Subgroups — C₁₉×#8430 #18014389

Order 4864.

760 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#559	—	2	2	no	—
9	C₁₉×#556	—	2	1	no	—
10	C₁₉×#555	C₄	1	2	yes	complemented
11	C₁₉×#553	—	2	2	no	—
12	C₁₉×#550	—	2	1	no	—
13	C₁₉×#547	C₄	1	2	yes	complemented
14	C₁₉×#538	—	2	2	no	—
15	C₁₉×#535	—	2	1	no	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#525	—	2	2	no	—
19	C₁₉×#520	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	—	2	1	no	—
25	C₁₉×#382	C₂²	1	1	yes	characteristic
26	C₁₉×#340	—	2	1	no	—
27	C₁₉×#332	—	2	1	no	—
28	C₁₉×#331	—	2	1	no	—
29	C₁₉×#328	—	2	2	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₁₉×Q₈⋊C₈	—	2	2	no	—
32	C₁₉×D₄⋊C₈	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
39	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
40	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
41	C₁₉×#127	—	2	2	no	—
42	C₁₉×#127	D₄	1	1	yes	characteristic
43	C₁₉×#126	—	2	4	no	—
44	C₁₉×#125	—	2	1	no	—
45	C₁₉×#124	—	2	2	no	—
46	C₁₉×#124	—	2	4	no	—
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#123	—	2	4	no	—
49	C₁₉×#123	—	2	4	no	—
50	C₁₉×C₂²⋊Q₈	—	2	1	no	—
51	C₁₉×C₂²⋊Q₈	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
53	C₁₉×#121	—	2	4	no	—
54	C₁₉×#121	—	2	2	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	—	2	1	no	—
58	C₁₉×#121	D₄	1	2	yes	—
59	C₁₉×#120	—	2	4	no	—
60	C₄×Q₈×C₁₉	—	2	2	no	—
61	C₄×Q₈×C₁₉	—	2	1	no	—
62	C₄×Q₈×C₁₉	D₄	1	2	yes	—
63	C₄×D₄×C₁₉	—	2	4	no	—
64	C₄×D₄×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	4	no	—
66	C₄×D₄×C₁₉	—	2	1	no	—
67	C₄×D₄×C₁₉	—	2	1	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₄×D₄×C₁₉	D₄	1	2	yes	—
72	C₁₉×#117	—	2	1	no	—
73	C₁₉×#117	—	2	2	no	—
74	C₁₉×#117	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	—	2	1	no	—
82	C₁₉×C₄⋊C₈	—	2	1	no	—
83	C₁₉×C₄⋊C₈	—	2	1	no	—
84	C₁₉×#102	—	4	2	no	—
85	C₁₉×C₂²⋊C₈	—	2	1	no	—
86	C₁₉×C₂²⋊C₈	—	2	1	no	—
87	C₄×C₈×C₁₉	—	2	1	no	—
88	C₄×C₈×C₁₉	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	#41×C₁₉	—	4	1	no	—
93	#41×C₁₉	—	4	1	no	—
94	#41×C₁₉	—	4	1	no	—
95	#41×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	8	4	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
111	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	8	2	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₂×C₈×C₁₉	—	4	1	no	—
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
139	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₄²×C₁₉	—	2	4	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
154	#8430	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	8	1	no	—
160	C₂³×C₁₉	—	8	1	no	—
161	C₂³×C₁₉	#120	1	1	yes	characteristic
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	4	2	no	—
164	Q₈×C₁₉	—	4	1	no	—
165	Q₈×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	2	2	no	—
167	D₄×C₁₉	—	2	2	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	8	1	no	—
176	D₄×C₁₉	—	8	4	no	—
177	D₄×C₁₉	—	8	4	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	8	2	no	—
188	C₂×C₄×C₁₉	—	8	1	no	—
189	C₂×C₄×C₁₉	—	8	4	no	—
190	C₂×C₄×C₁₉	—	8	1	no	—
191	C₂×C₄×C₁₉	—	8	1	no	—
192	C₂×C₄×C₁₉	—	8	1	no	—
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
201	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
203	C₈×C₁₉	—	8	1	no	—
204	C₈×C₁₉	—	8	1	no	—
205	C₈×C₁₉	—	8	1	no	—
206	#3506	C₂×C₁₉	1	1	yes	characteristic
207	#1804	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1540	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#1518	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1481	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	8	2	no	—
222	C₂²×C₁₉	—	8	2	no	—
223	C₂²×C₁₉	#379	1	1	yes	characteristic
224	C₂²×C₁₉	#449	1	1	yes	characteristic
225	C₂²×C₁₉	#452	1	1	yes	characteristic
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	16	1	no	—
235	C₄×C₁₉	#416	1	1	yes	characteristic
236	C₄×C₁₉	#417	1	1	yes	characteristic
237	C₄×C₁₉	#449	1	1	yes	characteristic
238	C₄×C₁₉	#452	1	1	yes	characteristic
239	#559	—	2	2	no	—
240	#556	—	2	1	no	—
241	#555	C₄×C₁₉	1	2	yes	complemented
242	#553	—	2	2	no	—
243	#550	—	2	1	no	—
244	#547	C₄×C₁₉	1	2	yes	complemented
245	#538	—	2	2	no	—
246	#535	—	2	1	no	—
247	#533	C₂²×C₁₉	1	1	yes	characteristic
248	#532	C₂²×C₁₉	1	1	yes	characteristic
249	#525	—	2	2	no	—
250	#520	—	2	1	no	—
251	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
252	#431	C₂²×C₁₉	1	1	yes	characteristic
253	#431	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×#102	—	2	1	no	—
256	#382	C₂²×C₁₉	1	1	yes	characteristic
257	#340	—	2	1	no	—
258	#332	—	2	1	no	—
259	#331	—	2	1	no	—
260	#328	—	2	2	no	—
261	#327	—	2	2	no	—
262	Q₈⋊C₈	—	2	2	no	—
263	D₄⋊C₈	—	2	2	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	8	2	no	—
267	C₂×C₁₉	—	8	2	no	—
268	C₂×C₁₉	#1788	1	1	yes	characteristic
269	C₂×C₁₉	#1794	1	1	yes	characteristic
270	C₂×C₁₉	#1795	1	1	yes	characteristic
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	1	no	—
273	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
277	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
278	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
279	#127	—	2	2	no	—
280	#127	D₄×C₁₉	1	1	yes	characteristic
281	#126	—	2	4	no	—
282	#125	—	2	1	no	—
283	#124	—	2	2	no	—
284	#124	—	2	4	no	—
285	#124	—	2	1	no	—
286	#123	—	2	4	no	—
287	#123	—	2	4	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
291	#121	—	2	4	no	—
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	#121	—	2	1	no	—
296	#121	D₄×C₁₉	1	2	yes	—
297	#120	—	2	4	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	D₄×C₁₉	1	2	yes	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
308	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
309	C₄×D₄	D₄×C₁₉	1	2	yes	—
310	#117	—	2	1	no	—
311	#117	—	2	2	no	—
312	#117	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	#102	—	4	2	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	C₁₉	#8430	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	1	no	—
331	#41	—	4	1	no	—
332	#41	—	4	1	no	—
333	#41	—	4	1	no	—
334	#41	—	4	1	no	—
335	#41	—	8	4	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
350	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	8	2	no	—
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
377	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
378	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	C₁₉×#120	1	1	yes	characteristic
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	1	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	8	1	no	—
414	D₄	—	8	4	no	—
415	D₄	—	8	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	8	1	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	—	8	1	no	—
429	C₂×C₄	—	8	1	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
435	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
436	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
437	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
438	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
439	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
441	C₈	—	8	1	no	—
442	C₈	—	8	1	no	—
443	C₈	—	8	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	C₁₉×#379	1	1	yes	characteristic
455	C₂²	C₁₉×#449	1	1	yes	characteristic
456	C₂²	C₁₉×#452	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	16	1	no	—
466	C₄	C₁₉×#416	1	1	yes	characteristic
467	C₄	C₁₉×#417	1	1	yes	characteristic
468	C₄	C₁₉×#449	1	1	yes	characteristic
469	C₄	C₁₉×#452	1	1	yes	characteristic
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	—	8	2	no	—
473	C₂	—	8	2	no	—
474	C₂	C₁₉×#1788	1	1	yes	characteristic
475	C₂	C₁₉×#1794	1	1	yes	characteristic
476	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3506	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1804	C₂	semidirect
3. C₁₉×#1540	C₂	semidirect
4. C₁₉×#1518	C₂	semidirect
5. C₁₉×#1517	C₂	semidirect
6. C₁₉×#1481	C₂	semidirect
7. C₁₉×#1478	C₂	semidirect
10. C₁₉×#555	C₄	semidirect
13. C₁₉×#547	C₄	semidirect
154. #8430	C₁₉	direct (N × H)
207. #1804	C₂×C₁₉	semidirect
208. #1540	C₂×C₁₉	semidirect
209. #1518	C₂×C₁₉	semidirect
210. #1517	C₂×C₁₉	semidirect
211. #1481	C₂×C₁₉	semidirect
212. #1478	C₂×C₁₉	semidirect
241. #555	C₄×C₁₉	semidirect
244. #547	C₄×C₁₉	semidirect
329. C₁₉	#8430	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×#3506	2
C₁₉×#1804	2
C₁₉×#1540	2
C₁₉×#1518	2
C₁₉×#1517	2
C₁₉×#1481	2
C₁₉×#1478	2
#8430	19

Subgroups — C19×#8430 #18014389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8430 #18014389