#546	1	2	yes	—
345	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
346	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
347	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
348	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
349	#548	—	2	2	no	—
350	#548	—	2	2	no	—
351	#548	—	2	2	no	—
352	#548	—	2	2	no	—
353	C₂×#124	C₄×C₁₉	1	2	yes	—
354	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#121	C₄×C₁₉	1	2	yes	—
358	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
362	#436	—	2	2	no	—
363	#435	—	2	2	no	—
364	#435	—	2	2	no	—
365	C₈×D₄	—	2	2	no	—
366	#423	C₂²×C₁₉	1	2	yes	—
367	#413	—	2	4	no	—
368	C₂×#101	—	2	4	no	—
369	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#101	C₂²×C₁₉	1	2	yes	—
372	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#101	C₂²×C₁₉	1	2	yes	—
374	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#100	C₂²×C₁₉	1	2	yes	—
376	C₂×#100	C₂²×C₁₉	1	2	yes	—
377	#407	C₂²×C₁₉	1	2	yes	—
378	#407	C₂²×C₁₉	1	2	yes	—
379	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
380	#343	C₂²×C₁₉	1	2	yes	—
381	#343	C₂²×C₁₉	1	2	yes	—
382	C₂×C₁₉	—	2	1	no	—
383	C₂×C₁₉	—	2	1	no	—
384	C₂×C₁₉	—	2	2	no	—
385	C₂×C₁₉	—	4	1	no	—
386	C₂×C₁₉	—	4	2	no	—
387	C₂×C₁₉	—	8	2	no	—
388	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
390	C₂×C₁₉	#2889	1	1	yes	characteristic
391	C₂×#41	—	2	2	no	—
392	C₂×#41	—	2	2	no	—
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	—	4	2	no	—
396	C₂²×Q₈	—	2	2	no	—
397	C₂²×Q₈	—	2	2	no	—
398	C₂²×Q₈	—	2	2	no	—
399	C₂²×Q₈	—	2	2	no	—
400	C₂²×Q₈	—	4	2	no	—
401	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
402	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
405	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
406	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
409	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
410	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂×M₁₆	—	2	2	no	—
413	C₂×M₁₆	—	2	2	no	—
414	C₂×M₁₆	—	2	4	no	—
415	C₂×M₁₆	—	2	4	no	—
416	C₂×M₁₆	—	4	2	no	—
417	C₂×M₁₆	—	4	2	no	—
418	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
419	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
420	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
421	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
422	C₂²×C₈	—	2	2	no	—
423	C₂²×C₈	—	2	2	no	—
424	#124	—	2	4	no	—
425	#124	—	2	4	no	—
426	#124	—	2	2	no	—
427	#124	—	2	2	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	4	no	—
431	C₂²⋊Q₈	—	2	4	no	—
432	#121	—	2	4	no	—
433	#121	—	2	4	no	—
434	#121	—	2	2	no	—
435	#121	—	2	2	no	—
436	C₄×Q₈	—	2	2	no	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	D₄×C₁₉	1	2	yes	—
443	C₄×D₄	D₄×C₁₉	1	2	yes	—
444	C₄×D₄	D₄×C₁₉	1	2	yes	—
445	C₄×D₄	D₄×C₁₉	1	2	yes	—
446	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
447	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
448	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
456	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
457	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
458	C₄⋊C₈	—	2	2	no	—
459	C₄⋊C₈	—	2	2	no	—
460	#101	—	2	2	no	—
461	#101	—	2	2	no	—
462	#101	—	2	2	no	—
463	#101	—	2	4	no	—
464	#101	—	4	2	no	—
465	#101	D₄×C₁₉	1	4	yes	complemented
466	#100	—	2	4	no	—
467	#100	—	4	2	no	—
468	C₂²⋊C₈	—	2	2	no	—
469	C₂²⋊C₈	—	2	2	no	—
470	C₂²⋊C₈	—	2	2	no	—
471	C₂²⋊C₈	—	2	2	no	—
472	#97	—	2	2	no	—
473	C₄×C₈	—	2	2	no	—
474	C₁₉	#22410	1	1	yes	characteristic, direct product factor, Sylow
475	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
476	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
477	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
478	#41	—	4	4	no	—
479	#41	—	4	4	no	—
480	#41	—	4	4	no	—
481	#41	—	4	4	no	—
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	2	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	2	no	—
489	C₂×Q₈	—	2	2	no	—
490	C₂×Q₈	—	4	2	no	—
491	C₂×Q₈	—	4	4	no	—
492	C₂×Q₈	—	4	4	no	—
493	C₂×Q₈	—	4	4	no	—
494	C₂×Q₈	—	4	4	no	—
495	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
496	C₂×Q₈	#41×C₁₉	1	2	yes	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	4	2	no	—
506	C₂×D₄	—	4	2	no	—
507	C₂×D₄	—	4	4	no	—
508	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
509	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
525	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
527	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
528	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
529	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
532	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
533	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
534	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
536	M₁₆	—	2	2	no	—
537	M₁₆	—	2	2	no	—
538	M₁₆	—	2	2	no	—
539	M₁₆	—	2	2	no	—
540	M₁₆	—	2	2	no	—
541	M₁₆	—	2	2	no	—
542	M₁₆	—	2	2	no	—
543	M₁₆	—	4	4	no	—
544	M₁₆	—	4	4	no	—
545	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	2	2	no	—
549	C₂×C₈	—	2	2	no	—
550	C₂×C₈	—	4	4	no	—
551	C₂×C₈	—	4	4	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
557	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
564	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
565	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
566	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
567	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
568	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	C₂×D₄×C₁₉	1	2	yes	—
572	C₄²	C₂×D₄×C₁₉	1	2	yes	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
587	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
588	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
589	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
590	Q₈	—	2	4	no	—
591	Q₈	—	2	4	no	—
592	Q₈	—	4	8	no	—
593	Q₈	—	4	2	no	—
594	Q₈	—	4	2	no	—
595	D₄	—	2	4	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	8	no	—
598	D₄	—	4	4	no	—
599	D₄	—	4	4	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
628	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
629	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
630	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
631	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
632	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
633	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
634	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
636	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
637	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
638	C₈	—	2	4	no	—
639	C₈	—	4	2	no	—
640	C₈	—	4	2	no	—
641	C₈	—	4	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	2	no	—
660	C₂²	—	8	2	no	—
661	C₂²	C₁₉×#413	1	2	yes	complemented
662	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
663	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
664	C₂²	C₁₉×#518	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	4	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	D₄²×C₁₉	1	2	yes	—
675	C₄	C₁₉×#546	1	2	yes	—
676	C₂	—	2	1	no	—
677	C₂	—	2	1	no	—
678	C₂	—	2	2	no	—
679	C₂	—	4	1	no	—
680	C₂	—	4	2	no	—
681	C₂	—	8	2	no	—
682	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
683	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
684	C₂	C₁₉×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#548	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₁₉	C₂	semidirect
3. C₂×C₁₉×#413	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
5. C₁₉×#1967	C₂	semidirect
6. C₁₉×#1901	C₂	semidirect
7. C₁₉×#1900	C₂	semidirect
8. C₁₉×#1801	C₂	semidirect
9. C₁₉×#1785	C₂	semidirect
10. C₁₉×#1784	C₂	semidirect
11. C₄×C₁₉×#101	C₂	semidirect
123. C₁₉×#101	D₄	semidirect
230. #22410	C₁₉	direct (N × H)
301. D₄×M₁₆	C₂×C₁₉	semidirect
302. C₂×#413	C₂×C₁₉	semidirect
303. C₂²×#101	C₂×C₁₉	semidirect
304. #1967	C₂×C₁₉	semidirect
305. #1901	C₂×C₁₉	semidirect
306. #1900	C₂×C₁₉	semidirect
307. #1801	C₂×C₁₉	semidirect
308. #1785	C₂×C₁₉	semidirect
309. #1784	C₂×C₁₉	semidirect
310. C₄×#101	C₂×C₁₉	semidirect
330. C₂²×C₁₉	#413	semidirect
465. #101	D₄×C₁₉	semidirect
474. C₁₉	#22410	direct (N × H)
661. C₂²	C₁₉×#413	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#548	2
D₄×M₁₆×C₁₉	2
C₂×C₁₉×#413	2
C₂²×C₁₉×#101	2
C₁₉×#1967	2
C₁₉×#1901	2
C₁₉×#1900	2
C₁₉×#1801	2
C₁₉×#1785	2
C₁₉×#1784	2
C₄×C₁₉×#101	2
#22410	19

Subgroups — C19×#22410 #18028369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22410 #18028369