Subgroups — C₁₉×#13080 #18019039

Order 4864.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2405	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#352	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1781	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1390	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	—	2	1	no	—
8	C₂×C₁₉×#123	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₉×#100	—	2	4	no	—
12	C₂×C₁₉×#100	—	2	1	no	—
13	C₂×C₁₉×#100	C₂²	1	2	yes	—
14	C₂×C₁₉×#99	—	2	1	no	—
15	C₂×C₁₉×#99	C₂²	1	2	yes	—
16	C₁₉×#394	—	2	1	no	—
17	C₁₉×#394	—	2	1	no	—
18	C₁₉×#386	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#386	C₂²	1	1	yes	characteristic
20	C₁₉×#385	—	2	1	no	—
21	C₁₉×#379	—	2	1	no	—
22	C₁₉×#379	—	2	1	no	—
23	C₁₉×#379	C₄	1	1	yes	characteristic, complemented
24	C₁₉×#352	—	2	4	no	—
25	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	4	2	no	—
30	C₂²×D₄×C₁₉	—	4	1	no	—
31	C₂²×D₄×C₁₉	—	4	1	no	—
32	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×M₁₆×C₁₉	—	2	4	no	—
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₂×M₁₆×C₁₉	—	4	1	no	—
42	C₂×M₁₆×C₁₉	—	4	2	no	—
43	C₂²×C₈×C₁₉	—	4	1	no	—
44	C₁₉×#123	—	2	2	no	—
45	C₁₉×#123	—	2	2	no	—
46	C₁₉×#123	—	4	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₁₉×#100	—	2	4	no	—
65	C₁₉×#100	—	2	2	no	—
66	C₁₉×#100	D₄	1	4	yes	—
67	C₁₉×#99	—	2	2	no	—
68	C₁₉×#99	—	2	2	no	—
69	C₁₉×#99	—	4	2	no	—
70	C₁₉×#95	—	2	1	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₂⁴×C₁₉	—	2	1	no	—
73	C₂⁴×C₁₉	—	2	1	no	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	—	4	1	no	—
79	C₂⁴×C₁₉	—	4	1	no	—
80	C₂⁴×C₁₉	—	4	2	no	—
81	C₂⁴×C₁₉	—	4	2	no	—
82	C₂⁴×C₁₉	—	8	1	no	—
83	C₂⁴×C₁₉	—	8	1	no	—
84	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	1	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	4	1	no	—
101	C₂×D₄×C₁₉	—	4	4	no	—
102	C₂×D₄×C₁₉	—	4	4	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	—	4	4	no	—
105	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	8	1	no	—
122	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	M₁₆×C₁₉	—	2	4	no	—
125	M₁₆×C₁₉	—	4	4	no	—
126	M₁₆×C₁₉	—	4	2	no	—
127	C₂×C₈×C₁₉	—	4	4	no	—
128	C₂×C₈×C₁₉	—	4	2	no	—
129	C₄⋊C₄×C₁₉	—	4	2	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	2	2	no	—
133	C₂²⋊C₄×C₁₉	—	4	2	no	—
134	C₂²⋊C₄×C₁₉	—	4	2	no	—
135	C₂²⋊C₄×C₁₉	—	4	2	no	—
136	C₂²⋊C₄×C₁₉	—	4	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₂²⋊C₄×C₁₉	—	4	2	no	—
141	C₂²⋊C₄×C₁₉	—	4	2	no	—
142	C₂²⋊C₄×C₁₉	—	8	1	no	—
143	C₂²⋊C₄×C₁₉	—	8	1	no	—
144	C₂²⋊C₄×C₁₉	—	8	1	no	—
145	C₂²⋊C₄×C₁₉	—	8	2	no	—
146	C₂²⋊C₄×C₁₉	—	8	2	no	—
147	#13080	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	2	1	no	—
153	C₂³×C₁₉	—	2	1	no	—
154	C₂³×C₁₉	—	2	1	no	—
155	C₂³×C₁₉	—	2	1	no	—
156	C₂³×C₁₉	—	2	1	no	—
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	—	2	1	no	—
159	C₂³×C₁₉	—	2	1	no	—
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	8	1	no	—
179	C₂³×C₁₉	—	8	1	no	—
180	C₂³×C₁₉	—	8	1	no	—
181	C₂³×C₁₉	—	8	1	no	—
182	C₂³×C₁₉	—	8	4	no	—
183	C₂³×C₁₉	—	8	4	no	—
184	C₂³×C₁₉	—	8	4	no	—
185	C₂³×C₁₉	—	8	4	no	—
186	C₂³×C₁₉	#99	1	1	yes	characteristic
187	C₂³×C₁₉	#99	1	1	yes	characteristic
188	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₄×D₄	1	2	yes	—
190	C₂³×C₁₉	#121	1	2	yes	—
191	D₄×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	4	no	—
194	D₄×C₁₉	—	4	4	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	8	2	no	—
218	C₂×C₄×C₁₉	—	8	2	no	—
219	C₂×C₄×C₁₉	—	8	2	no	—
220	C₂×C₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	#99	1	2	yes	—
223	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
225	C₈×C₁₉	—	4	4	no	—
226	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic
227	#2405	C₂×C₁₉	1	1	yes	characteristic
228	C₂×#352	C₂×C₁₉	1	2	yes	complemented
229	#1781	C₂×C₁₉	1	1	yes	characteristic
230	#1390	C₂×C₁₉	1	2	yes	complemented
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	1	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	4	no	—
258	C₂²×C₁₉	—	8	4	no	—
259	C₂²×C₁₉	—	8	1	no	—
260	C₂²×C₁₉	—	8	1	no	—
261	C₂²×C₁₉	—	8	1	no	—
262	C₂²×C₁₉	—	8	4	no	—
263	C₂²×C₁₉	—	8	4	no	—
264	C₂²×C₁₉	#352	1	2	yes	complemented
265	C₂²×C₁₉	#386	1	1	yes	characteristic
266	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	8	1	no	—
272	C₄×C₁₉	—	8	1	no	—
273	C₄×C₁₉	—	8	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	16	2	no	—
276	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₂²×M₁₆	—	2	1	no	—
278	C₂×#123	C₄×C₁₉	1	1	yes	characteristic, complemented
279	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
281	C₂×#100	—	2	1	no	—
282	C₂×#100	—	2	4	no	—
283	C₂×#100	C₂²×C₁₉	1	2	yes	—
284	C₂×#99	—	2	1	no	—
285	C₂×#99	C₂²×C₁₉	1	2	yes	—
286	#394	—	2	1	no	—
287	#394	—	2	1	no	—
288	#386	C₄×C₁₉	1	1	yes	characteristic, complemented
289	#386	C₂²×C₁₉	1	1	yes	characteristic
290	#385	—	2	1	no	—
291	#379	—	2	1	no	—
292	#379	—	2	1	no	—
293	#379	C₄×C₁₉	1	1	yes	characteristic, complemented
294	#352	—	2	4	no	—
295	C₂×C₁₉	—	2	1	no	—
296	C₂×C₁₉	—	2	1	no	—
297	C₂×C₁₉	—	2	2	no	—
298	C₂×C₁₉	—	4	2	no	—
299	C₂×C₁₉	—	4	1	no	—
300	C₂×C₁₉	—	4	2	no	—
301	C₂×C₁₉	—	8	1	no	—
302	C₂×C₁₉	—	8	1	no	—
303	C₂×C₁₉	#1898	1	1	yes	characteristic
304	C₂×C₁₉	C₂×#352	1	1	yes	characteristic
305	C₂×C₁₉	#2121	1	1	yes	characteristic
306	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
307	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	—	4	2	no	—
311	C₂²×D₄	—	4	1	no	—
312	C₂²×D₄	—	4	1	no	—
313	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
314	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
315	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
317	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
318	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
319	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
320	C₂×M₁₆	—	2	4	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	4	1	no	—
323	C₂×M₁₆	—	4	2	no	—
324	C₂²×C₈	—	4	1	no	—
325	#123	—	2	2	no	—
326	#123	—	2	2	no	—
327	#123	—	4	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	4	1	no	—
340	C₂×C₂²⋊C₄	—	4	1	no	—
341	C₂×C₂²⋊C₄	—	4	1	no	—
342	C₂×C₂²⋊C₄	—	4	1	no	—
343	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
345	#100	—	2	4	no	—
346	#100	—	2	2	no	—
347	#100	D₄×C₁₉	1	4	yes	—
348	#99	—	2	2	no	—
349	#99	—	2	2	no	—
350	#99	—	4	2	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	C₁₉	#13080	1	1	yes	characteristic, direct product factor, Sylow
354	C₂⁴	—	2	1	no	—
355	C₂⁴	—	2	1	no	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	—	2	1	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	4	1	no	—
361	C₂⁴	—	4	1	no	—
362	C₂⁴	—	4	2	no	—
363	C₂⁴	—	4	2	no	—
364	C₂⁴	—	8	1	no	—
365	C₂⁴	—	8	1	no	—
366	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
367	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
368	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
369	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
370	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
388	C₂×D₄	#41×C₁₉	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	8	1	no	—
404	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	M₁₆	—	2	4	no	—
407	M₁₆	—	4	4	no	—
408	M₁₆	—	4	2	no	—
409	C₂×C₈	—	4	4	no	—
410	C₂×C₈	—	4	2	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	—	4	1	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	8	1	no	—
425	C₂²⋊C₄	—	8	1	no	—
426	C₂²⋊C₄	—	8	1	no	—
427	C₂²⋊C₄	—	8	2	no	—
428	C₂²⋊C₄	—	8	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	8	1	no	—
460	C₂³	—	8	1	no	—
461	C₂³	—	8	1	no	—
462	C₂³	—	8	1	no	—
463	C₂³	—	8	4	no	—
464	C₂³	—	8	4	no	—
465	C₂³	—	8	4	no	—
466	C₂³	—	8	4	no	—
467	C₂³	C₁₉×#99	1	1	yes	characteristic
468	C₂³	C₁₉×#99	1	1	yes	characteristic
469	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
470	C₂³	C₄×D₄×C₁₉	1	2	yes	—
471	C₂³	C₁₉×#121	1	2	yes	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	—	8	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	C₁₉×#99	1	2	yes	—
504	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
506	C₈	—	4	4	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	4	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	4	no	—
539	C₂²	—	8	4	no	—
540	C₂²	C₁₉×#352	1	2	yes	complemented
541	C₂²	C₁₉×#386	1	1	yes	characteristic
542	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
543	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	16	2	no	—
552	C₂	—	2	1	no	—
553	C₂	—	2	1	no	—
554	C₂	—	2	2	no	—
555	C₂	—	4	2	no	—
556	C₂	—	4	1	no	—
557	C₂	—	4	2	no	—
558	C₂	—	8	1	no	—
559	C₂	—	8	1	no	—
560	C₂	C₁₉×#1898	1	1	yes	characteristic
561	C₂	C₂×C₁₉×#352	1	1	yes	characteristic
562	C₂	C₁₉×#2121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂³×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#352	C₂	semidirect
5. C₁₉×#1390	C₂	semidirect
8. C₂×C₁₉×#123	C₄	semidirect
10. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
18. C₁₉×#386	C₄	semidirect
23. C₁₉×#379	C₄	semidirect
147. #13080	C₁₉	direct (N × H)
228. C₂×#352	C₂×C₁₉	semidirect
230. #1390	C₂×C₁₉	semidirect
264. C₂²×C₁₉	#352	semidirect
278. C₂×#123	C₄×C₁₉	semidirect
280. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
288. #386	C₄×C₁₉	semidirect
293. #379	C₄×C₁₉	semidirect
353. C₁₉	#13080	direct (N × H)
540. C₂²	C₁₉×#352	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#100	2
C₁₉×#2405	2
C₂×C₁₉×#352	2
C₁₉×#1781	2
C₁₉×#1390	2
#13080	19

Subgroups — C19×#13080 #18019039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13080 #18019039