Subgroups — C₁₉×#8406 #18014365

Order 4864.

868 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1872	C₂	1	2	yes	maximal
3	C₂×C₁₉×#328	C₂	1	2	yes	maximal
4	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#544	—	2	4	no	—
7	C₁₉×#544	—	2	2	no	—
8	C₁₉×#544	C₄	1	4	yes	complemented
9	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
10	C₂×C₁₉×#125	—	2	2	no	—
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₉×#117	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#103	—	2	2	no	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₂×C₁₉×#95	—	2	1	no	—
20	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
21	C₁₉×#340	—	2	2	no	—
22	C₁₉×#328	—	2	4	no	—
23	C₁₉×#324	—	2	2	no	—
24	C₂²×Q₈×C₁₉	—	2	1	no	—
25	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₁₉×C₄⋊Q₈	—	2	8	no	—
33	C₁₉×C₄⋊Q₈	—	2	8	no	—
34	C₁₉×#125	—	2	8	no	—
35	C₁₉×#125	—	2	8	no	—
36	C₁₉×C₂²⋊Q₈	—	2	4	no	—
37	C₁₉×C₂²⋊Q₈	—	2	4	no	—
38	C₁₉×C₂²⋊Q₈	—	2	2	no	—
39	C₁₉×C₂²⋊Q₈	—	2	2	no	—
40	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
41	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
42	C₁₉×#117	—	2	4	no	—
43	C₁₉×#117	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	—	2	2	no	—
58	C₁₉×#103	—	4	4	no	—
59	C₁₉×C₂²⋊C₈	—	2	2	no	—
60	C₁₉×C₂²⋊C₈	—	2	2	no	—
61	C₁₉×#95	—	2	2	no	—
62	C₁₉×#95	—	4	2	no	—
63	C₁₉×#95	—	4	2	no	—
64	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×Q₈×C₁₉	—	2	4	no	—
66	C₂×Q₈×C₁₉	—	2	2	no	—
67	C₂×Q₈×C₁₉	—	4	2	no	—
68	C₂×Q₈×C₁₉	—	4	2	no	—
69	C₂×Q₈×C₁₉	—	8	1	no	—
70	C₂×Q₈×C₁₉	—	8	1	no	—
71	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	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	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
101	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₉	—	4	2	no	—
107	C₂×C₈×C₁₉	—	4	2	no	—
108	C₂×C₈×C₁₉	—	4	2	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	4	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	4	2	no	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
121	C₂²⋊C₄×C₁₉	—	2	4	no	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₄²×C₁₉	—	2	8	no	—
124	#8406	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₉	#120	1	1	yes	characteristic
131	C₂³×C₁₉	#120	1	1	yes	characteristic
132	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
134	C₂³×C₁₉	#137	1	1	yes	characteristic
135	C₂³×C₁₉	#137	1	1	yes	characteristic
136	Q₈×C₁₉	—	4	4	no	—
137	Q₈×C₁₉	—	8	2	no	—
138	Q₈×C₁₉	—	8	4	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	#103	1	4	yes	complemented
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₉	#120	1	2	yes	—
178	C₈×C₁₉	—	8	2	no	—
179	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
180	#1872	C₂×C₁₉	1	2	yes	—
181	C₂×#328	C₂×C₁₉	1	2	yes	—
182	C₂×#324	C₂×C₁₉	1	1	yes	characteristic
183	#1441	C₂×C₁₉	1	1	yes	characteristic
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	#379	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
198	C₂²×C₁₉	#419	1	1	yes	characteristic
199	C₂²×C₁₉	#448	1	1	yes	characteristic
200	C₂²×C₁₉	#448	1	1	yes	characteristic
201	C₂²×C₁₉	#451	1	1	yes	characteristic
202	C₂²×C₁₉	#451	1	1	yes	characteristic
203	C₂²×C₁₉	#454	1	1	yes	characteristic
204	C₂²×C₁₉	#456	1	1	yes	characteristic
205	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
206	C₂²×C₁₉	#458	1	1	yes	characteristic
207	C₄×C₁₉	—	2	4	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	4	4	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	—	4	4	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	—	8	2	no	—
215	#544	—	2	4	no	—
216	#544	—	2	2	no	—
217	#544	C₄×C₁₉	1	4	yes	complemented
218	C₂×C₄⋊Q₈	—	2	2	no	—
219	C₂×#125	—	2	2	no	—
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
222	C₂×#117	—	2	1	no	—
223	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#103	—	2	2	no	—
226	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
227	C₂×#95	—	2	1	no	—
228	C₂×#95	—	2	1	no	—
229	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
230	#340	—	2	2	no	—
231	#328	—	2	4	no	—
232	#324	—	2	2	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	#1599	1	1	yes	characteristic
238	C₂×C₁₉	#1605	1	1	yes	characteristic
239	C₂×C₁₉	#1611	1	1	yes	characteristic
240	C₂×C₁₉	#1617	1	1	yes	characteristic
241	C₂×C₁₉	#1787	1	1	yes	characteristic
242	C₂×C₁₉	#1790	1	1	yes	characteristic
243	C₂×C₁₉	#1793	1	1	yes	characteristic
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂²×C₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	8	no	—
253	C₄⋊Q₈	—	2	8	no	—
254	#125	—	2	8	no	—
255	#125	—	2	8	no	—
256	C₂²⋊Q₈	—	2	4	no	—
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	—	2	2	no	—
259	C₂²⋊Q₈	—	2	2	no	—
260	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
261	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
262	#117	—	2	4	no	—
263	#117	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	4	2	no	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
274	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
275	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	#103	—	4	4	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	4	2	no	—
283	#95	—	4	2	no	—
284	C₁₉	#8406	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	8	1	no	—
291	C₂×Q₈	—	8	1	no	—
292	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
321	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
322	C₂²×C₄	Q₁₆×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	—	2	8	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
350	C₂³	C₁₉×#120	1	1	yes	characteristic
351	C₂³	C₁₉×#120	1	1	yes	characteristic
352	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
353	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
354	C₂³	C₁₉×#137	1	1	yes	characteristic
355	C₂³	C₁₉×#137	1	1	yes	characteristic
356	Q₈	—	4	4	no	—
357	Q₈	—	8	2	no	—
358	Q₈	—	8	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	C₁₉×#103	1	4	yes	complemented
396	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
397	C₂×C₄	C₁₉×#120	1	2	yes	—
398	C₈	—	8	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	C₁₉×#379	1	1	yes	characteristic
412	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
413	C₂²	C₁₉×#419	1	1	yes	characteristic
414	C₂²	C₁₉×#448	1	1	yes	characteristic
415	C₂²	C₁₉×#448	1	1	yes	characteristic
416	C₂²	C₁₉×#451	1	1	yes	characteristic
417	C₂²	C₁₉×#451	1	1	yes	characteristic
418	C₂²	C₁₉×#454	1	1	yes	characteristic
419	C₂²	C₁₉×#456	1	1	yes	characteristic
420	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
421	C₂²	C₁₉×#458	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	2	no	—
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	C₁₉×#1599	1	1	yes	characteristic
435	C₂	C₁₉×#1605	1	1	yes	characteristic
436	C₂	C₁₉×#1611	1	1	yes	characteristic
437	C₂	C₁₉×#1617	1	1	yes	characteristic
438	C₂	C₁₉×#1787	1	1	yes	characteristic
439	C₂	C₁₉×#1790	1	1	yes	characteristic
440	C₂	C₁₉×#1793	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₉×#544	C₄	semidirect
124. #8406	C₁₉	direct (N × H)
175. C₂×C₄×C₁₉	#103	semidirect
217. #544	C₄×C₁₉	semidirect
284. C₁₉	#8406	direct (N × H)
395. C₂×C₄	C₁₉×#103	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#544	2
C₁₉×#1872	2
C₂×C₁₉×#328	2
C₂×C₁₉×#324	2
C₁₉×#1441	2
#8406	19

Subgroups — C19×#8406 #18014365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8406 #18014365