Subgroups — C₁₉×#8380 #18014339

Order 4864.

818 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#554	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1824	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1520	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#554	—	2	4	no	—
7	C₁₉×#554	—	2	4	no	—
8	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₉×#125	—	2	1	no	—
10	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#99	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#380	C₂²	1	2	yes	—
22	C₁₉×#342	—	2	1	no	—
23	C₁₉×#340	—	2	4	no	—
24	C₁₉×#328	—	2	4	no	—
25	C₁₉×#324	—	2	1	no	—
26	C₁₉×#323	—	2	1	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	—	2	2	no	—
35	C₁₉×C₄⋊Q₈	—	2	2	no	—
36	C₁₉×C₄⋊Q₈	—	2	2	no	—
37	C₁₉×#125	—	2	8	no	—
38	C₁₉×C₂²⋊Q₈	—	2	8	no	—
39	C₁₉×C₂²⋊Q₈	—	2	8	no	—
40	C₁₉×C₂²⋊Q₈	—	2	2	no	—
41	C₁₉×C₂²⋊Q₈	—	2	2	no	—
42	C₁₉×C₂²⋊Q₈	—	2	2	no	—
43	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
44	C₄×Q₈×C₁₉	—	2	2	no	—
45	C₄×Q₈×C₁₉	—	2	2	no	—
46	C₄×D₄×C₁₉	—	2	8	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₁₉×#99	—	4	2	no	—
72	C₁₉×C₂²⋊C₈	—	2	2	no	—
73	C₁₉×C₂²⋊C₈	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	4	2	no	—
80	C₂×Q₈×C₁₉	—	8	2	no	—
81	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
85	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	8	2	no	—
98	C₂²×C₄×C₁₉	—	8	2	no	—
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
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	4	no	—
107	C₂×C₈×C₁₉	—	4	2	no	—
108	C₄⋊C₄×C₁₉	—	2	4	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	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	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	—	4	4	no	—
119	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	2	no	—
127	C₂²⋊C₄×C₁₉	—	4	2	no	—
128	C₄²×C₁₉	—	2	4	no	—
129	C₄²×C₁₉	—	2	1	no	—
130	C₄²×C₁₉	—	2	1	no	—
131	#8380	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	#103	1	2	yes	—
139	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₁₉	#120	1	2	yes	—
141	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
143	C₂³×C₁₉	#137	1	2	yes	—
144	Q₈×C₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	4	2	no	—
146	Q₈×C₁₉	—	8	4	no	—
147	D₄×C₁₉	—	2	4	no	—
148	D₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	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	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	8	4	no	—
170	C₂×C₄×C₁₉	—	8	4	no	—
171	C₂×C₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	—	8	2	no	—
173	C₂×C₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	#103	1	2	yes	—
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	2	yes	—
178	C₈×C₁₉	—	8	2	no	—
179	C₂×#554	C₂×C₁₉	1	1	yes	characteristic
180	#1824	C₂×C₁₉	1	2	yes	complemented
181	#1799	C₂×C₁₉	1	1	yes	characteristic
182	#1520	C₂×C₁₉	1	2	yes	complemented
183	#1459	C₂×C₁₉	1	1	yes	characteristic
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	4	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	2	yes	—
200	C₂²×C₁₉	#451	1	2	yes	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	4	1	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	16	2	no	—
211	C₄×C₁₉	#410	1	2	yes	—
212	#554	—	2	4	no	—
213	#554	—	2	4	no	—
214	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
215	C₂×#125	—	2	1	no	—
216	C₂×C₂²⋊Q₈	—	2	1	no	—
217	C₂×C₂²⋊Q₈	—	2	1	no	—
218	C₂×C₂²⋊Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
219	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#99	—	2	1	no	—
226	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
227	#380	C₂²×C₁₉	1	2	yes	—
228	#342	—	2	1	no	—
229	#340	—	2	4	no	—
230	#328	—	2	4	no	—
231	#324	—	2	1	no	—
232	#323	—	2	1	no	—
233	C₂×C₁₉	—	2	2	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	2	2	no	—
237	C₂×C₁₉	—	4	2	no	—
238	C₂×C₁₉	#1782	1	1	yes	characteristic
239	C₂×C₁₉	#1787	1	1	yes	characteristic
240	C₂×C₁₉	#1795	1	1	yes	characteristic
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
243	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂²×C₈	—	2	2	no	—
249	C₄⋊Q₈	—	2	2	no	—
250	C₄⋊Q₈	—	2	2	no	—
251	#125	—	2	8	no	—
252	C₂²⋊Q₈	—	2	8	no	—
253	C₂²⋊Q₈	—	2	8	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	1	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	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂×C₄×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	D₄×C₁₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
285	#99	—	4	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	#95	—	2	2	no	—
289	C₁₉	#8380	1	1	yes	characteristic, direct product factor, Sylow
290	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
291	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
300	C₂×D₄	Q₁₆×C₁₉	1	2	yes	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	—	8	2	no	—
314	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₈	—	4	4	no	—
322	C₂×C₈	—	4	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
336	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	C₁₉×#103	1	2	yes	—
353	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
354	C₂³	C₁₉×#120	1	2	yes	—
355	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
356	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
357	C₂³	C₁₉×#137	1	2	yes	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	4	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	4	no	—
384	C₂×C₄	—	8	4	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	C₁₉×#103	1	2	yes	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#120	1	2	yes	—
392	C₈	—	8	2	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	C₁₉×#379	1	1	yes	characteristic
406	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
407	C₂²	C₁₉×#419	1	1	yes	characteristic
408	C₂²	C₁₉×#448	1	2	yes	—
409	C₂²	C₁₉×#451	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	16	2	no	—
420	C₄	C₁₉×#410	1	2	yes	—
421	C₂	—	2	2	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	2	no	—
425	C₂	—	4	2	no	—
426	C₂	C₁₉×#1782	1	1	yes	characteristic
427	C₂	C₁₉×#1787	1	1	yes	characteristic
428	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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×#1824	C₂	semidirect
4. C₁₉×#1520	C₂	semidirect
8. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
12. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
14. C₂×C₄×Q₈×C₁₉	C₄	semidirect
17. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
131. #8380	C₁₉	direct (N × H)
180. #1824	C₂×C₁₉	semidirect
182. #1520	C₂×C₁₉	semidirect
214. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
218. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
220. C₂×C₄×Q₈	C₄×C₁₉	semidirect
223. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
289. C₁₉	#8380	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×#554	2
C₁₉×#1824	2
C₁₉×#1799	2
C₁₉×#1520	2
C₁₉×#1459	2
#8380	19

Subgroups — C19×#8380 #18014339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8380 #18014339