Subgroups — C₁₉×#8372 #18014331

Order 4864.

788 conjugacy classes of subgroups.

The subgroup lattice has 394 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	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1528	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1490	C₂	1	2	yes	maximal
5	C₁₉×#1467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#554	—	2	4	no	—
7	C₁₉×#554	—	2	4	no	—
8	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
9	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
10	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₁₉×#432	C₂²	1	2	yes	—
20	C₂×C₁₉×#101	—	2	1	no	—
21	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#343	—	2	1	no	—
23	C₁₉×#330	—	2	4	no	—
24	C₁₉×D₄⋊C₈	—	2	4	no	—
25	C₁₉×#324	—	2	1	no	—
26	C₁₉×#324	—	2	1	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₁₉×C₄⋊Q₈	—	2	2	no	—
35	C₁₉×C₄⋊Q₈	—	2	2	no	—
36	C₁₉×#125	—	2	2	no	—
37	C₁₉×#125	—	2	2	no	—
38	C₁₉×#125	—	2	2	no	—
39	C₁₉×#125	D₄	1	4	yes	—
40	C₁₉×C₂²⋊Q₈	—	2	8	no	—
41	C₁₉×C₂²⋊Q₈	—	2	8	no	—
42	C₁₉×C₂²⋊Q₈	—	2	8	no	—
43	C₄×Q₈×C₁₉	—	2	2	no	—
44	C₄×Q₈×C₁₉	—	2	2	no	—
45	C₄×D₄×C₁₉	—	2	2	no	—
46	C₄×D₄×C₁₉	—	2	2	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₄×D₄×C₁₉	—	2	2	no	—
50	C₄×D₄×C₁₉	D₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×C₄⋊C₈	—	2	2	no	—
70	C₁₉×#101	—	2	4	no	—
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×#97	—	2	2	no	—
73	C₁₉×#97	—	2	2	no	—
74	C₄×C₈×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	2	4	no	—
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	8	2	no	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	8	2	no	—
93	C₂²×C₄×C₁₉	—	8	2	no	—
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²×C₄	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	M₁₆×C₁₉	—	2	4	no	—
102	M₁₆×C₁₉	—	4	2	no	—
103	C₂×C₈×C₁₉	—	4	2	no	—
104	C₂×C₈×C₁₉	—	4	2	no	—
105	C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
117	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₁₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₉	—	2	4	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₄²×C₁₉	—	2	1	no	—
125	C₄²×C₁₉	—	2	1	no	—
126	C₄²×C₁₉	C₂×D₄	1	2	yes	—
127	C₄²×C₁₉	C₂×D₄	1	2	yes	—
128	#8372	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	2	4	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	Q₈×C₁₉	—	4	4	no	—
136	Q₈×C₁₉	—	8	4	no	—
137	D₄×C₁₉	—	2	4	no	—
138	D₄×C₁₉	—	2	2	no	—
139	D₄×C₁₉	#101	1	4	yes	complemented
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	8	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	8	4	no	—
162	C₂×C₄×C₁₉	—	8	4	no	—
163	C₂×C₄×C₁₉	#104	1	2	yes	—
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#120	1	2	yes	—
167	C₂×C₄×C₁₉	#120	1	2	yes	—
168	C₈×C₁₉	—	4	4	no	—
169	C₈×C₁₉	—	8	2	no	—
170	C₂×#554	C₂×C₁₉	1	1	yes	characteristic
171	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
172	#1528	C₂×C₁₉	1	2	yes	complemented
173	#1490	C₂×C₁₉	1	2	yes	—
174	#1467	C₂×C₁₉	1	1	yes	characteristic, complemented
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	4	no	—
178	C₂²×C₁₉	—	4	4	no	—
179	C₂²×C₁₉	—	4	4	no	—
180	C₂²×C₁₉	—	4	2	no	—
181	C₂²×C₁₉	—	4	2	no	—
182	C₂²×C₁₉	#379	1	1	yes	characteristic
183	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
184	C₂²×C₁₉	#421	1	1	yes	characteristic
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	2	no	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	4	2	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₄×C₁₉	—	4	1	no	—
192	C₄×C₁₉	—	4	1	no	—
193	C₄×C₁₉	—	4	1	no	—
194	C₄×C₁₉	—	4	2	no	—
195	C₄×C₁₉	C₂×#101	1	2	yes	—
196	#554	—	2	4	no	—
197	#554	—	2	4	no	—
198	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
199	C₂×#125	C₄×C₁₉	1	1	yes	characteristic
200	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
201	C₂×C₂²⋊Q₈	—	2	1	no	—
202	C₂×C₂²⋊Q₈	—	2	1	no	—
203	C₂×C₂²⋊Q₈	—	2	1	no	—
204	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
206	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	—	2	1	no	—
209	#432	C₂²×C₁₉	1	2	yes	—
210	C₂×#101	—	2	1	no	—
211	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
212	#343	—	2	1	no	—
213	#330	—	2	4	no	—
214	D₄⋊C₈	—	2	4	no	—
215	#324	—	2	1	no	—
216	#324	—	2	1	no	—
217	C₂×C₁₉	—	2	1	no	—
218	C₂×C₁₉	—	2	1	no	—
219	C₂×C₁₉	—	4	4	no	—
220	C₂×C₁₉	#1784	1	1	yes	characteristic
221	C₂×C₁₉	#1789	1	1	yes	characteristic
222	C₂×C₁₉	#1795	1	1	yes	characteristic
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
225	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	—	2	1	no	—
228	C₂³×C₄	—	2	1	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	#125	—	2	2	no	—
233	#125	—	2	2	no	—
234	#125	—	2	2	no	—
235	#125	D₄×C₁₉	1	4	yes	—
236	C₂²⋊Q₈	—	2	8	no	—
237	C₂²⋊Q₈	—	2	8	no	—
238	C₂²⋊Q₈	—	2	8	no	—
239	C₄×Q₈	—	2	2	no	—
240	C₄×Q₈	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	D₄×C₁₉	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	8	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
265	C₄⋊C₈	—	2	2	no	—
266	#101	—	2	4	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	#97	—	2	2	no	—
269	#97	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₁₉	#8372	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	8	2	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	8	2	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
298	M₁₆	—	2	4	no	—
299	M₁₆	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
314	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
315	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	C₂×D₄×C₁₉	1	2	yes	—
324	C₄²	C₂×D₄×C₁₉	1	2	yes	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
331	Q₈	—	4	4	no	—
332	Q₈	—	8	4	no	—
333	D₄	—	2	4	no	—
334	D₄	—	2	2	no	—
335	D₄	C₁₉×#101	1	4	yes	complemented
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	C₁₉×#104	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
362	C₂×C₄	C₁₉×#120	1	2	yes	—
363	C₂×C₄	C₁₉×#120	1	2	yes	—
364	C₈	—	4	4	no	—
365	C₈	—	8	2	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	C₁₉×#379	1	1	yes	characteristic
374	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
375	C₂²	C₁₉×#421	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	C₂×C₁₉×#101	1	2	yes	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	4	4	no	—
390	C₂	C₁₉×#1784	1	1	yes	characteristic
391	C₂	C₁₉×#1789	1	1	yes	characteristic
392	C₂	C₁₉×#1795	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	C₂²×D₄×C₁₉	C₂×C₄
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. C₄×C₁₉×#101	C₂	semidirect
3. C₁₉×#1528	C₂	semidirect
5. C₁₉×#1467	C₂	semidirect
128. #8372	C₁₉	direct (N × H)
139. D₄×C₁₉	#101	semidirect
171. C₄×#101	C₂×C₁₉	semidirect
172. #1528	C₂×C₁₉	semidirect
174. #1467	C₂×C₁₉	semidirect
271. C₁₉	#8372	direct (N × H)
335. D₄	C₁₉×#101	semidirect

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
C₄×C₁₉×#101	2
C₁₉×#1528	2
C₁₉×#1490	2
C₁₉×#1467	2
#8372	19

Subgroups — C19×#8372 #18014331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8372 #18014331