Subgroups — C₁₉×#19686 #18025645

Order 4864.

712 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1720	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1719	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1718	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1716	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₁₉×#501	—	2	2	no	—
17	C₁₉×#500	C₂²	1	2	yes	—
18	C₁₉×#498	C₂²	1	1	yes	characteristic
19	C₁₉×#498	C₂²	1	2	yes	—
20	C₁₉×#498	C₂²	1	2	yes	—
21	C₁₉×#494	C₂²	1	2	yes	—
22	C₁₉×#492	C₂²	1	1	yes	characteristic
23	C₁₉×#489	—	2	2	no	—
24	C₁₉×#487	—	2	2	no	—
25	C₁₉×#487	C₂²	1	1	yes	characteristic
26	C₁₉×#487	C₂²	1	2	yes	—
27	C₁₉×#487	C₂²	1	2	yes	—
28	C₁₉×#487	C₂²	1	2	yes	—
29	C₁₉×#487	C₂²	1	2	yes	—
30	C₁₉×#486	C₂²	1	1	yes	characteristic
31	C₁₉×#486	C₂²	1	2	yes	—
32	C₁₉×#486	C₂²	1	2	yes	—
33	C₁₉×#481	—	2	2	no	—
34	C₁₉×#476	—	2	2	no	—
35	C₁₉×#465	—	2	2	no	—
36	C₁₉×#462	—	2	2	no	—
37	C₁₉×#451	—	2	2	no	—
38	C₄×SD₁₆×C₁₉	—	2	2	no	—
39	C₁₉×#431	C₂²	1	1	yes	characteristic
40	C₁₉×#428	—	2	2	no	—
41	C₁₉×#417	—	2	2	no	—
42	C₂×C₁₉×#103	—	2	2	no	—
43	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#322	C₂²	1	2	yes	—
46	C₁₉×#322	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂×Q₁₆×C₁₉	—	2	4	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
53	C₂²×C₈×C₁₉	D₄	1	2	yes	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₉×#127	C₂³	1	1	yes	characteristic
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₁₉×#121	—	2	1	no	—
71	C₁₉×#121	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	—	2	1	no	—
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	4	no	—
83	C₁₉×#106	—	2	4	no	—
84	C₁₉×#106	—	2	2	no	—
85	C₁₉×#106	—	2	4	no	—
86	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
87	C₁₉×#103	—	2	4	no	—
88	C₁₉×#103	—	2	4	no	—
89	C₁₉×#103	—	2	4	no	—
90	C₁₉×#103	—	2	2	no	—
91	C₁₉×#103	—	2	4	no	—
92	C₁₉×#102	—	2	4	no	—
93	C₁₉×#102	—	2	2	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
96	C₁₉×#97	D₄	1	2	yes	—
97	C₄×C₈×C₁₉	D₄	1	2	yes	—
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₉	C₂³	1	2	yes	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	#41×C₁₉	—	4	4	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	4	4	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	8	2	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	Q₁₆×C₁₉	—	8	4	no	—
123	SD₁₆×C₁₉	—	4	4	no	—
124	M₁₆×C₁₉	—	2	4	no	—
125	C₂×C₈×C₁₉	—	4	2	no	—
126	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
129	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₂²⋊C₄×C₁₉	—	4	1	no	—
147	C₂²⋊C₄×C₁₉	—	4	1	no	—
148	C₂²⋊C₄×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	—	4	1	no	—
150	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
154	#19686	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	#127	1	1	yes	characteristic
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	4	no	—
160	Q₈×C₁₉	—	4	2	no	—
161	Q₈×C₁₉	—	4	4	no	—
162	Q₈×C₁₉	—	8	2	no	—
163	Q₈×C₁₉	—	8	2	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	—	8	2	no	—
177	C₂×C₄×C₁₉	—	8	2	no	—
178	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#137	1	4	yes	—
182	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₈×C₁₉	—	2	4	no	—
186	C₈×C₁₉	—	2	2	no	—
187	C₈×C₁₉	—	2	2	no	—
188	C₈×C₁₉	—	2	4	no	—
189	#3227	C₂×C₁₉	1	1	yes	characteristic
190	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#3167	C₂×C₁₉	1	1	yes	characteristic
192	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#3141	C₂×C₁₉	1	1	yes	characteristic
194	C₂×#487	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1720	C₂×C₁₉	1	2	yes	complemented
196	#1719	C₂×C₁₉	1	2	yes	complemented
197	#1718	C₂×C₁₉	1	2	yes	complemented
198	#1716	C₂×C₁₉	1	2	yes	complemented
199	#1451	C₂×C₁₉	1	1	yes	characteristic, complemented
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	#497	1	2	yes	—
206	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	8	1	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	—	8	1	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	—	8	1	no	—
214	C₄×C₁₉	#497	1	2	yes	—
215	C₄×C₁₉	C₂×#137	1	2	yes	—
216	C₄×C₁₉	#575	1	2	yes	—
217	C₄×C₁₉	#577	1	2	yes	—
218	#533	C₂²×C₁₉	1	1	yes	characteristic
219	#532	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
222	#501	—	2	2	no	—
223	#500	C₂²×C₁₉	1	2	yes	—
224	#498	C₂²×C₁₉	1	2	yes	—
225	#498	C₂²×C₁₉	1	1	yes	characteristic
226	#498	C₂²×C₁₉	1	2	yes	—
227	#494	C₂²×C₁₉	1	2	yes	—
228	#492	C₂²×C₁₉	1	1	yes	characteristic
229	#489	—	2	2	no	—
230	#487	—	2	2	no	—
231	#487	C₂²×C₁₉	1	2	yes	—
232	#487	C₂²×C₁₉	1	2	yes	—
233	#487	C₂²×C₁₉	1	2	yes	—
234	#487	C₂²×C₁₉	1	1	yes	characteristic
235	#487	C₂²×C₁₉	1	2	yes	—
236	#486	C₂²×C₁₉	1	2	yes	—
237	#486	C₂²×C₁₉	1	1	yes	characteristic
238	#486	C₂²×C₁₉	1	2	yes	—
239	#481	—	2	2	no	—
240	#476	—	2	2	no	—
241	#465	—	2	2	no	—
242	#462	—	2	2	no	—
243	#451	—	2	2	no	—
244	C₄×SD₁₆	—	2	2	no	—
245	#431	C₂²×C₁₉	1	1	yes	characteristic
246	#428	—	2	2	no	—
247	#417	—	2	2	no	—
248	C₂×#103	—	2	2	no	—
249	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
251	#322	C₂²×C₁₉	1	2	yes	—
252	#322	C₂²×C₁₉	1	2	yes	—
253	C₂×C₁₉	—	2	2	no	—
254	C₂×C₁₉	—	16	1	no	—
255	C₂×C₁₉	C₂×#497	1	1	yes	characteristic
256	C₂×C₁₉	#3153	1	1	yes	characteristic
257	C₂×C₁₉	#3154	1	1	yes	characteristic
258	C₂×#41	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂×Q₁₆	—	2	4	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
264	C₂²×C₈	D₄×C₁₉	1	2	yes	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
272	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
273	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
274	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
276	#127	C₂³×C₁₉	1	1	yes	characteristic
277	#125	—	2	1	no	—
278	#124	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	#117	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
293	#107	—	2	4	no	—
294	#106	—	2	4	no	—
295	#106	—	2	2	no	—
296	#106	—	2	4	no	—
297	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
298	#103	—	2	4	no	—
299	#103	—	2	4	no	—
300	#103	—	2	4	no	—
301	#103	—	2	2	no	—
302	#103	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	—	2	2	no	—
305	#102	—	2	4	no	—
306	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
307	#97	D₄×C₁₉	1	2	yes	—
308	C₄×C₈	D₄×C₁₉	1	2	yes	—
309	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₁₉	1	2	yes	—
312	C₄×C₈	C₂³×C₁₉	1	2	yes	—
313	C₁₉	#19686	1	1	yes	characteristic, direct product factor, Sylow
314	#41	—	4	4	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	Q₁₆	—	8	4	no	—
335	SD₁₆	—	4	4	no	—
336	M₁₆	—	2	4	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
341	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
366	C₂³	—	4	1	no	—
367	C₂³	C₁₉×#127	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	4	no	—
373	Q₈	—	8	2	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
392	C₂×C₄	C₁₉×#137	1	4	yes	—
393	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
396	C₈	—	2	4	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	4	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₁₉×#497	1	2	yes	—
406	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	C₁₉×#497	1	2	yes	—
415	C₄	C₂×C₁₉×#137	1	2	yes	—
416	C₄	C₁₉×#575	1	2	yes	—
417	C₄	C₁₉×#577	1	2	yes	—
418	C₂	—	2	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₁₉×#497	1	1	yes	characteristic
421	C₂	C₁₉×#3153	1	1	yes	characteristic
422	C₂	C₁₉×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
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
2. C₁₉×#3209	C₂	semidirect
4. C₁₉×#3165	C₂	semidirect
6. C₂×C₁₉×#487	C₂	semidirect
7. C₁₉×#1720	C₂	semidirect
8. C₁₉×#1719	C₂	semidirect
9. C₁₉×#1718	C₂	semidirect
10. C₁₉×#1716	C₂	semidirect
11. C₁₉×#1451	C₂	semidirect
154. #19686	C₁₉	direct (N × H)
190. #3209	C₂×C₁₉	semidirect
192. #3165	C₂×C₁₉	semidirect
194. C₂×#487	C₂×C₁₉	semidirect
195. #1720	C₂×C₁₉	semidirect
196. #1719	C₂×C₁₉	semidirect
197. #1718	C₂×C₁₉	semidirect
198. #1716	C₂×C₁₉	semidirect
199. #1451	C₂×C₁₉	semidirect
313. C₁₉	#19686	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×#3227	2
C₁₉×#3209	2
C₁₉×#3167	2
C₁₉×#3165	2
C₁₉×#3141	2
C₂×C₁₉×#487	2
C₁₉×#1720	2
C₁₉×#1719	2
C₁₉×#1718	2
C₁₉×#1716	2
C₁₉×#1451	2
#19686	19

Subgroups — C19×#19686 #18025645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19686 #18025645