Subgroups — C₁₉×#22408 #18028367

Order 4864.

1544 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#546	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×#100	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×#1800	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1785	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	2	no	—
18	C₁₉×#546	—	2	2	no	—
19	C₁₉×#546	—	2	2	no	—
20	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#123	C₄	1	2	yes	—
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₄	1	2	yes	—
24	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#120	C₄	1	2	yes	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
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	complemented
34	C₁₉×#413	—	2	4	no	—
35	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
36	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
37	C₂×C₁₉×#100	—	2	4	no	—
38	C₂×C₁₉×#100	C₂²	1	2	yes	—
39	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#100	C₂²	1	2	yes	—
43	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
44	C₁₉×#407	C₂²	1	2	yes	—
45	C₁₉×#407	C₂²	1	2	yes	complemented
46	C₄×M₁₆×C₁₉	C₂²	1	2	yes	complemented
47	C₁₉×#343	C₂²	1	2	yes	complemented
48	C₁₉×#343	C₂²	1	2	yes	complemented
49	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
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	—	2	2	no	—
54	C₂×#41×C₁₉	—	4	2	no	—
55	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	—	2	2	no	—
57	C₂²×D₄×C₁₉	—	2	2	no	—
58	C₂²×D₄×C₁₉	—	2	2	no	—
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	4	2	no	—
61	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
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	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
68	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₉	—	2	2	no	—
72	C₂×M₁₆×C₁₉	—	2	2	no	—
73	C₂×M₁₆×C₁₉	—	2	4	no	—
74	C₂×M₁₆×C₁₉	—	2	4	no	—
75	C₂×M₁₆×C₁₉	—	4	2	no	—
76	C₂×M₁₆×C₁₉	—	4	2	no	—
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	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₉	—	2	2	no	—
82	C₂²×C₈×C₁₉	—	2	2	no	—
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	—	2	2	no	—
85	C₁₉×#123	—	2	4	no	—
86	C₁₉×#123	—	2	4	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	4	no	—
92	C₁₉×#121	—	2	4	no	—
93	C₁₉×#120	—	2	4	no	—
94	C₁₉×#120	—	2	4	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	D₄	1	2	yes	—
98	C₄×D₄×C₁₉	D₄	1	2	yes	—
99	C₄×D₄×C₁₉	D₄	1	2	yes	—
100	C₄×D₄×C₁₉	D₄	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
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	2	yes	—
113	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
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	4	no	—
119	C₁₉×#101	—	4	2	no	—
120	C₁₉×#100	—	2	2	no	—
121	C₁₉×#100	—	2	2	no	—
122	C₁₉×#100	—	2	2	no	—
123	C₁₉×#100	—	2	4	no	—
124	C₁₉×#100	—	4	2	no	—
125	C₁₉×#100	D₄	1	4	yes	complemented
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	—	2	2	no	—
133	C₂⁴×C₁₉	—	2	2	no	—
134	C₂⁴×C₁₉	—	2	4	no	—
135	C₂⁴×C₁₉	—	4	2	no	—
136	C₂⁴×C₁₉	—	4	4	no	—
137	C₂⁴×C₁₉	—	8	2	no	—
138	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
140	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
142	#41×C₁₉	—	4	4	no	—
143	#41×C₁₉	—	4	4	no	—
144	#41×C₁₉	—	4	4	no	—
145	#41×C₁₉	—	4	4	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	4	no	—
151	C₂×D₄×C₁₉	—	2	4	no	—
152	C₂×D₄×C₁₉	—	2	4	no	—
153	C₂×D₄×C₁₉	—	2	4	no	—
154	C₂×D₄×C₁₉	—	2	4	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	4	4	no	—
162	C₂×D₄×C₁₉	—	4	4	no	—
163	C₂×D₄×C₁₉	—	4	4	no	—
164	C₂×D₄×C₁₉	—	4	4	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	4	2	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	8	2	no	—
169	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
170	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
171	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₂×D₄×C₁₉	#41	1	2	yes	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	4	no	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	4	2	no	—
185	C₂²×C₄×C₁₉	—	8	2	no	—
186	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
190	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
197	M₁₆×C₁₉	—	2	2	no	—
198	M₁₆×C₁₉	—	2	2	no	—
199	M₁₆×C₁₉	—	2	2	no	—
200	M₁₆×C₁₉	—	2	2	no	—
201	M₁₆×C₁₉	—	2	2	no	—
202	M₁₆×C₁₉	—	2	2	no	—
203	M₁₆×C₁₉	—	2	2	no	—
204	M₁₆×C₁₉	—	4	4	no	—
205	M₁₆×C₁₉	—	4	4	no	—
206	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
207	C₂×C₈×C₁₉	—	2	2	no	—
208	C₂×C₈×C₁₉	—	2	2	no	—
209	C₂×C₈×C₁₉	—	2	2	no	—
210	C₂×C₈×C₁₉	—	2	2	no	—
211	C₂×C₈×C₁₉	—	4	4	no	—
212	C₂×C₈×C₁₉	—	4	4	no	—
213	C₄⋊C₄×C₁₉	—	2	4	no	—
214	C₄⋊C₄×C₁₉	—	2	2	no	—
215	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
216	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
226	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
228	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
229	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
230	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
231	C₄²×C₁₉	C₂×D₄	1	2	yes	—
232	C₄²×C₁₉	C₂×D₄	1	2	yes	—
233	#22408	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	1	no	—
237	C₂³×C₁₉	—	2	2	no	—
238	C₂³×C₁₉	—	2	2	no	—
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	2	2	no	—
243	C₂³×C₁₉	—	2	2	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	4	no	—
248	C₂³×C₁₉	—	4	4	no	—
249	C₂³×C₁₉	—	4	2	no	—
250	C₂³×C₁₉	—	4	2	no	—
251	C₂³×C₁₉	—	4	4	no	—
252	C₂³×C₁₉	—	4	2	no	—
253	C₂³×C₁₉	—	4	2	no	—
254	C₂³×C₁₉	—	4	4	no	—
255	C₂³×C₁₉	—	8	2	no	—
256	C₂³×C₁₉	—	8	2	no	—
257	C₂³×C₁₉	—	8	8	no	—
258	C₂³×C₁₉	—	8	8	no	—
259	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂³×C₁₉	C₄×D₄	1	4	yes	—
263	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
264	Q₈×C₁₉	—	4	2	no	—
265	Q₈×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	2	4	no	—
267	D₄×C₁₉	—	2	4	no	—
268	D₄×C₁₉	—	2	4	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	4	8	no	—
271	D₄×C₁₉	—	4	8	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	2	no	—
274	D₄×C₁₉	—	8	4	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	4	no	—
294	C₂×C₄×C₁₉	—	4	4	no	—
295	C₂×C₄×C₁₉	—	4	2	no	—
296	C₂×C₄×C₁₉	—	8	2	no	—
297	C₂×C₄×C₁₉	—	8	2	no	—
298	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
308	C₈×C₁₉	—	2	4	no	—
309	C₈×C₁₉	—	4	2	no	—
310	C₈×C₁₉	—	4	2	no	—
311	C₈×C₁₉	—	4	2	no	—
312	C₂×#546	C₂×C₁₉	1	1	yes	characteristic
313	D₄×M₁₆	C₂×C₁₉	1	2	yes	complemented
314	C₂×#413	C₂×C₁₉	1	1	yes	characteristic, complemented
315	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1967	C₂×C₁₉	1	2	yes	complemented
317	#1901	C₂×C₁₉	1	2	yes	complemented
318	#1900	C₂×C₁₉	1	2	yes	complemented
319	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#1785	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
322	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂²×C₁₉	—	2	1	no	—
324	C₂²×C₁₉	—	2	1	no	—
325	C₂²×C₁₉	—	2	1	no	—
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	2	2	no	—
328	C₂²×C₁₉	—	2	1	no	—
329	C₂²×C₁₉	—	2	4	no	—
330	C₂²×C₁₉	—	2	2	no	—
331	C₂²×C₁₉	—	2	1	no	—
332	C₂²×C₁₉	—	2	2	no	—
333	C₂²×C₁₉	—	2	1	no	—
334	C₂²×C₁₉	—	4	2	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	4	4	no	—
337	C₂²×C₁₉	—	4	4	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	4	2	no	—
341	C₂²×C₁₉	—	4	2	no	—
342	C₂²×C₁₉	—	4	2	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	—	8	8	no	—
346	C₂²×C₁₉	—	8	2	no	—
347	C₂²×C₁₉	—	8	2	no	—
348	C₂²×C₁₉	—	8	8	no	—
349	C₂²×C₁₉	#413	1	2	yes	complemented
350	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
351	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
352	C₂²×C₁₉	#518	1	1	yes	characteristic
353	C₄×C₁₉	—	2	1	no	—
354	C₄×C₁₉	—	2	1	no	—
355	C₄×C₁₉	—	2	2	no	—
356	C₄×C₁₉	—	2	2	no	—
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	2	1	no	—
359	C₄×C₁₉	—	4	2	no	—
360	C₄×C₁₉	—	4	2	no	—
361	C₄×C₁₉	D₄²	1	2	yes	—
362	C₄×C₁₉	#546	1	2	yes	—
363	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
364	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
365	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
366	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
367	#546	—	2	2	no	—
368	#546	—	2	2	no	—
369	#546	—	2	2	no	—
370	#546	—	2	2	no	—
371	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#123	C₄×C₁₉	1	2	yes	—
373	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#121	C₄×C₁₉	1	2	yes	—
375	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#120	C₄×C₁₉	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
380	#436	—	2	2	no	—
381	#435	—	2	2	no	—
382	#435	—	2	2	no	—
383	C₈×D₄	—	2	2	no	—
384	#423	C₂²×C₁₉	1	2	yes	complemented
385	#413	—	2	4	no	—
386	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
387	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
388	C₂×#100	—	2	4	no	—
389	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×#100	C₂²×C₁₉	1	2	yes	—
392	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#100	C₂²×C₁₉	1	2	yes	—
394	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
395	#407	C₂²×C₁₉	1	2	yes	—
396	#407	C₂²×C₁₉	1	2	yes	complemented
397	C₄×M₁₆	C₂²×C₁₉	1	2	yes	complemented
398	#343	C₂²×C₁₉	1	2	yes	complemented
399	#343	C₂²×C₁₉	1	2	yes	complemented
400	C₂×C₁₉	—	2	1	no	—
401	C₂×C₁₉	—	2	1	no	—
402	C₂×C₁₉	—	2	2	no	—
403	C₂×C₁₉	—	4	1	no	—
404	C₂×C₁₉	—	4	2	no	—
405	C₂×C₁₉	—	4	4	no	—
406	C₂×C₁₉	—	8	2	no	—
407	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
408	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
409	C₂×C₁₉	#2888	1	1	yes	characteristic
410	C₂⁵	C₂×C₄×C₁₉	1	2	yes	—
411	C₂×#41	—	2	2	no	—
412	C₂×#41	—	2	2	no	—
413	C₂×#41	—	2	2	no	—
414	C₂×#41	—	2	2	no	—
415	C₂×#41	—	4	2	no	—
416	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₂²×D₄	—	2	2	no	—
418	C₂²×D₄	—	2	2	no	—
419	C₂²×D₄	—	2	2	no	—
420	C₂²×D₄	—	2	2	no	—
421	C₂²×D₄	—	4	2	no	—
422	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
423	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
424	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
425	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
426	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
428	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
429	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
430	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×M₁₆	—	2	2	no	—
433	C₂×M₁₆	—	2	2	no	—
434	C₂×M₁₆	—	2	4	no	—
435	C₂×M₁₆	—	2	4	no	—
436	C₂×M₁₆	—	4	2	no	—
437	C₂×M₁₆	—	4	2	no	—
438	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
439	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
440	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
441	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
442	C₂²×C₈	—	2	2	no	—
443	C₂²×C₈	—	2	2	no	—
444	#124	—	2	2	no	—
445	#124	—	2	2	no	—
446	#123	—	2	4	no	—
447	#123	—	2	4	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	#121	—	2	2	no	—
451	#121	—	2	2	no	—
452	#121	—	2	4	no	—
453	#121	—	2	4	no	—
454	#120	—	2	4	no	—
455	#120	—	2	4	no	—
456	C₄×D₄	—	2	2	no	—
457	C₄×D₄	—	2	2	no	—
458	C₄×D₄	D₄×C₁₉	1	2	yes	—
459	C₄×D₄	D₄×C₁₉	1	2	yes	—
460	C₄×D₄	D₄×C₁₉	1	2	yes	—
461	C₄×D₄	D₄×C₁₉	1	2	yes	—
462	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
463	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	—	2	2	no	—
466	C₂×C₂²⋊C₄	—	2	2	no	—
467	C₂×C₂²⋊C₄	—	2	2	no	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
477	C₄⋊C₈	—	2	2	no	—
478	C₄⋊C₈	—	2	2	no	—
479	#101	—	2	4	no	—
480	#101	—	4	2	no	—
481	#100	—	2	2	no	—
482	#100	—	2	2	no	—
483	#100	—	2	2	no	—
484	#100	—	2	4	no	—
485	#100	—	4	2	no	—
486	#100	D₄×C₁₉	1	4	yes	complemented
487	C₂²⋊C₈	—	2	2	no	—
488	C₂²⋊C₈	—	2	2	no	—
489	C₂²⋊C₈	—	2	2	no	—
490	C₂²⋊C₈	—	2	2	no	—
491	#97	—	2	2	no	—
492	C₄×C₈	—	2	2	no	—
493	C₁₉	#22408	1	1	yes	characteristic, direct product factor, Sylow
494	C₂⁴	—	2	2	no	—
495	C₂⁴	—	2	2	no	—
496	C₂⁴	—	2	4	no	—
497	C₂⁴	—	4	2	no	—
498	C₂⁴	—	4	4	no	—
499	C₂⁴	—	8	2	no	—
500	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
501	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
502	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
503	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
504	#41	—	4	4	no	—
505	#41	—	4	4	no	—
506	#41	—	4	4	no	—
507	#41	—	4	4	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	4	4	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	2	no	—
528	C₂×D₄	—	4	2	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	—	8	2	no	—
531	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
532	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
533	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
534	C₂×D₄	#41×C₁₉	1	2	yes	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	8	2	no	—
548	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
549	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
550	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
552	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
555	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
556	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
557	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
559	M₁₆	—	2	2	no	—
560	M₁₆	—	2	2	no	—
561	M₁₆	—	2	2	no	—
562	M₁₆	—	2	2	no	—
563	M₁₆	—	2	2	no	—
564	M₁₆	—	2	2	no	—
565	M₁₆	—	2	2	no	—
566	M₁₆	—	4	4	no	—
567	M₁₆	—	4	4	no	—
568	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	—	2	2	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	—	4	4	no	—
574	C₂×C₈	—	4	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
578	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
588	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
589	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
590	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
591	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
592	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
593	C₄²	C₂×D₄×C₁₉	1	2	yes	—
594	C₄²	C₂×D₄×C₁₉	1	2	yes	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	4	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	4	2	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	4	4	no	—
613	C₂³	—	4	2	no	—
614	C₂³	—	4	2	no	—
615	C₂³	—	4	4	no	—
616	C₂³	—	8	2	no	—
617	C₂³	—	8	2	no	—
618	C₂³	—	8	8	no	—
619	C₂³	—	8	8	no	—
620	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
621	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
622	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
623	C₂³	C₄×D₄×C₁₉	1	4	yes	—
624	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
625	Q₈	—	4	2	no	—
626	Q₈	—	4	2	no	—
627	D₄	—	2	4	no	—
628	D₄	—	2	4	no	—
629	D₄	—	2	4	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	8	no	—
632	D₄	—	4	8	no	—
633	D₄	—	4	2	no	—
634	D₄	—	4	2	no	—
635	D₄	—	8	4	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	4	no	—
655	C₂×C₄	—	4	4	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	8	2	no	—
658	C₂×C₄	—	8	2	no	—
659	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
660	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
661	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
662	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
663	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
664	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
665	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
667	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
668	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
669	C₈	—	2	4	no	—
670	C₈	—	4	2	no	—
671	C₈	—	4	2	no	—
672	C₈	—	4	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	8	no	—
696	C₂²	—	8	2	no	—
697	C₂²	—	8	2	no	—
698	C₂²	—	8	8	no	—
699	C₂²	C₁₉×#413	1	2	yes	complemented
700	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
701	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
702	C₂²	C₁₉×#518	1	1	yes	characteristic
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	D₄²×C₁₉	1	2	yes	—
712	C₄	C₁₉×#546	1	2	yes	—
713	C₂	—	2	1	no	—
714	C₂	—	2	1	no	—
715	C₂	—	2	2	no	—
716	C₂	—	4	1	no	—
717	C₂	—	4	2	no	—
718	C₂	—	4	4	no	—
719	C₂	—	8	2	no	—
720	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
721	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
722	C₂	C₁₉×#2888	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×#546	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×#100	C₂	semidirect
5. C₁₉×#1967	C₂	semidirect
6. C₁₉×#1901	C₂	semidirect
7. C₁₉×#1900	C₂	semidirect
8. C₁₉×#1800	C₂	semidirect
9. C₁₉×#1785	C₂	semidirect
10. C₁₉×#1783	C₂	semidirect
11. C₄×C₁₉×#100	C₂	semidirect
15. C₂²×M₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#423	C₂²	semidirect
35. C₂×C₁₉×#101	C₂²	semidirect
36. C₂×C₁₉×#101	C₂²	semidirect
45. C₁₉×#407	C₂²	semidirect
46. C₄×M₁₆×C₁₉	C₂²	semidirect
47. C₁₉×#343	C₂²	semidirect
48. C₁₉×#343	C₂²	semidirect
125. C₁₉×#100	D₄	semidirect
233. #22408	C₁₉	direct (N × H)
313. D₄×M₁₆	C₂×C₁₉	semidirect
314. C₂×#413	C₂×C₁₉	semidirect
315. C₂²×#100	C₂×C₁₉	semidirect
316. #1967	C₂×C₁₉	semidirect
317. #1901	C₂×C₁₉	semidirect
318. #1900	C₂×C₁₉	semidirect
319. #1800	C₂×C₁₉	semidirect
320. #1785	C₂×C₁₉	semidirect
321. #1783	C₂×C₁₉	semidirect
322. C₄×#100	C₂×C₁₉	semidirect
349. C₂²×C₁₉	#413	semidirect
366. C₂²×M₁₆	C₂²×C₁₉	semidirect
384. #423	C₂²×C₁₉	semidirect
386. C₂×#101	C₂²×C₁₉	semidirect
387. C₂×#101	C₂²×C₁₉	semidirect
396. #407	C₂²×C₁₉	semidirect
397. C₄×M₁₆	C₂²×C₁₉	semidirect
398. #343	C₂²×C₁₉	semidirect
399. #343	C₂²×C₁₉	semidirect
486. #100	D₄×C₁₉	semidirect
493. C₁₉	#22408	direct (N × H)
699. 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×#546	2
D₄×M₁₆×C₁₉	2
C₂×C₁₉×#413	2
C₂²×C₁₉×#100	2
C₁₉×#1967	2
C₁₉×#1901	2
C₁₉×#1900	2
C₁₉×#1800	2
C₁₉×#1785	2
C₁₉×#1783	2
C₄×C₁₉×#100	2
#22408	19

Subgroups — C19×#22408 #18028367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22408 #18028367