Subgroups — C₁₉×#11001 #18016960

Order 4864.

1306 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#416	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₉	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#537	C₄	1	4	yes	complemented
10	C₁₉×#536	—	2	2	no	—
11	C₁₉×#535	—	2	2	no	—
12	C₁₉×#534	—	2	2	no	—
13	C₁₉×#532	—	2	2	no	—
14	C₁₉×#525	—	2	4	no	—
15	C₂×C₁₉×#117	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#421	—	2	4	no	—
18	C₁₉×#421	—	2	4	no	—
19	C₂×C₁₉×#104	—	2	4	no	—
20	C₁₉×#416	—	2	4	no	—
21	C₁₉×#416	—	2	4	no	—
22	C₂×C₁₉×#103	—	2	2	no	—
23	C₂×C₁₉×#102	—	2	2	no	—
24	C₁₉×#342	—	2	2	no	—
25	C₁₉×#336	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
37	C₂×#41×C₁₉	D₄	1	4	yes	—
38	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	D₄	1	2	yes	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	D₄	1	2	yes	complemented
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₂²×C₈×C₁₉	D₄	1	2	yes	complemented
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#124	—	2	4	no	—
56	C₁₉×#123	—	2	8	no	—
57	C₁₉×C₂²⋊Q₈	—	2	8	no	—
58	C₁₉×#121	—	2	8	no	—
59	C₁₉×#121	—	2	8	no	—
60	C₁₉×#120	—	2	8	no	—
61	C₄×D₄×C₁₉	—	2	8	no	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	—	2	2	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	D₄	1	4	yes	complemented
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
72	C₂×C₄²×C₁₉	—	2	2	no	—
73	C₂×C₄²×C₁₉	D₄	1	2	yes	—
74	C₁₉×#104	—	2	16	no	—
75	C₁₉×#103	—	2	8	no	—
76	C₁₉×#102	—	2	8	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	—	2	4	no	—
82	#41×C₁₉	—	2	4	no	—
83	#41×C₁₉	—	2	4	no	—
84	#41×C₁₉	—	2	4	no	—
85	#41×C₁₉	—	2	4	no	—
86	#41×C₁₉	—	2	4	no	—
87	#41×C₁₉	—	4	2	no	—
88	#41×C₁₉	—	4	2	no	—
89	#41×C₁₉	—	4	2	no	—
90	#41×C₁₉	—	4	2	no	—
91	#41×C₁₉	—	4	2	no	—
92	#41×C₁₉	—	4	2	no	—
93	#41×C₁₉	—	4	2	no	—
94	#41×C₁₉	—	4	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	8	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	#41	1	2	yes	—
133	M₁₆×C₁₉	—	2	4	no	—
134	M₁₆×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	2	4	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	4	1	no	—
139	C₂×C₈×C₁₉	—	4	1	no	—
140	C₂×C₈×C₁₉	—	4	2	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	—	2	8	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	4	no	—
146	C₄⋊C₄×C₁₉	—	4	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	16	no	—
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	2	4	no	—
154	C₄²×C₁₉	—	4	2	no	—
155	#11001	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	8	4	no	—
161	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂³×C₁₉	#120	1	2	yes	—
163	C₂³×C₁₉	#121	1	2	yes	—
164	C₂³×C₁₉	#124	1	1	yes	characteristic
165	C₂³×C₁₉	#127	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	4	no	—
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	2	4	no	—
171	D₄×C₁₉	—	2	4	no	—
172	D₄×C₁₉	—	4	4	no	—
173	D₄×C₁₉	—	4	4	no	—
174	D₄×C₁₉	—	4	4	no	—
175	D₄×C₁₉	—	4	4	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	8	8	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	8	4	no	—
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₉	#120	1	2	yes	—
195	C₂×C₄×C₁₉	#120	1	2	yes	—
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#121	1	2	yes	—
199	C₂×C₄×C₁₉	#121	1	2	yes	—
200	C₂×C₄×C₁₉	#121	1	2	yes	—
201	C₂×C₄×C₁₉	#121	1	2	yes	—
202	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#123	1	2	yes	—
205	C₂×C₄×C₁₉	#123	1	2	yes	—
206	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	2	no	—
210	#3449	C₂×C₁₉	1	1	yes	characteristic
211	C₂×#421	C₂×C₁₉	1	2	yes	complemented
212	C₂×#416	C₂×C₁₉	1	2	yes	complemented
213	#1740	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1729	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	—	4	8	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	8	4	no	—
223	C₂²×C₁₉	—	8	4	no	—
224	C₂²×C₁₉	#379	1	1	yes	characteristic
225	C₂²×C₁₉	#390	1	1	yes	characteristic
226	C₂²×C₁₉	#390	1	1	yes	characteristic
227	C₂²×C₁₉	#392	1	2	yes	—
228	C₂²×C₁₉	#394	1	2	yes	—
229	C₄×C₁₉	—	4	4	no	—
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	—	8	4	no	—
232	C₄×C₁₉	#386	1	2	yes	—
233	C₄×C₁₉	#386	1	2	yes	—
234	C₄×C₁₉	#392	1	1	yes	characteristic
235	C₄×C₁₉	#392	1	1	yes	characteristic
236	C₄×C₁₉	#394	1	1	yes	characteristic
237	C₄×C₁₉	#394	1	1	yes	characteristic
238	C₂²×#41	C₂²×C₁₉	1	2	yes	—
239	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
240	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
241	#537	C₄×C₁₉	1	4	yes	complemented
242	#536	—	2	2	no	—
243	#535	—	2	2	no	—
244	#534	—	2	2	no	—
245	#532	—	2	2	no	—
246	#525	—	2	4	no	—
247	C₂×#117	C₂²×C₁₉	1	2	yes	—
248	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
249	#421	—	2	4	no	—
250	#421	—	2	4	no	—
251	C₂×#104	—	2	4	no	—
252	#416	—	2	4	no	—
253	#416	—	2	4	no	—
254	C₂×#103	—	2	2	no	—
255	C₂×#102	—	2	2	no	—
256	#342	—	2	2	no	—
257	#336	—	2	2	no	—
258	C₂×C₁₉	—	2	2	no	—
259	C₂×C₁₉	—	2	2	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	8	4	no	—
263	C₂×C₁₉	#1438	1	1	yes	characteristic
264	C₂×C₁₉	#1794	1	2	yes	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
276	C₂×#41	D₄×C₁₉	1	4	yes	—
277	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	D₄×C₁₉	1	2	yes	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	D₄×C₁₉	1	2	yes	complemented
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	D₄×C₁₉	1	2	yes	complemented
292	C₄⋊Q₈	—	2	2	no	—
293	#127	—	2	2	no	—
294	#124	—	2	4	no	—
295	#123	—	2	8	no	—
296	C₂²⋊Q₈	—	2	8	no	—
297	#121	—	2	8	no	—
298	#121	—	2	8	no	—
299	#120	—	2	8	no	—
300	C₄×D₄	—	2	8	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	#117	D₄×C₁₉	1	4	yes	complemented
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	D₄×C₁₉	1	2	yes	—
313	#104	—	2	16	no	—
314	#103	—	2	8	no	—
315	#102	—	2	8	no	—
316	C₁₉	#11001	1	1	yes	characteristic, direct product factor, Sylow
317	C₂⁴	—	2	2	no	—
318	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	4	2	no	—
334	#41	—	4	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	#41×C₁₉	1	2	yes	—
373	M₁₆	—	2	4	no	—
374	M₁₆	—	4	2	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	1	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	—	4	1	no	—
382	C₂×C₈	—	4	1	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	2	16	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	4	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	8	4	no	—
400	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
401	C₂³	C₁₉×#120	1	2	yes	—
402	C₂³	C₁₉×#121	1	2	yes	—
403	C₂³	C₁₉×#124	1	1	yes	characteristic
404	C₂³	C₁₉×#127	1	1	yes	characteristic
405	Q₈	—	2	4	no	—
406	Q₈	—	2	4	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	4	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	8	4	no	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
430	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
433	C₂×C₄	C₁₉×#120	1	2	yes	—
434	C₂×C₄	C₁₉×#120	1	2	yes	—
435	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
436	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
437	C₂×C₄	C₁₉×#121	1	2	yes	—
438	C₂×C₄	C₁₉×#121	1	2	yes	—
439	C₂×C₄	C₁₉×#121	1	2	yes	—
440	C₂×C₄	C₁₉×#121	1	2	yes	—
441	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
443	C₂×C₄	C₁₉×#123	1	2	yes	—
444	C₂×C₄	C₁₉×#123	1	2	yes	—
445	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
446	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	8	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	8	4	no	—
458	C₂²	C₁₉×#379	1	1	yes	characteristic
459	C₂²	C₁₉×#390	1	1	yes	characteristic
460	C₂²	C₁₉×#390	1	1	yes	characteristic
461	C₂²	C₁₉×#392	1	2	yes	—
462	C₂²	C₁₉×#394	1	2	yes	—
463	C₄	—	4	4	no	—
464	C₄	—	4	4	no	—
465	C₄	—	8	4	no	—
466	C₄	C₁₉×#386	1	2	yes	—
467	C₄	C₁₉×#386	1	2	yes	—
468	C₄	C₁₉×#392	1	1	yes	characteristic
469	C₄	C₁₉×#392	1	1	yes	characteristic
470	C₄	C₁₉×#394	1	1	yes	characteristic
471	C₄	C₁₉×#394	1	1	yes	characteristic
472	C₂	—	2	2	no	—
473	C₂	—	2	2	no	—
474	C₂	—	2	1	no	—
475	C₂	—	2	1	no	—
476	C₂	—	8	4	no	—
477	C₂	C₁₉×#1438	1	1	yes	characteristic
478	C₂	C₁₉×#1794	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#379
prime radical	C₁₉×#3449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#421	C₂	semidirect
3. C₂×C₁₉×#416	C₂	semidirect
4. C₁₉×#1740	C₂	semidirect
5. C₁₉×#1729	C₂	semidirect
9. C₁₉×#537	C₄	semidirect
46. C₂×M₁₆×C₁₉	D₄	semidirect
52. C₂²×C₈×C₁₉	D₄	semidirect
67. C₁₉×#117	D₄	semidirect
155. #11001	C₁₉	direct (N × H)
211. C₂×#421	C₂×C₁₉	semidirect
212. C₂×#416	C₂×C₁₉	semidirect
213. #1740	C₂×C₁₉	semidirect
214. #1729	C₂×C₁₉	semidirect
241. #537	C₄×C₁₉	semidirect
285. C₂×M₁₆	D₄×C₁₉	semidirect
291. C₂²×C₈	D₄×C₁₉	semidirect
306. #117	D₄×C₁₉	semidirect
316. C₁₉	#11001	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3449	2
C₂×C₁₉×#421	2
C₂×C₁₉×#416	2
C₁₉×#1740	2
C₁₉×#1729	2
#11001	19

Subgroups — C19×#11001 #18016960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11001 #18016960