Subgroups — C₁₉×#11226 #18017185

Order 4864.

882 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#339	C₂	1	2	yes	maximal
4	C₂×C₁₉×#339	C₂	1	2	yes	maximal
5	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic
6	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#389	C₄	1	2	yes	complemented
13	C₁₉×#389	C₄	1	2	yes	complemented
14	C₁₉×#385	—	2	1	no	—
15	C₁₉×#385	—	2	1	no	—
16	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
17	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₁₉×#339	—	2	4	no	—
20	C₁₉×#339	—	2	4	no	—
21	C₁₉×#336	—	2	2	no	—
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₁₉	—	2	2	no	—
27	C₂×M₁₆×C₁₉	—	2	2	no	—
28	C₂×M₁₆×C₁₉	—	2	2	no	—
29	C₂×M₁₆×C₁₉	—	2	2	no	—
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	Q₈	1	4	yes	—
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₁₉×#117	—	2	1	no	—
34	C₁₉×#117	—	2	1	no	—
35	C₁₉×#117	—	2	2	no	—
36	C₁₉×#117	—	2	2	no	—
37	C₁₉×#117	D₄	1	2	yes	—
38	C₁₉×#117	Q₈	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	2	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	2	no	—
51	C₂×C₄²×C₁₉	—	2	2	no	—
52	C₂×C₄²×C₁₉	—	2	2	no	—
53	C₂×C₄²×C₁₉	—	2	2	no	—
54	C₂×C₄²×C₁₉	—	2	2	no	—
55	C₂×C₄²×C₁₉	—	2	2	no	—
56	C₂×C₄²×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₉	D₄	1	4	yes	—
59	C₂×C₄²×C₁₉	D₄	1	2	yes	—
60	C₁₉×#95	—	2	4	no	—
61	C₁₉×#95	—	2	2	no	—
62	C₁₉×#95	—	2	2	no	—
63	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	2	8	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	4	4	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	4	2	no	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	2	yes	—
89	C₂²×C₄×C₁₉	#41	1	2	yes	—
90	M₁₆×C₁₉	—	2	4	no	—
91	M₁₆×C₁₉	—	2	4	no	—
92	M₁₆×C₁₉	—	4	2	no	—
93	M₁₆×C₁₉	—	4	2	no	—
94	C₂×C₈×C₁₉	—	2	4	no	—
95	C₂×C₈×C₁₉	—	4	2	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₄⋊C₄×C₁₉	—	2	16	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	4	4	no	—
102	C₄⋊C₄×C₁₉	—	4	4	no	—
103	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	complemented
104	C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₂²⋊C₄×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	2	4	no	—
109	C₄²×C₁₉	—	2	4	no	—
110	C₄²×C₁₉	—	2	2	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄²×C₁₉	—	2	4	no	—
113	C₄²×C₁₉	—	2	4	no	—
114	C₄²×C₁₉	—	4	2	no	—
115	C₄²×C₁₉	—	4	2	no	—
116	C₄²×C₁₉	—	4	2	no	—
117	#11226	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₉	#120	1	1	yes	characteristic
122	C₂³×C₁₉	#121	1	1	yes	characteristic
123	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
124	C₂³×C₁₉	#123	1	1	yes	characteristic
125	C₂³×C₁₉	#124	1	1	yes	characteristic
126	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₁₉	—	2	4	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	8	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	4	8	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	8	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	#104	1	4	yes	—
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₁₉	#121	1	2	yes	—
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	2	yes	—
156	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	2	yes	—
161	C₂×C₄×C₁₉	#125	1	2	yes	—
162	C₂×C₄×C₁₉	#125	1	2	yes	—
163	C₂×C₄×C₁₉	#126	1	2	yes	—
164	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
165	C₈×C₁₉	—	4	4	no	—
166	#2296	C₂×C₁₉	1	1	yes	characteristic
167	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
168	C₂×#339	C₂×C₁₉	1	2	yes	—
169	C₂×#339	C₂×C₁₉	1	2	yes	—
170	#1728	C₂×C₁₉	1	1	yes	characteristic
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	#380	1	1	yes	characteristic
180	C₂²×C₁₉	#386	1	1	yes	characteristic
181	C₂²×C₁₉	#391	1	1	yes	characteristic
182	C₂²×C₁₉	#394	1	1	yes	characteristic
183	C₂²×C₁₉	#395	1	1	yes	characteristic
184	C₂²×C₁₉	#398	1	1	yes	characteristic
185	C₂²×C₁₉	#400	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#104	1	2	yes	—
187	C₂²×C₁₉	#421	1	2	yes	—
188	C₄×C₁₉	—	2	4	no	—
189	C₄×C₁₉	—	4	8	no	—
190	C₄×C₁₉	—	4	4	no	—
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₄×C₁₉	—	8	1	no	—
194	C₄×C₁₉	#387	1	2	yes	—
195	C₄×C₁₉	#389	1	2	yes	—
196	C₄×C₁₉	#396	1	2	yes	—
197	C₄×C₁₉	#398	1	2	yes	—
198	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
199	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	—	2	1	no	—
202	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
203	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
204	#389	C₄×C₁₉	1	2	yes	complemented
205	#389	C₄×C₁₉	1	2	yes	complemented
206	#385	—	2	1	no	—
207	#385	—	2	1	no	—
208	C₄×C₄⋊C₄	—	2	4	no	—
209	C₄×C₄⋊C₄	—	2	2	no	—
210	C₂×#95	—	2	1	no	—
211	#339	—	2	4	no	—
212	#339	—	2	4	no	—
213	#336	—	2	2	no	—
214	C₂×C₁₉	—	2	1	no	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	—	2	1	no	—
217	C₂×C₁₉	—	2	1	no	—
218	C₂×C₁₉	#1441	1	1	yes	characteristic
219	C₂×C₁₉	#1806	1	2	yes	—
220	C₂×C₁₉	#1896	1	1	yes	characteristic
221	C₂×C₁₉	#1897	1	1	yes	characteristic
222	C₂×C₁₉	#1986	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
225	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	Q₈×C₁₉	1	4	yes	—
233	C₂²×C₈	—	2	2	no	—
234	#117	—	2	1	no	—
235	#117	—	2	1	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	D₄×C₁₉	1	2	yes	—
239	#117	Q₈×C₁₉	1	2	yes	—
240	C₂×C₄⋊C₄	—	2	8	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
259	C₂×C₄²	D₄×C₁₉	1	4	yes	—
260	C₂×C₄²	D₄×C₁₉	1	2	yes	—
261	#95	—	2	4	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	C₁₉	#11226	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
281	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
288	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	#41×C₁₉	1	2	yes	—
291	C₂²×C₄	#41×C₁₉	1	2	yes	—
292	M₁₆	—	2	4	no	—
293	M₁₆	—	2	4	no	—
294	M₁₆	—	4	2	no	—
295	M₁₆	—	4	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₄⋊C₄	—	2	16	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₄⋊C₄	C₄⋊C₄×C₁₉	1	4	yes	complemented
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	4	no	—
315	C₄²	—	2	4	no	—
316	C₄²	—	4	2	no	—
317	C₄²	—	4	2	no	—
318	C₄²	—	4	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
322	C₂³	C₁₉×#120	1	1	yes	characteristic
323	C₂³	C₁₉×#121	1	1	yes	characteristic
324	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
325	C₂³	C₁₉×#123	1	1	yes	characteristic
326	C₂³	C₁₉×#124	1	1	yes	characteristic
327	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	8	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	C₁₉×#104	1	4	yes	—
350	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
353	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
354	C₂×C₄	C₁₉×#121	1	2	yes	—
355	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
356	C₂×C₄	C₁₉×#121	1	2	yes	—
357	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
358	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
359	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
360	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
361	C₂×C₄	C₁₉×#123	1	2	yes	—
362	C₂×C₄	C₁₉×#125	1	2	yes	—
363	C₂×C₄	C₁₉×#125	1	2	yes	—
364	C₂×C₄	C₁₉×#126	1	2	yes	—
365	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
366	C₈	—	4	4	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	C₁₉×#380	1	1	yes	characteristic
376	C₂²	C₁₉×#386	1	1	yes	characteristic
377	C₂²	C₁₉×#391	1	1	yes	characteristic
378	C₂²	C₁₉×#394	1	1	yes	characteristic
379	C₂²	C₁₉×#395	1	1	yes	characteristic
380	C₂²	C₁₉×#398	1	1	yes	characteristic
381	C₂²	C₁₉×#400	1	1	yes	characteristic
382	C₂²	C₂×C₁₉×#104	1	2	yes	—
383	C₂²	C₁₉×#421	1	2	yes	—
384	C₄	—	2	4	no	—
385	C₄	—	4	8	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	C₁₉×#387	1	2	yes	—
391	C₄	C₁₉×#389	1	2	yes	—
392	C₄	C₁₉×#396	1	2	yes	—
393	C₄	C₁₉×#398	1	2	yes	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	2	1	no	—
397	C₂	—	2	1	no	—
398	C₂	C₁₉×#1441	1	1	yes	characteristic
399	C₂	C₁₉×#1806	1	2	yes	—
400	C₂	C₁₉×#1896	1	1	yes	characteristic
401	C₂	C₁₉×#1897	1	1	yes	characteristic
402	C₂	C₁₉×#1986	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₁₉×#389	C₄	semidirect
13. C₁₉×#389	C₄	semidirect
103. C₄⋊C₄×C₁₉	C₄⋊C₄	semidirect
117. #11226	C₁₉	direct (N × H)
204. #389	C₄×C₁₉	semidirect
205. #389	C₄×C₁₉	semidirect
264. C₁₉	#11226	direct (N × H)
305. C₄⋊C₄	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2296	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#339	2
C₁₉×#1728	2
#11226	19

Subgroups — C19×#11226 #18017185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11226 #18017185