Subgroups — C₁₉×#20962 #18026921

Order 4864.

1742 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3428	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2310	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1890	C₂	1	8	yes	maximal, complemented
6	C₁₉×#1740	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#536	—	2	4	no	—
10	C₁₉×#536	C₄	1	8	yes	complemented
11	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×#124	—	2	1	no	—
13	C₂×C₁₉×#123	C₂²	1	4	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
15	C₁₉×#520	—	2	4	no	—
16	C₁₉×#519	—	2	1	no	—
17	C₁₉×#518	—	2	1	no	—
18	C₁₉×#518	C₂²	1	4	yes	—
19	C₄×#41×C₁₉	—	2	4	no	—
20	C₂×C₁₉×#117	—	2	2	no	—
21	C₂×C₁₉×#117	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₁₉×#410	—	2	4	no	—
25	C₂×C₁₉×#99	C₂²	1	4	yes	—
26	C₁₉×#391	—	2	4	no	—
27	C₁₉×#391	—	2	4	no	—
28	C₁₉×#381	C₂²	1	8	yes	—
29	C₁₉×#342	C₂²	1	8	yes	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	4	no	—
33	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
34	C₂×#41×C₁₉	D₄	1	4	yes	—
35	C₂²×Q₈×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	—	2	4	no	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	D₄	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	—	2	8	no	—
49	C₁₉×#124	—	2	8	no	—
50	C₁₉×#123	—	2	8	no	—
51	C₁₉×#123	C₂×C₄	1	16	yes	complemented
52	C₁₉×C₂²⋊Q₈	—	2	16	no	—
53	C₄×Q₈×C₁₉	—	2	8	no	—
54	C₄×D₄×C₁₉	—	2	8	no	—
55	C₄×D₄×C₁₉	—	2	16	no	—
56	C₁₉×#117	—	2	4	no	—
57	C₁₉×#117	—	2	4	no	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	—	2	4	no	—
60	C₁₉×#117	—	2	2	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	—	2	4	no	—
65	C₁₉×#117	—	2	4	no	—
66	C₁₉×#117	C₂×C₄	1	4	yes	complemented
67	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₉	—	2	4	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	D₄	1	4	yes	—
81	C₁₉×#99	—	2	8	no	—
82	C₁₉×#95	—	2	16	no	—
83	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
84	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
85	#41×C₁₉	—	2	8	no	—
86	#41×C₁₉	—	2	8	no	—
87	#41×C₁₉	—	2	8	no	—
88	#41×C₁₉	—	2	8	no	—
89	C₂×Q₈×C₁₉	—	2	4	no	—
90	C₂×Q₈×C₁₉	—	2	4	no	—
91	C₂×Q₈×C₁₉	—	2	8	no	—
92	C₂×Q₈×C₁₉	—	2	8	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	4	1	no	—
96	C₂×Q₈×C₁₉	—	4	2	no	—
97	C₂×Q₈×C₁₉	—	4	1	no	—
98	C₂×Q₈×C₁₉	—	4	4	no	—
99	C₂×Q₈×C₁₉	—	4	4	no	—
100	C₂×Q₈×C₁₉	—	4	2	no	—
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
108	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
109	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	8	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
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	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	#41	1	4	yes	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	16	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	4	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	8	no	—
138	C₂²⋊C₄×C₁₉	—	2	16	no	—
139	C₂²⋊C₄×C₁₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	2	4	no	—
144	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
145	C₄²×C₁₉	—	2	8	no	—
146	C₄²×C₁₉	—	2	4	no	—
147	C₄²×C₁₉	—	2	4	no	—
148	C₄²×C₁₉	—	2	4	no	—
149	C₄²×C₁₉	—	4	4	no	—
150	#20962	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	4	no	—
155	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
157	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
159	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
160	C₂³×C₁₉	C₂×#41	1	2	yes	—
161	Q₈×C₁₉	—	2	8	no	—
162	Q₈×C₁₉	—	4	4	no	—
163	Q₈×C₁₉	—	4	4	no	—
164	Q₈×C₁₉	—	4	8	no	—
165	D₄×C₁₉	—	2	8	no	—
166	D₄×C₁₉	—	2	8	no	—
167	D₄×C₁₉	—	2	8	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	8	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	8	no	—
175	C₂×C₄×C₁₉	—	2	8	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	8	no	—
181	C₂×C₄×C₁₉	—	4	8	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	8	8	no	—
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
189	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#120	1	2	yes	—
191	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	4	yes	—
193	C₂×C₄×C₁₉	#121	1	4	yes	—
194	C₂×C₄×C₁₉	#123	1	2	yes	—
195	C₂×C₄×C₁₉	#123	1	2	yes	—
196	C₂×#536	C₂×C₁₉	1	1	yes	characteristic
197	#3428	C₂×C₁₉	1	1	yes	characteristic
198	C₂×#410	C₂×C₁₉	1	1	yes	characteristic
199	#2310	C₂×C₁₉	1	2	yes	complemented
200	#1890	C₂×C₁₉	1	8	yes	complemented
201	#1740	C₂×C₁₉	1	2	yes	complemented
202	C₂²×C₁₉	—	2	4	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	4	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	4	no	—
209	C₂²×C₁₉	—	4	4	no	—
210	C₂²×C₁₉	—	8	2	no	—
211	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
213	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×#121	1	2	yes	—
215	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
216	C₄×C₁₉	—	2	4	no	—
217	C₄×C₁₉	—	4	4	no	—
218	C₄×C₁₉	—	4	8	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	8	4	no	—
221	C₄×C₁₉	#386	1	2	yes	—
222	C₄×C₁₉	#386	1	2	yes	—
223	C₄×C₁₉	#386	1	4	yes	—
224	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
225	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
226	#536	—	2	4	no	—
227	#536	C₄×C₁₉	1	8	yes	complemented
228	C₂×C₄⋊Q₈	—	2	1	no	—
229	C₂×#124	—	2	1	no	—
230	C₂×#123	C₂²×C₁₉	1	4	yes	—
231	C₂×C₂²⋊Q₈	—	2	2	no	—
232	#520	—	2	4	no	—
233	#519	—	2	1	no	—
234	#518	—	2	1	no	—
235	#518	C₂²×C₁₉	1	4	yes	—
236	C₄×#41	—	2	4	no	—
237	C₂×#117	—	2	2	no	—
238	C₂×#117	C₂²×C₁₉	1	2	yes	—
239	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×#117	C₂²×C₁₉	1	2	yes	—
241	#410	—	2	4	no	—
242	C₂×#99	C₂²×C₁₉	1	4	yes	—
243	#391	—	2	4	no	—
244	#391	—	2	4	no	—
245	#381	C₂²×C₁₉	1	8	yes	—
246	#342	C₂²×C₁₉	1	8	yes	—
247	C₂×C₁₉	—	2	1	no	—
248	C₂×C₁₉	—	2	2	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	2	no	—
251	C₂×C₁₉	—	4	4	no	—
252	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
253	C₂×C₁₉	#3028	1	2	yes	—
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
258	C₂×#41	D₄×C₁₉	1	4	yes	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	—	2	2	no	—
262	C₂²×Q₈	—	2	2	no	—
263	C₂²×Q₈	—	2	2	no	—
264	C₂²×Q₈	—	2	4	no	—
265	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
266	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
267	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
268	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
269	C₂³×C₄	D₄×C₁₉	1	2	yes	—
270	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	8	no	—
273	#124	—	2	8	no	—
274	#123	—	2	8	no	—
275	#123	C₂×C₄×C₁₉	1	16	yes	complemented
276	C₂²⋊Q₈	—	2	16	no	—
277	C₄×Q₈	—	2	8	no	—
278	C₄×D₄	—	2	8	no	—
279	C₄×D₄	—	2	16	no	—
280	#117	—	2	4	no	—
281	#117	—	2	4	no	—
282	#117	—	2	2	no	—
283	#117	—	2	4	no	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	#117	—	2	4	no	—
289	#117	—	2	4	no	—
290	#117	C₂×C₄×C₁₉	1	4	yes	complemented
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
296	C₂×C₂²⋊C₄	—	2	4	no	—
297	C₂×C₂²⋊C₄	—	2	4	no	—
298	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
301	C₂×C₄²	—	2	4	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	D₄×C₁₉	1	4	yes	—
305	#99	—	2	8	no	—
306	#95	—	2	16	no	—
307	C₁₉	#20962	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
309	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
310	#41	—	2	8	no	—
311	#41	—	2	8	no	—
312	#41	—	2	8	no	—
313	#41	—	2	8	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	8	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
333	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
334	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
346	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
347	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
355	C₂²×C₄	#41×C₁₉	1	4	yes	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	16	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	16	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
370	C₄²	—	2	8	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	4	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	4	no	—
379	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
380	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
381	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
383	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
384	C₂³	C₂×#41×C₁₉	1	2	yes	—
385	Q₈	—	2	8	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	4	4	no	—
388	Q₈	—	4	8	no	—
389	D₄	—	2	8	no	—
390	D₄	—	2	8	no	—
391	D₄	—	2	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	8	8	no	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
410	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
412	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
413	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#120	1	2	yes	—
415	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
416	C₂×C₄	C₁₉×#121	1	4	yes	—
417	C₂×C₄	C₁₉×#121	1	4	yes	—
418	C₂×C₄	C₁₉×#123	1	2	yes	—
419	C₂×C₄	C₁₉×#123	1	2	yes	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
430	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
431	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
432	C₂²	C₂×C₁₉×#121	1	2	yes	—
433	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	8	no	—
437	C₄	—	4	4	no	—
438	C₄	—	8	4	no	—
439	C₄	C₁₉×#386	1	2	yes	—
440	C₄	C₁₉×#386	1	2	yes	—
441	C₄	C₁₉×#386	1	4	yes	—
442	C₂	—	2	1	no	—
443	C₂	—	2	2	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	4	no	—
447	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
448	C₂	C₁₉×#3028	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#2310	C₂	semidirect
5. C₁₉×#1890	C₂	semidirect
6. C₁₉×#1740	C₂	semidirect
10. C₁₉×#536	C₄	semidirect
41. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
51. C₁₉×#123	C₂×C₄	semidirect
66. C₁₉×#117	C₂×C₄	semidirect
150. #20962	C₁₉	direct (N × H)
199. #2310	C₂×C₁₉	semidirect
200. #1890	C₂×C₁₉	semidirect
201. #1740	C₂×C₁₉	semidirect
227. #536	C₄×C₁₉	semidirect
265. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
275. #123	C₂×C₄×C₁₉	semidirect
290. #117	C₂×C₄×C₁₉	semidirect
307. C₁₉	#20962	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×#536	2
C₁₉×#3428	2
C₂×C₁₉×#410	2
C₁₉×#2310	2
C₁₉×#1890	2
C₁₉×#1740	2
#20962	19

Subgroups — C19×#20962 #18026921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20962 #18026921