Subgroups — C₁₉×#18541 #18024500

Order 4864.

886 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1653	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1648	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#557	—	2	2	no	—
11	C₁₉×#557	—	2	2	no	—
12	C₁₉×#557	—	2	2	no	—
13	C₁₉×#557	C₂²	1	4	yes	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	—	2	2	no	—
18	C₂×C₁₉×#125	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#501	—	2	2	no	—
24	C₁₉×#500	C₂²	1	2	yes	—
25	C₁₉×#498	C₂²	1	2	yes	—
26	C₁₉×#483	—	2	1	no	—
27	C₁₉×#483	—	2	1	no	—
28	C₁₉×#475	C₂²	1	2	yes	—
29	C₁₉×#475	C₂²	1	2	yes	—
30	C₁₉×#462	C₂²	1	2	yes	—
31	C₁₉×#462	C₂²	1	2	yes	—
32	C₁₉×#451	—	2	1	no	—
33	C₁₉×#451	—	2	1	no	—
34	C₁₉×#441	—	2	2	no	—
35	C₁₉×#441	—	2	2	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	2	no	—
39	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#332	C₂²	1	4	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	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×Q₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	—	2	4	no	—
50	C₁₉×C₄⋊Q₈	—	2	4	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
54	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₁₉×#125	—	2	8	no	—
58	C₁₉×#125	—	2	4	no	—
59	C₁₉×#125	—	2	8	no	—
60	C₁₉×#125	—	2	4	no	—
61	C₁₉×#125	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₄×Q₈×C₁₉	—	2	4	no	—
65	C₄×Q₈×C₁₉	—	2	4	no	—
66	C₄×Q₈×C₁₉	—	2	4	no	—
67	C₄×Q₈×C₁₉	—	2	4	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	D₄	1	2	yes	—
75	C₄×Q₈×C₁₉	D₄	1	2	yes	—
76	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
77	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
78	C₁₉×#117	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	—	2	2	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#107	—	2	4	no	—
93	C₁₉×#106	—	2	4	no	—
94	C₁₉×#106	—	2	2	no	—
95	C₁₉×#106	—	2	2	no	—
96	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
97	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	—	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	C₂³	1	2	yes	—
108	C₂×Q₈×C₁₉	—	2	4	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	4	4	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	Q₁₆×C₁₉	—	4	4	no	—
128	Q₁₆×C₁₉	—	4	4	no	—
129	M₁₆×C₁₉	—	2	4	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	8	no	—
134	C₄⋊C₄×C₁₉	—	2	8	no	—
135	C₄⋊C₄×C₁₉	—	2	8	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₄²×C₁₉	—	2	8	no	—
156	C₄²×C₁₉	—	2	2	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
165	#18541	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	#120	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	2	2	no	—
169	Q₈×C₁₉	—	2	2	no	—
170	Q₈×C₁₉	—	2	2	no	—
171	Q₈×C₁₉	—	4	2	no	—
172	Q₈×C₁₉	—	4	4	no	—
173	Q₈×C₁₉	—	4	4	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	#137	1	4	yes	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₉	—	2	4	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₂×#557	C₂×C₁₉	1	1	yes	characteristic
202	#3165	C₂×C₁₉	1	1	yes	characteristic
203	#3113	C₂×C₁₉	1	1	yes	characteristic
204	#3113	C₂×C₁₉	1	1	yes	characteristic
205	#1653	C₂×C₁₉	1	4	yes	complemented
206	#1648	C₂×C₁₉	1	4	yes	complemented
207	#1556	C₂×C₁₉	1	1	yes	characteristic
208	#1491	C₂×C₁₉	1	1	yes	characteristic
209	#1491	C₂×C₁₉	1	1	yes	characteristic
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	#456	1	2	yes	—
213	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
214	C₄×C₁₉	—	2	4	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	C₂×#137	1	2	yes	—
226	C₄×C₁₉	#575	1	2	yes	—
227	#557	—	2	2	no	—
228	#557	—	2	2	no	—
229	#557	—	2	2	no	—
230	#557	C₂²×C₁₉	1	4	yes	—
231	#533	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	—	2	1	no	—
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#125	—	2	2	no	—
235	C₂×#125	—	2	1	no	—
236	C₂×C₄×Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	—	2	1	no	—
238	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
240	#501	—	2	2	no	—
241	#500	C₂²×C₁₉	1	2	yes	—
242	#498	C₂²×C₁₉	1	2	yes	—
243	#483	—	2	1	no	—
244	#483	—	2	1	no	—
245	#475	C₂²×C₁₉	1	2	yes	—
246	#475	C₂²×C₁₉	1	2	yes	—
247	#462	C₂²×C₁₉	1	2	yes	—
248	#462	C₂²×C₁₉	1	2	yes	—
249	#451	—	2	1	no	—
250	#451	—	2	1	no	—
251	#441	—	2	2	no	—
252	#441	—	2	2	no	—
253	#432	C₂²×C₁₉	1	1	yes	characteristic
254	#432	C₂²×C₁₉	1	1	yes	characteristic
255	#428	—	2	2	no	—
256	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
257	#332	C₂²×C₁₉	1	4	yes	—
258	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
259	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
260	C₂×C₁₉	—	2	2	no	—
261	C₂×C₁₉	#3004	1	1	yes	characteristic
262	C₂×C₁₉	#3005	1	1	yes	characteristic
263	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
266	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄⋊Q₈	—	2	4	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
275	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
277	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
278	#125	—	2	8	no	—
279	#125	—	2	4	no	—
280	#125	—	2	8	no	—
281	#125	—	2	4	no	—
282	#125	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	—	2	4	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	4	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	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	D₄×C₁₉	1	2	yes	—
296	C₄×Q₈	D₄×C₁₉	1	2	yes	—
297	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
298	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
299	#117	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
313	#107	—	2	4	no	—
314	#106	—	2	4	no	—
315	#106	—	2	2	no	—
316	#106	—	2	2	no	—
317	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
318	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	#97	—	2	1	no	—
326	#97	—	2	1	no	—
327	#97	—	2	1	no	—
328	C₄×C₈	C₂³×C₁₉	1	2	yes	—
329	C₁₉	#18541	1	1	yes	characteristic, direct product factor, Sylow
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
340	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
349	Q₁₆	—	4	4	no	—
350	Q₁₆	—	4	4	no	—
351	M₁₆	—	2	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
375	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₄²	—	2	8	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	4	1	no	—
383	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
387	C₂³	C₁₉×#120	1	1	yes	characteristic
388	Q₈	—	2	4	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	4	no	—
394	Q₈	—	4	4	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	C₁₉×#137	1	4	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
415	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
419	C₈	—	2	4	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	C₁₉×#456	1	2	yes	—
425	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	C₂×C₁₉×#137	1	2	yes	—
438	C₄	C₁₉×#575	1	2	yes	—
439	C₂	—	2	2	no	—
440	C₂	C₁₉×#3004	1	1	yes	characteristic
441	C₂	C₁₉×#3005	1	1	yes	characteristic
442	C₂	C₂×C₁₉×#456	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×#1653	C₂	semidirect
6. C₁₉×#1648	C₂	semidirect
165. #18541	C₁₉	direct (N × H)
205. #1653	C₂×C₁₉	semidirect
206. #1648	C₂×C₁₉	semidirect
329. C₁₉	#18541	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#557	2
C₁₉×#3165	2
C₁₉×#3113	2
C₁₉×#1653	2
C₁₉×#1648	2
C₁₉×#1556	2
C₁₉×#1491	2
#18541	19

Subgroups — C19×#18541 #18024500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18541 #18024500