Subgroups — C₁₉×#9242 #18015201

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1507	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1471	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1293	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1282	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₁₉×#482	—	2	1	no	—
11	C₁₉×#482	—	2	1	no	—
12	C₁₉×#482	—	2	1	no	—
13	C₁₉×#482	—	2	1	no	—
14	C₁₉×#433	—	2	2	no	—
15	C₁₉×#432	—	2	1	no	—
16	C₁₉×#431	—	2	1	no	—
17	C₂×C₁₉×#107	C₄	1	1	yes	characteristic, complemented
18	C₂×C₁₉×#106	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#424	—	2	1	no	—
20	C₂×C₁₉×#102	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₉×#102	C₄	1	1	yes	characteristic, complemented
22	C₁₉×#407	C₂²	1	1	yes	characteristic
23	C₁₉×#407	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#405	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#339	—	2	1	no	—
29	C₁₉×#339	—	2	1	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₁₉×#323	—	2	1	no	—
32	C₁₉×#323	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#121	—	2	1	no	—
43	C₁₉×#121	—	2	1	no	—
44	C₁₉×#121	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₁₉×#117	D₄	1	1	yes	characteristic
48	C₁₉×#117	D₄	1	1	yes	characteristic
49	C₁₉×#117	D₄	1	1	yes	characteristic
50	C₁₉×#117	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	—	2	1	no	—
59	C₁₉×#107	—	2	1	no	—
60	C₁₉×#107	—	2	1	no	—
61	C₁₉×#106	—	2	1	no	—
62	C₁₉×#106	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	2	no	—
64	C₁₉×C₄⋊C₈	—	2	2	no	—
65	C₁₉×#102	—	2	1	no	—
66	C₁₉×#102	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×#102	—	2	1	no	—
69	C₁₉×C₂²⋊C₈	—	2	1	no	—
70	C₁₉×C₂²⋊C₈	—	2	1	no	—
71	C₁₉×C₂²⋊C₈	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
76	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
77	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
78	C₁₉×#97	—	2	2	no	—
79	C₄×C₈×C₁₉	—	2	2	no	—
80	C₁₉×#95	—	2	1	no	—
81	C₂⁴×C₁₉	—	2	1	no	—
82	C₂⁴×C₁₉	#41	1	1	yes	characteristic
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	8	2	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₄²×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	—	2	1	no	—
134	C₄²×C₁₉	—	2	1	no	—
135	C₄²×C₁₉	—	2	1	no	—
136	C₄²×C₁₉	—	4	1	no	—
137	C₄²×C₁₉	—	4	1	no	—
138	#9242	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	2	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	—	8	1	no	—
148	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	C₂³×C₁₉	#123	1	1	yes	characteristic
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	—	4	1	no	—
185	C₈×C₁₉	—	4	1	no	—
186	C₈×C₁₉	—	8	1	no	—
187	C₂×#482	C₂×C₁₉	1	1	yes	characteristic
188	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1826	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1507	C₂×C₁₉	1	1	yes	characteristic
191	#1471	C₂×C₁₉	1	1	yes	characteristic
192	#1293	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1282	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	16	1	no	—
208	C₂²×C₁₉	—	16	1	no	—
209	C₂²×C₁₉	#386	1	1	yes	characteristic
210	C₂²×C₁₉	#443	1	1	yes	characteristic
211	C₂²×C₁₉	#444	1	1	yes	characteristic
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	4	1	no	—
216	C₄×C₁₉	—	4	1	no	—
217	C₄×C₁₉	—	4	1	no	—
218	C₄×C₁₉	—	4	1	no	—
219	C₄×C₁₉	—	8	2	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	#410	1	1	yes	characteristic
222	C₄×C₁₉	#410	1	1	yes	characteristic
223	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
225	#482	—	2	1	no	—
226	#482	—	2	1	no	—
227	#482	—	2	1	no	—
228	#482	—	2	1	no	—
229	#433	—	2	2	no	—
230	#432	—	2	1	no	—
231	#431	—	2	1	no	—
232	C₂×#107	C₄×C₁₉	1	1	yes	characteristic, complemented
233	C₂×#106	C₄×C₁₉	1	1	yes	characteristic, complemented
234	#424	—	2	1	no	—
235	C₂×#102	C₄×C₁₉	1	1	yes	characteristic, complemented
236	C₂×#102	C₄×C₁₉	1	1	yes	characteristic, complemented
237	#407	C₂²×C₁₉	1	1	yes	characteristic
238	#407	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
241	#405	—	2	1	no	—
242	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
243	#339	—	2	1	no	—
244	#339	—	2	1	no	—
245	#327	—	2	2	no	—
246	#323	—	2	1	no	—
247	#323	—	2	1	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	4	1	no	—
251	C₂×C₁₉	—	4	1	no	—
252	C₂×C₁₉	—	16	1	no	—
253	C₂×C₁₉	#1876	1	1	yes	characteristic
254	C₂×C₁₉	#1899	1	1	yes	characteristic
255	C₂×C₁₉	#1903	1	1	yes	characteristic
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
263	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	#121	—	2	1	no	—
267	#121	—	2	1	no	—
268	#117	—	2	1	no	—
269	#117	—	2	1	no	—
270	#117	D₄×C₁₉	1	1	yes	characteristic
271	#117	D₄×C₁₉	1	1	yes	characteristic
272	#117	D₄×C₁₉	1	1	yes	characteristic
273	#117	D₄×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#106	—	2	1	no	—
285	#106	—	2	1	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	2	no	—
288	#102	—	2	1	no	—
289	#102	—	2	1	no	—
290	#102	—	2	1	no	—
291	#102	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
299	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
300	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
301	#97	—	2	2	no	—
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	1	no	—
304	C₁₉	#9242	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁴	—	2	1	no	—
306	C₂⁴	#41×C₁₉	1	1	yes	characteristic
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
326	M₁₆	—	4	1	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
345	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
346	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
347	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	8	1	no	—
370	C₂³	—	8	1	no	—
371	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
372	C₂³	C₁₉×#121	1	1	yes	characteristic
373	C₂³	C₁₉×#123	1	1	yes	characteristic
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	2	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	8	1	no	—
397	C₂×C₄	—	8	1	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
401	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
403	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	8	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	16	1	no	—
424	C₂²	—	16	1	no	—
425	C₂²	C₁₉×#386	1	1	yes	characteristic
426	C₂²	C₁₉×#443	1	1	yes	characteristic
427	C₂²	C₁₉×#444	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	1	no	—
437	C₄	C₁₉×#410	1	1	yes	characteristic
438	C₄	C₁₉×#410	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	4	1	no	—
442	C₂	—	4	1	no	—
443	C₂	—	16	1	no	—
444	C₂	C₁₉×#1876	1	1	yes	characteristic
445	C₂	C₁₉×#1899	1	1	yes	characteristic
446	C₂	C₁₉×#1903	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2924	C₂	semidirect
3. C₁₉×#1826	C₂	semidirect
6. C₁₉×#1293	C₂	semidirect
7. C₁₉×#1282	C₂	semidirect
17. C₂×C₁₉×#107	C₄	semidirect
18. C₂×C₁₉×#106	C₄	semidirect
20. C₂×C₁₉×#102	C₄	semidirect
21. C₂×C₁₉×#102	C₄	semidirect
138. #9242	C₁₉	direct (N × H)
188. #2924	C₂×C₁₉	semidirect
189. #1826	C₂×C₁₉	semidirect
192. #1293	C₂×C₁₉	semidirect
193. #1282	C₂×C₁₉	semidirect
232. C₂×#107	C₄×C₁₉	semidirect
233. C₂×#106	C₄×C₁₉	semidirect
235. C₂×#102	C₄×C₁₉	semidirect
236. C₂×#102	C₄×C₁₉	semidirect
304. C₁₉	#9242	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#482	2
C₁₉×#2924	2
C₁₉×#1826	2
C₁₉×#1507	2
C₁₉×#1471	2
C₁₉×#1293	2
C₁₉×#1282	2
#9242	19

Subgroups — C19×#9242 #18015201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9242 #18015201