Subgroups — C₁₉×#8349 #18014308

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3493	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1532	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1494	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#556	—	2	2	no	—
7	C₁₉×#555	—	2	2	no	—
8	C₁₉×#553	—	2	2	no	—
9	C₁₉×#552	—	2	2	no	—
10	C₁₉×#544	C₄	1	1	yes	characteristic
11	C₁₉×#538	—	2	1	no	—
12	C₁₉×#538	C₄	1	2	yes	—
13	C₁₉×#537	C₄	1	1	yes	characteristic
14	C₁₉×#529	—	2	1	no	—
15	C₁₉×#529	C₂²	1	2	yes	—
16	C₁₉×#525	—	2	1	no	—
17	C₁₉×#520	—	2	1	no	—
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₁₉×#432	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
21	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#336	—	2	1	no	—
24	C₁₉×#330	—	2	2	no	—
25	C₁₉×#329	—	2	2	no	—
26	C₁₉×Q₈⋊C₈	—	2	2	no	—
27	C₁₉×D₄⋊C₈	—	2	2	no	—
28	C₁₉×#324	—	2	1	no	—
29	C₁₉×#323	—	2	1	no	—
30	C₂×#41×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	2	no	—
35	C₁₉×#126	—	2	2	no	—
36	C₁₉×#126	—	2	2	no	—
37	C₁₉×#126	—	2	2	no	—
38	C₁₉×#126	—	2	2	no	—
39	C₁₉×#125	—	2	1	no	—
40	C₁₉×#125	—	2	2	no	—
41	C₁₉×#125	D₄	1	2	yes	—
42	C₁₉×#124	—	2	1	no	—
43	C₁₉×#124	—	2	2	no	—
44	C₁₉×#124	—	2	2	no	—
45	C₁₉×#124	D₄	1	2	yes	—
46	C₁₉×#123	—	2	2	no	—
47	C₁₉×#123	—	2	2	no	—
48	C₁₉×#123	—	2	2	no	—
49	C₁₉×C₂²⋊Q₈	—	2	1	no	—
50	C₁₉×C₂²⋊Q₈	—	2	1	no	—
51	C₁₉×C₂²⋊Q₈	—	2	1	no	—
52	C₁₉×C₂²⋊Q₈	—	2	2	no	—
53	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
54	C₁₉×#121	—	2	1	no	—
55	C₁₉×#121	—	2	1	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	—	2	2	no	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	1	no	—
60	C₁₉×#121	C₂×C₄	1	2	yes	—
61	C₁₉×#120	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	—	2	1	no	—
64	C₄×Q₈×C₁₉	D₄	1	2	yes	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	—	2	2	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	D₄	1	2	yes	—
72	C₁₉×#117	—	2	2	no	—
73	C₁₉×#117	—	2	2	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₂²⋊C₈	—	2	4	no	—
87	C₁₉×C₂²⋊C₈	—	2	2	no	—
88	C₁₉×#97	—	2	2	no	—
89	C₁₉×#97	—	2	2	no	—
90	C₄×C₈×C₁₉	—	2	2	no	—
91	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	#41×C₁₉	—	4	2	no	—
93	#41×C₁₉	—	4	2	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	1	no	—
102	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	1	no	—
151	C₄²×C₁₉	—	2	1	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	C₄²×C₁₉	C₂×D₄	1	2	yes	—
155	#8349	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	1	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	1	no	—
159	C₂³×C₁₉	—	2	1	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	Q₈×C₁₉	—	4	2	no	—
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	8	1	no	—
166	D₄×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	8	2	no	—
171	D₄×C₁₉	—	8	1	no	—
172	D₄×C₁₉	—	8	2	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	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	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	#104	1	2	yes	—
192	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₁₉	#120	1	2	yes	—
194	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
196	C₈×C₁₉	—	4	2	no	—
197	C₈×C₁₉	—	4	2	no	—
198	C₈×C₁₉	—	8	2	no	—
199	#3493	C₂×C₁₉	1	1	yes	characteristic
200	#1750	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#1532	C₂×C₁₉	1	2	yes	complemented
202	#1494	C₂×C₁₉	1	2	yes	complemented
203	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	#379	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
216	C₂²×C₁₉	#421	1	1	yes	characteristic
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	4	1	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	4	2	no	—
227	#556	—	2	2	no	—
228	#555	—	2	2	no	—
229	#553	—	2	2	no	—
230	#552	—	2	2	no	—
231	#544	C₄×C₁₉	1	1	yes	characteristic
232	#538	—	2	1	no	—
233	#538	C₄×C₁₉	1	2	yes	—
234	#537	C₄×C₁₉	1	1	yes	characteristic
235	#529	—	2	1	no	—
236	#529	C₂²×C₁₉	1	2	yes	—
237	#525	—	2	1	no	—
238	#520	—	2	1	no	—
239	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
240	#432	C₂²×C₁₉	1	2	yes	—
241	C₂×C₂²⋊C₈	—	2	1	no	—
242	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
244	#336	—	2	1	no	—
245	#330	—	2	2	no	—
246	#329	—	2	2	no	—
247	Q₈⋊C₈	—	2	2	no	—
248	D₄⋊C₈	—	2	2	no	—
249	#324	—	2	1	no	—
250	#323	—	2	1	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	8	2	no	—
254	C₂×C₁₉	—	8	1	no	—
255	C₂×C₁₉	#1789	1	1	yes	characteristic
256	C₂×C₁₉	#1791	1	1	yes	characteristic
257	C₂×C₁₉	#1794	1	1	yes	characteristic
258	C₂×#41	—	2	1	no	—
259	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	#126	—	2	2	no	—
264	#126	—	2	2	no	—
265	#126	—	2	2	no	—
266	#126	—	2	2	no	—
267	#125	—	2	1	no	—
268	#125	—	2	2	no	—
269	#125	D₄×C₁₉	1	2	yes	—
270	#124	—	2	1	no	—
271	#124	—	2	2	no	—
272	#124	—	2	2	no	—
273	#124	D₄×C₁₉	1	2	yes	—
274	#123	—	2	2	no	—
275	#123	—	2	2	no	—
276	#123	—	2	2	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	2	2	no	—
281	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
282	#121	—	2	1	no	—
283	#121	—	2	1	no	—
284	#121	—	2	2	no	—
285	#121	—	2	2	no	—
286	#121	—	2	2	no	—
287	#121	—	2	1	no	—
288	#121	C₂×C₄×C₁₉	1	2	yes	—
289	#120	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	D₄×C₁₉	1	2	yes	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	D₄×C₁₉	1	2	yes	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	—	2	1	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
313	C₄⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	#97	—	2	2	no	—
317	#97	—	2	2	no	—
318	C₄×C₈	—	2	2	no	—
319	C₁₉	#8349	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
321	#41	—	4	2	no	—
322	#41	—	4	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
365	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	2	no	—
382	C₄²	C₂×D₄×C₁₉	1	2	yes	—
383	C₄²	C₂×D₄×C₁₉	1	2	yes	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	8	1	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	8	1	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	C₁₉×#104	1	2	yes	—
420	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
421	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
422	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
423	C₂×C₄	C₁₉×#120	1	2	yes	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	8	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	C₁₉×#379	1	1	yes	characteristic
438	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
439	C₂²	C₁₉×#421	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	2	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	8	1	no	—
453	C₂	—	8	2	no	—
454	C₂	C₁₉×#1789	1	1	yes	characteristic
455	C₂	C₁₉×#1791	1	1	yes	characteristic
456	C₂	C₁₉×#1794	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3493	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#1750	C₂	semidirect
3. C₁₉×#1532	C₂	semidirect
4. C₁₉×#1494	C₂	semidirect
5. C₁₉×#1464	C₂	semidirect
155. #8349	C₁₉	direct (N × H)
200. #1750	C₂×C₁₉	semidirect
201. #1532	C₂×C₁₉	semidirect
202. #1494	C₂×C₁₉	semidirect
203. #1464	C₂×C₁₉	semidirect
319. C₁₉	#8349	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×#3493	2
C₁₉×#1750	2
C₁₉×#1532	2
C₁₉×#1494	2
C₁₉×#1464	2
#8349	19

Subgroups — C19×#8349 #18014308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8349 #18014308