Subgroups — C₁₉×#18925 #18024884

Order 4864.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3502	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1648	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1645	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1542	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1481	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₁₉	—	2	1	no	—
11	Q₈²×C₁₉	C₂²	1	2	yes	—
12	C₁₉×#557	—	2	1	no	—
13	C₁₉×#557	—	2	2	no	—
14	C₁₉×#557	—	2	2	no	—
15	C₁₉×#557	C₂²	1	2	yes	—
16	C₁₉×#544	—	2	2	no	—
17	C₁₉×#544	—	2	1	no	—
18	C₁₉×#533	—	2	2	no	—
19	C₁₉×#533	C₂²	1	1	yes	characteristic
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₉×#519	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#500	C₂²	1	2	yes	—
25	C₁₉×#494	—	2	1	no	—
26	C₁₉×#487	—	2	1	no	—
27	C₁₉×#487	C₂²	1	2	yes	—
28	C₁₉×#484	—	2	2	no	—
29	C₁₉×#477	—	2	2	no	—
30	C₁₉×#475	—	2	2	no	—
31	C₁₉×#475	C₂²	1	4	yes	—
32	C₁₉×#462	C₂²	1	4	yes	—
33	C₁₉×#451	—	2	2	no	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#106	—	2	1	no	—
37	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#103	—	2	1	no	—
39	C₁₉×#333	C₂²	1	2	yes	—
40	C₁₉×#332	C₂²	1	2	yes	—
41	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₉	—	2	4	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	4	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	4	no	—
51	C₁₉×C₄⋊Q₈	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×#125	—	2	4	no	—
62	C₁₉×#125	—	2	4	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	4	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	4	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
72	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	2	4	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	D₄	1	2	yes	—
85	C₄×Q₈×C₁₉	D₄	1	2	yes	—
86	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
87	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
88	C₁₉×#117	—	2	4	no	—
89	C₁₉×#117	—	2	1	no	—
90	C₁₉×#117	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#107	—	2	4	no	—
98	C₁₉×#106	—	2	4	no	—
99	C₁₉×C₄⋊C₈	—	2	1	no	—
100	C₁₉×C₄⋊C₈	—	2	1	no	—
101	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
102	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
103	C₁₉×#103	—	2	4	no	—
104	C₁₉×#103	—	2	4	no	—
105	C₁₉×#103	—	2	4	no	—
106	C₁₉×C₂²⋊C₈	—	2	1	no	—
107	C₁₉×C₂²⋊C₈	—	2	1	no	—
108	C₄×C₈×C₁₉	—	2	1	no	—
109	C₄×C₈×C₁₉	C₂³	1	2	yes	—
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	8	2	no	—
118	C₂×Q₈×C₁₉	Q₁₆	1	4	yes	complemented
119	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	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	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₁₉	—	8	4	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	4	2	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	4	no	—
137	C₄⋊C₄×C₁₉	—	2	4	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	4	no	—
161	C₄²×C₁₉	—	2	4	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
170	#18925	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	#120	1	1	yes	characteristic
172	Q₈×C₁₉	—	2	2	no	—
173	Q₈×C₁₉	—	2	4	no	—
174	Q₈×C₁₉	—	2	4	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	4	no	—
178	Q₈×C₁₉	—	8	1	no	—
179	Q₈×C₁₉	—	8	2	no	—
180	Q₈×C₁₉	—	8	4	no	—
181	Q₈×C₁₉	C₂×Q₁₆	1	4	yes	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	8	1	no	—
193	C₂×C₄×C₁₉	—	8	2	no	—
194	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
198	C₂×C₄×C₁₉	#137	1	2	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₈×C₁₉	—	4	2	no	—
205	#3502	C₂×C₁₉	1	1	yes	characteristic
206	#3230	C₂×C₁₉	1	1	yes	characteristic
207	#3209	C₂×C₁₉	1	1	yes	characteristic
208	C₂×#475	C₂×C₁₉	1	1	yes	characteristic
209	#1648	C₂×C₁₉	1	4	yes	complemented
210	#1645	C₂×C₁₉	1	4	yes	complemented
211	#1542	C₂×C₁₉	1	1	yes	characteristic
212	#1481	C₂×C₁₉	1	1	yes	characteristic
213	#1479	C₂×C₁₉	1	1	yes	characteristic
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	#451	1	2	yes	—
217	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
218	C₄×C₁₉	—	2	4	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	#451	1	2	yes	—
229	C₄×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
230	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
231	C₄×C₁₉	#577	1	2	yes	—
232	Q₈²	—	2	1	no	—
233	Q₈²	C₂²×C₁₉	1	2	yes	—
234	#557	—	2	1	no	—
235	#557	—	2	2	no	—
236	#557	—	2	2	no	—
237	#557	C₂²×C₁₉	1	2	yes	—
238	#544	—	2	2	no	—
239	#544	—	2	1	no	—
240	#533	—	2	2	no	—
241	#533	C₂²×C₁₉	1	1	yes	characteristic
242	#533	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	#519	—	2	1	no	—
245	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
246	#500	C₂²×C₁₉	1	2	yes	—
247	#494	—	2	1	no	—
248	#487	—	2	1	no	—
249	#487	C₂²×C₁₉	1	2	yes	—
250	#484	—	2	2	no	—
251	#477	—	2	2	no	—
252	#475	—	2	2	no	—
253	#475	C₂²×C₁₉	1	4	yes	—
254	#462	C₂²×C₁₉	1	4	yes	—
255	#451	—	2	2	no	—
256	#431	C₂²×C₁₉	1	1	yes	characteristic
257	#431	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#106	—	2	1	no	—
259	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#103	—	2	1	no	—
261	#333	C₂²×C₁₉	1	2	yes	—
262	#332	C₂²×C₁₉	1	2	yes	—
263	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
264	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
265	C₂×C₁₉	—	2	2	no	—
266	C₂×C₁₉	C₂×#451	1	1	yes	characteristic
267	C₂×C₁₉	#3010	1	1	yes	characteristic
268	C₂×C₁₉	#3022	1	1	yes	characteristic
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
271	C₂×Q₁₆	—	2	4	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	4	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
283	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
284	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
285	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
287	#125	—	2	4	no	—
288	#125	—	2	4	no	—
289	#125	—	2	2	no	—
290	#125	—	2	4	no	—
291	#125	—	2	2	no	—
292	#125	—	2	1	no	—
293	#125	—	2	1	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
298	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	D₄×C₁₉	1	2	yes	—
311	C₄×Q₈	D₄×C₁₉	1	2	yes	—
312	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
313	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
314	#117	—	2	4	no	—
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
323	#107	—	2	4	no	—
324	#106	—	2	4	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
328	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
329	#103	—	2	4	no	—
330	#103	—	2	4	no	—
331	#103	—	2	4	no	—
332	C₂²⋊C₈	—	2	1	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₄×C₈	—	2	1	no	—
335	C₄×C₈	C₂³×C₁₉	1	2	yes	—
336	C₁₉	#18925	1	1	yes	characteristic, direct product factor, Sylow
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	1	no	—
344	C₂×Q₈	—	8	2	no	—
345	C₂×Q₈	Q₁₆×C₁₉	1	4	yes	complemented
346	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
347	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
348	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	Q₁₆	—	8	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
383	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
397	C₂³	C₁₉×#120	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	4	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	4	no	—
404	Q₈	—	8	1	no	—
405	Q₈	—	8	2	no	—
406	Q₈	—	8	4	no	—
407	Q₈	C₂×Q₁₆×C₁₉	1	4	yes	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	1	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
422	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
423	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
424	C₂×C₄	C₁₉×#137	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	C₁₉×#451	1	2	yes	—
434	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	2	no	—
445	C₄	C₁₉×#451	1	2	yes	—
446	C₄	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
447	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
448	C₄	C₁₉×#577	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	C₂×C₁₉×#451	1	1	yes	characteristic
451	C₂	C₁₉×#3010	1	1	yes	characteristic
452	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#120
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
5. C₁₉×#1648	C₂	semidirect
6. C₁₉×#1645	C₂	semidirect
118. C₂×Q₈×C₁₉	Q₁₆	semidirect
170. #18925	C₁₉	direct (N × H)
209. #1648	C₂×C₁₉	semidirect
210. #1645	C₂×C₁₉	semidirect
336. C₁₉	#18925	direct (N × H)
345. C₂×Q₈	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3502	2
C₁₉×#3230	2
C₁₉×#3209	2
C₂×C₁₉×#475	2
C₁₉×#1648	2
C₁₉×#1645	2
C₁₉×#1542	2
C₁₉×#1481	2
C₁₉×#1479	2
#18925	19

Subgroups — C19×#18925 #18024884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18925 #18024884