Subgroups — C₁₉×#19363 #18025322

Order 4864.

596 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2966	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1699	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1680	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1679	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₉×#529	C₂²	1	1	yes	characteristic
15	C₁₉×#501	—	2	1	no	—
16	C₁₉×#497	—	2	1	no	—
17	C₁₉×#491	—	2	1	no	—
18	C₁₉×#489	—	2	1	no	—
19	C₁₉×#487	—	2	1	no	—
20	C₁₉×#487	—	2	1	no	—
21	C₁₉×#487	C₂²	1	2	yes	—
22	C₁₉×#487	C₂²	1	2	yes	—
23	C₁₉×#484	—	2	1	no	—
24	C₁₉×#481	—	2	1	no	—
25	C₁₉×#475	C₂²	1	2	yes	—
26	C₁₉×#474	C₂²	1	2	yes	—
27	C₁₉×#462	C₂²	1	2	yes	—
28	C₁₉×#461	C₂²	1	2	yes	—
29	C₁₉×#451	—	2	1	no	—
30	C₁₉×#448	—	2	1	no	—
31	C₁₉×#446	C₂²	1	1	yes	characteristic
32	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#436	C₂²	1	1	yes	characteristic
34	C₁₉×#435	—	2	1	no	—
35	C₈×D₄×C₁₉	—	2	1	no	—
36	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#433	—	2	1	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#432	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#103	—	2	1	no	—
42	C₂×C₁₉×#103	—	2	1	no	—
43	C₁₉×#405	—	2	1	no	—
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#335	C₂²	1	2	yes	—
46	C₁₉×#334	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₁₉×#332	C₂²	1	2	yes	—
50	C₁₉×#332	C₂²	1	2	yes	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₉×#126	—	2	1	no	—
68	C₁₉×#125	D₄	1	1	yes	characteristic
69	C₁₉×#124	D₄	1	1	yes	characteristic
70	C₁₉×#123	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₉×#121	D₄	1	1	yes	characteristic
73	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×#117	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#107	—	2	2	no	—
83	C₁₉×#106	—	2	2	no	—
84	C₁₉×C₄⋊C₈	—	2	1	no	—
85	C₁₉×C₄⋊C₈	—	2	1	no	—
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₉×#103	—	2	2	no	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#103	—	2	2	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#102	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	—	2	1	no	—
99	C₁₉×C₂²⋊C₈	—	2	1	no	—
100	C₁₉×C₂²⋊C₈	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×#97	—	2	1	no	—
104	C₁₉×#97	—	2	1	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	1	no	—
108	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
110	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	4	2	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	8	2	no	—
119	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	Q₁₆×C₁₉	—	8	2	no	—
129	SD₁₆×C₁₉	—	8	2	no	—
130	M₁₆×C₁₉	—	4	2	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	4	1	no	—
136	C₂×C₈×C₁₉	—	4	1	no	—
137	C₂×C₈×C₁₉	—	4	2	no	—
138	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₉	—	2	1	no	—
157	C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂²⋊C₄×C₁₉	—	2	1	no	—
160	C₂²⋊C₄×C₁₉	—	2	1	no	—
161	C₄²×C₁₉	—	2	1	no	—
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	#41	1	1	yes	characteristic
165	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
166	#19363	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	#121	1	1	yes	characteristic
169	Q₈×C₁₉	—	2	2	no	—
170	Q₈×C₁₉	—	4	2	no	—
171	Q₈×C₁₉	—	4	2	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	8	2	no	—
175	Q₈×C₁₉	—	8	2	no	—
176	D₄×C₁₉	—	2	2	no	—
177	D₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
197	C₈×C₁₉	—	2	1	no	—
198	C₈×C₁₉	—	2	1	no	—
199	C₈×C₁₉	—	2	1	no	—
200	C₈×C₁₉	—	2	1	no	—
201	C₈×C₁₉	—	4	1	no	—
202	C₈×C₁₉	—	4	1	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₈×C₁₉	—	4	2	no	—
205	#3239	C₂×C₁₉	1	1	yes	characteristic
206	#3218	C₂×C₁₉	1	1	yes	characteristic
207	C₂×#487	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#2966	C₂×C₁₉	1	1	yes	characteristic
209	#1700	C₂×C₁₉	1	2	yes	complemented
210	#1699	C₂×C₁₉	1	2	yes	complemented
211	#1680	C₂×C₁₉	1	2	yes	complemented
212	#1679	C₂×C₁₉	1	2	yes	complemented
213	#1568	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	—	4	1	no	—
221	C₂²×C₁₉	#473	1	2	yes	—
222	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	4	1	no	—
230	C₄×C₁₉	—	8	2	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	#575	1	1	yes	characteristic
233	C₄×C₁₉	#575	1	1	yes	characteristic
234	C₄×C₁₉	#577	1	2	yes	—
235	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	#529	C₂²×C₁₉	1	1	yes	characteristic
238	#501	—	2	1	no	—
239	#497	—	2	1	no	—
240	#491	—	2	1	no	—
241	#489	—	2	1	no	—
242	#487	—	2	1	no	—
243	#487	—	2	1	no	—
244	#487	C₂²×C₁₉	1	2	yes	—
245	#487	C₂²×C₁₉	1	2	yes	—
246	#484	—	2	1	no	—
247	#481	—	2	1	no	—
248	#475	C₂²×C₁₉	1	2	yes	—
249	#474	C₂²×C₁₉	1	2	yes	—
250	#462	C₂²×C₁₉	1	2	yes	—
251	#461	C₂²×C₁₉	1	2	yes	—
252	#451	—	2	1	no	—
253	#448	—	2	1	no	—
254	#446	C₂²×C₁₉	1	1	yes	characteristic
255	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
256	#436	C₂²×C₁₉	1	1	yes	characteristic
257	#435	—	2	1	no	—
258	C₈×D₄	—	2	1	no	—
259	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
260	#433	—	2	1	no	—
261	#432	C₂²×C₁₉	1	1	yes	characteristic
262	#432	C₂²×C₁₉	1	1	yes	characteristic
263	#432	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×#103	—	2	1	no	—
265	C₂×#103	—	2	1	no	—
266	#405	—	2	1	no	—
267	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
268	#335	C₂²×C₁₉	1	2	yes	—
269	#334	C₂²×C₁₉	1	2	yes	—
270	#332	C₂²×C₁₉	1	2	yes	—
271	#332	C₂²×C₁₉	1	2	yes	—
272	#332	C₂²×C₁₉	1	2	yes	—
273	#332	C₂²×C₁₉	1	2	yes	—
274	C₂×C₁₉	—	2	2	no	—
275	C₂×C₁₉	—	8	1	no	—
276	C₂×C₁₉	#3040	1	1	yes	characteristic
277	C₂×C₁₉	#3057	1	1	yes	characteristic
278	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
295	#126	—	2	1	no	—
296	#125	D₄×C₁₉	1	1	yes	characteristic
297	#124	D₄×C₁₉	1	1	yes	characteristic
298	#123	—	2	1	no	—
299	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
300	#121	D₄×C₁₉	1	1	yes	characteristic
301	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
310	#107	—	2	2	no	—
311	#106	—	2	2	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
317	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#103	—	2	2	no	—
324	#103	—	2	2	no	—
325	#102	—	2	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	#97	—	2	1	no	—
332	#97	—	2	1	no	—
333	#97	—	2	1	no	—
334	#97	—	2	1	no	—
335	C₄×C₈	—	2	1	no	—
336	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
337	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
338	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₁₉	#19363	1	1	yes	characteristic, direct product factor, Sylow
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	4	1	no	—
347	C₂×Q₈	—	8	2	no	—
348	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
357	Q₁₆	—	8	2	no	—
358	SD₁₆	—	8	2	no	—
359	M₁₆	—	4	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₄²	#41×C₁₉	1	1	yes	characteristic
394	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
395	C₂³	—	2	1	no	—
396	C₂³	C₁₉×#121	1	1	yes	characteristic
397	Q₈	—	2	2	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	8	2	no	—
403	Q₈	—	8	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	C₁₉×#473	1	2	yes	—
439	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	2	no	—
449	C₄	C₁₉×#575	1	1	yes	characteristic
450	C₄	C₁₉×#575	1	1	yes	characteristic
451	C₄	C₁₉×#577	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	8	1	no	—
454	C₂	C₁₉×#3040	1	1	yes	characteristic
455	C₂	C₁₉×#3057	1	1	yes	characteristic
456	C₂	C₂×C₁₉×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	D₄
LCS	G ▷ C₄² ▷ 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
3. C₂×C₁₉×#487	C₂	semidirect
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1699	C₂	semidirect
7. C₁₉×#1680	C₂	semidirect
8. C₁₉×#1679	C₂	semidirect
9. C₁₉×#1568	C₂	semidirect
10. C₁₉×#1556	C₂	semidirect
11. C₁₉×#1556	C₂	semidirect
166. #19363	C₁₉	direct (N × H)
207. C₂×#487	C₂×C₁₉	semidirect
209. #1700	C₂×C₁₉	semidirect
210. #1699	C₂×C₁₉	semidirect
211. #1680	C₂×C₁₉	semidirect
212. #1679	C₂×C₁₉	semidirect
213. #1568	C₂×C₁₉	semidirect
214. #1556	C₂×C₁₉	semidirect
215. #1556	C₂×C₁₉	semidirect
340. C₁₉	#19363	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×#3239	2
C₁₉×#3218	2
C₂×C₁₉×#487	2
C₁₉×#2966	2
C₁₉×#1700	2
C₁₉×#1699	2
C₁₉×#1680	2
C₁₉×#1679	2
C₁₉×#1568	2
C₁₉×#1556	2
#19363	19

Subgroups — C19×#19363 #18025322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19363 #18025322