Subgroups — C₁₉×#17780 #18023739

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2990	C₂	1	2	yes	maximal
3	C₁₉×#1559	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1554	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1552	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1550	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1542	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#557	—	2	2	no	—
11	C₁₉×#556	—	2	2	no	—
12	C₁₉×#552	—	2	2	no	—
13	C₁₉×#552	—	2	2	no	—
14	C₁₉×#541	C₄	1	4	yes	—
15	C₁₉×#536	C₄	1	2	yes	—
16	C₁₉×#533	C₂²	1	2	yes	—
17	C₁₉×#533	C₂²	1	2	yes	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#519	C₄	1	2	yes	—
21	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#446	—	2	2	no	—
23	C₁₉×#435	—	2	2	no	—
24	C₁₉×#435	—	2	2	no	—
25	C₈×D₄×C₁₉	—	2	2	no	—
26	C₁₉×#432	C₂²	1	2	yes	—
27	C₁₉×#432	C₂²	1	2	yes	—
28	C₁₉×#431	C₂²	1	2	yes	—
29	C₁₉×#423	C₂²	1	2	yes	—
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
32	C₁₉×#333	C₂²	1	1	yes	characteristic
33	C₁₉×#333	C₂²	1	2	yes	—
34	C₁₉×#333	C₂²	1	1	yes	characteristic
35	C₁₉×#333	C₂²	1	2	yes	—
36	C₁₉×#333	C₂²	1	1	yes	characteristic
37	C₁₉×#333	C₂²	1	1	yes	characteristic
38	C₁₉×#332	C₂²	1	2	yes	—
39	C₁₉×#332	C₂²	1	2	yes	—
40	C₁₉×#332	C₂²	1	2	yes	—
41	C₁₉×#332	C₂²	1	2	yes	—
42	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂²×C₈×C₁₉	—	2	2	no	—
46	C₂²×C₈×C₁₉	—	2	2	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
50	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
51	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₁₉×#126	—	2	4	no	—
54	C₁₉×#126	—	2	4	no	—
55	C₁₉×#125	—	2	4	no	—
56	C₁₉×#125	—	2	4	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	C₂×C₄	1	2	yes	—
60	C₁₉×#124	—	2	2	no	—
61	C₁₉×#123	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
66	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
67	C₄×Q₈×C₁₉	—	2	4	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
73	C₄×Q₈×C₁₉	D₄	1	2	yes	—
74	C₄×D₄×C₁₉	D₄	1	2	yes	—
75	C₄×D₄×C₁₉	D₄	1	2	yes	—
76	C₄×D₄×C₁₉	D₄	1	2	yes	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	C₂×C₄	1	2	yes	—
82	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
83	C₁₉×#117	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×C₄⋊C₈	—	2	2	no	—
89	C₁₉×C₄⋊C₈	—	2	2	no	—
90	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₉×C₂²⋊C₈	—	2	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	2	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×#97	—	2	2	no	—
98	C₁₉×#97	—	2	2	no	—
99	C₄×C₈×C₁₉	—	2	2	no	—
100	#41×C₁₉	—	4	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	4	4	no	—
104	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
108	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	M₁₆×C₁₉	—	8	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	8	2	no	—
121	C₂×C₈×C₁₉	—	8	2	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
133	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
134	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
135	C₂²⋊C₄×C₁₉	—	2	2	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	4	no	—
138	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
141	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
142	C₄²×C₁₉	—	2	4	no	—
143	C₄²×C₁₉	—	2	4	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₉	C₂×D₄	1	2	yes	—
148	C₄²×C₁₉	C₂×D₄	1	2	yes	—
149	C₄²×C₁₉	C₂×D₄	1	2	yes	—
150	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
151	#17780	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	4	2	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	Q₈×C₁₉	—	4	4	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	2	4	no	—
161	D₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
181	C₈×C₁₉	—	4	2	no	—
182	C₈×C₁₉	—	4	2	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	—	4	2	no	—
185	#3509	C₂×C₁₉	1	1	yes	characteristic
186	#2990	C₂×C₁₉	1	2	yes	—
187	#1559	C₂×C₁₉	1	2	yes	complemented
188	#1558	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1554	C₂×C₁₉	1	2	yes	complemented
190	#1552	C₂×C₁₉	1	2	yes	complemented
191	#1550	C₂×C₁₉	1	2	yes	complemented
192	#1542	C₂×C₁₉	1	2	yes	complemented
193	C₂×#333	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	#413	1	2	yes	—
199	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	#577	1	2	yes	—
210	C₄×C₁₉	#578	1	2	yes	—
211	#557	—	2	2	no	—
212	#556	—	2	2	no	—
213	#552	—	2	2	no	—
214	#552	—	2	2	no	—
215	#541	C₄×C₁₉	1	4	yes	—
216	#536	C₄×C₁₉	1	2	yes	—
217	#533	C₂²×C₁₉	1	2	yes	—
218	#533	C₂²×C₁₉	1	2	yes	—
219	#533	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
221	#519	C₄×C₁₉	1	2	yes	—
222	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
223	#446	—	2	2	no	—
224	#435	—	2	2	no	—
225	#435	—	2	2	no	—
226	C₈×D₄	—	2	2	no	—
227	#432	C₂²×C₁₉	1	2	yes	—
228	#432	C₂²×C₁₉	1	2	yes	—
229	#431	C₂²×C₁₉	1	2	yes	—
230	#423	C₂²×C₁₉	1	2	yes	—
231	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
232	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
233	#333	C₂²×C₁₉	1	1	yes	characteristic
234	#333	C₂²×C₁₉	1	2	yes	—
235	#333	C₂²×C₁₉	1	1	yes	characteristic
236	#333	C₂²×C₁₉	1	2	yes	—
237	#333	C₂²×C₁₉	1	1	yes	characteristic
238	#333	C₂²×C₁₉	1	1	yes	characteristic
239	#332	C₂²×C₁₉	1	2	yes	—
240	#332	C₂²×C₁₉	1	2	yes	—
241	#332	C₂²×C₁₉	1	2	yes	—
242	#332	C₂²×C₁₉	1	2	yes	—
243	C₂×C₁₉	—	2	2	no	—
244	C₂×C₁₉	—	4	2	no	—
245	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
246	C₂×C₁₉	#2898	1	2	yes	—
247	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
248	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
255	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
256	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
258	#126	—	2	4	no	—
259	#126	—	2	4	no	—
260	#125	—	2	4	no	—
261	#125	—	2	4	no	—
262	#125	—	2	2	no	—
263	#125	—	2	2	no	—
264	#125	C₂×C₄×C₁₉	1	2	yes	—
265	#124	—	2	2	no	—
266	#123	—	2	4	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	C₂²⋊Q₈	—	2	2	no	—
270	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
271	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
277	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
278	C₄×Q₈	D₄×C₁₉	1	2	yes	—
279	C₄×D₄	D₄×C₁₉	1	2	yes	—
280	C₄×D₄	D₄×C₁₉	1	2	yes	—
281	C₄×D₄	D₄×C₁₉	1	2	yes	—
282	#117	—	2	2	no	—
283	#117	—	2	2	no	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	#117	C₂×C₄×C₁₉	1	2	yes	—
287	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
288	#117	C₂×C₄×C₁₉	1	2	yes	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
296	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
297	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
298	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	#97	—	2	2	no	—
303	#97	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	C₁₉	#17780	1	1	yes	characteristic, direct product factor, Sylow
306	#41	—	4	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
311	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
312	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
313	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
314	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
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	2	yes	—
321	M₁₆	—	8	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	8	2	no	—
327	C₂×C₈	—	8	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
338	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
339	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
340	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
345	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
346	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
347	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
352	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₁₉	1	2	yes	—
354	C₄²	C₂×D₄×C₁₉	1	2	yes	—
355	C₄²	C₂×D₄×C₁₉	1	2	yes	—
356	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
357	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
358	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
359	Q₈	—	4	1	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	4	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	4	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
384	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	C₁₉×#413	1	2	yes	—
395	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	4	no	—
405	C₄	C₁₉×#577	1	2	yes	—
406	C₄	C₁₉×#578	1	2	yes	—
407	C₂	—	2	2	no	—
408	C₂	—	4	2	no	—
409	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
410	C₂	C₁₉×#2898	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1559	C₂	semidirect
4. C₁₉×#1558	C₂	semidirect
5. C₁₉×#1554	C₂	semidirect
6. C₁₉×#1552	C₂	semidirect
7. C₁₉×#1550	C₂	semidirect
8. C₁₉×#1542	C₂	semidirect
9. C₂×C₁₉×#333	C₂	semidirect
151. #17780	C₁₉	direct (N × H)
187. #1559	C₂×C₁₉	semidirect
188. #1558	C₂×C₁₉	semidirect
189. #1554	C₂×C₁₉	semidirect
190. #1552	C₂×C₁₉	semidirect
191. #1550	C₂×C₁₉	semidirect
192. #1542	C₂×C₁₉	semidirect
193. C₂×#333	C₂×C₁₉	semidirect
305. C₁₉	#17780	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×#3509	2
C₁₉×#2990	2
C₁₉×#1559	2
C₁₉×#1558	2
C₁₉×#1554	2
C₁₉×#1552	2
C₁₉×#1550	2
C₁₉×#1542	2
C₂×C₁₉×#333	2
#17780	19

Subgroups — C19×#17780 #18023739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17780 #18023739