Subgroups — C₁₉×#21411 #18027370

Order 4864.

1174 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×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1991	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1958	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1895	C₂	1	2	yes	maximal
7	C₁₉×#1894	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1763	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1762	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#529	—	2	4	no	—
12	C₁₉×#529	C₄	1	8	yes	complemented
13	C₂×C₁₉×#126	—	2	1	no	—
14	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#123	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	—	2	1	no	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	4	yes	—
25	C₂×C₁₉×#102	C₂²	1	4	yes	—
26	C₄×M₁₆×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#383	—	2	1	no	—
30	C₁₉×#382	C₂²	1	2	yes	—
31	C₁₉×#381	—	2	1	no	—
32	C₁₉×#380	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
35	C₁₉×#376	—	2	1	no	—
36	C₁₉×#340	C₂²	1	4	yes	—
37	C₁₉×#340	C₂²	1	4	yes	—
38	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	—	2	8	no	—
47	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
48	C₁₉×#126	—	2	8	no	—
49	C₁₉×#125	—	2	2	no	—
50	C₁₉×#125	C₂×C₄	1	4	yes	—
51	C₁₉×#124	—	2	2	no	—
52	C₁₉×#124	C₂×C₄	1	4	yes	—
53	C₁₉×#123	—	2	8	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	C₂×C₄	1	4	yes	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
60	C₄×D₄×C₁₉	—	2	8	no	—
61	C₄×D₄×C₁₉	—	2	2	no	—
62	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
63	C₁₉×#117	—	2	8	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
80	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	D₄	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#103	—	2	8	no	—
86	C₁₉×#102	—	2	8	no	—
87	C₁₉×#97	—	2	4	no	—
88	C₄×C₈×C₁₉	—	2	4	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	4	no	—
97	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₁₉	—	2	4	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	4	4	no	—
102	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	4	no	—
112	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
113	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
114	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₁₉	—	2	16	no	—
123	C₂×C₈×C₁₉	—	2	4	no	—
124	C₂×C₈×C₁₉	—	2	4	no	—
125	C₂×C₈×C₁₉	#41	1	8	yes	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	4	no	—
138	C₂²⋊C₄×C₁₉	—	2	4	no	—
139	C₂²⋊C₄×C₁₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₉	—	4	4	no	—
142	C₄²×C₁₉	—	2	4	no	—
143	C₄²×C₁₉	—	4	4	no	—
144	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
145	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
146	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
148	C₄²×C₁₉	C₂×D₄	1	2	yes	—
149	C₄²×C₁₉	C₂×D₄	1	2	yes	—
150	#21411	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	—	2	2	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₉	—	2	4	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	2	4	no	—
163	D₄×C₁₉	—	4	8	no	—
164	D₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	8	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	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	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
192	C₈×C₁₉	—	2	8	no	—
193	C₂×#529	C₂×C₁₉	1	1	yes	characteristic
194	C₂×C₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#2283	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1991	C₂×C₁₉	1	2	yes	complemented
197	#1958	C₂×C₁₉	1	2	yes	complemented
198	#1895	C₂×C₁₉	1	2	yes	—
199	#1894	C₂×C₁₉	1	2	yes	complemented
200	#1763	C₂×C₁₉	1	2	yes	complemented
201	#1762	C₂×C₁₉	1	2	yes	complemented
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	8	4	no	—
210	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₁₉	#532	1	2	yes	—
212	C₂²×C₁₉	#575	1	2	yes	—
213	C₂²×C₁₉	#575	1	2	yes	—
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	8	4	no	—
223	C₄×C₁₉	C₄×#41	1	2	yes	—
224	C₄×C₁₉	#525	1	2	yes	—
225	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
226	#529	—	2	4	no	—
227	#529	C₄×C₁₉	1	8	yes	complemented
228	C₂×#126	—	2	1	no	—
229	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×#123	—	2	1	no	—
232	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#117	—	2	1	no	—
238	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#103	C₂²×C₁₉	1	4	yes	—
240	C₂×#102	C₂²×C₁₉	1	4	yes	—
241	C₄×M₁₆	—	2	4	no	—
242	C₂×#97	C₂²×C₁₉	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
244	#383	—	2	1	no	—
245	#382	C₂²×C₁₉	1	2	yes	—
246	#381	—	2	1	no	—
247	#380	C₂²×C₁₉	1	2	yes	—
248	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
249	C₄×C₂²⋊C₄	—	2	1	no	—
250	#376	—	2	1	no	—
251	#340	C₂²×C₁₉	1	4	yes	—
252	#340	C₂²×C₁₉	1	4	yes	—
253	C₂×C₁₉	—	4	2	no	—
254	C₂×C₁₉	—	8	2	no	—
255	C₂×C₁₉	#2297	1	1	yes	characteristic
256	C₂×C₁₉	#2896	1	1	yes	characteristic
257	C₂×C₁₉	#2896	1	1	yes	characteristic
258	C₂×C₁₉	#3183	1	4	yes	—
259	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
265	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	—	2	8	no	—
268	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
269	#126	—	2	8	no	—
270	#125	—	2	2	no	—
271	#125	C₂×C₄×C₁₉	1	4	yes	—
272	#124	—	2	2	no	—
273	#124	C₂×C₄×C₁₉	1	4	yes	—
274	#123	—	2	8	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
277	#121	—	2	2	no	—
278	#121	C₂×C₄×C₁₉	1	4	yes	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
281	C₄×D₄	—	2	8	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
284	#117	—	2	8	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
301	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₁₉	1	4	yes	—
304	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
306	#103	—	2	8	no	—
307	#102	—	2	8	no	—
308	#97	—	2	4	no	—
309	C₄×C₈	—	2	4	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₁₉	#21411	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	—	2	1	no	—
316	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
335	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
336	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
344	M₁₆	—	2	16	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	#41×C₁₉	1	8	yes	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
357	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	4	4	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	4	4	no	—
366	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
367	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
368	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
369	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
370	C₄²	C₂×D₄×C₁₉	1	2	yes	—
371	C₄²	C₂×D₄×C₁₉	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
380	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
381	Q₈	—	2	4	no	—
382	Q₈	—	4	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	8	no	—
385	D₄	—	4	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
410	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
413	C₈	—	2	8	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	4	no	—
422	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
423	C₂²	C₁₉×#532	1	2	yes	—
424	C₂²	C₁₉×#575	1	2	yes	—
425	C₂²	C₁₉×#575	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	4	no	—
435	C₄	C₄×#41×C₁₉	1	2	yes	—
436	C₄	C₁₉×#525	1	2	yes	—
437	C₂	—	4	2	no	—
438	C₂	—	8	2	no	—
439	C₂	C₁₉×#2297	1	1	yes	characteristic
440	C₂	C₁₉×#2896	1	1	yes	characteristic
441	C₂	C₁₉×#2896	1	1	yes	characteristic
442	C₂	C₁₉×#3183	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#2283	C₂	semidirect
4. C₁₉×#1991	C₂	semidirect
5. C₁₉×#1958	C₂	semidirect
7. C₁₉×#1894	C₂	semidirect
8. C₁₉×#1763	C₂	semidirect
9. C₁₉×#1762	C₂	semidirect
12. C₁₉×#529	C₄	semidirect
150. #21411	C₁₉	direct (N × H)
194. C₂×C₄×M₁₆	C₂×C₁₉	semidirect
195. #2283	C₂×C₁₉	semidirect
196. #1991	C₂×C₁₉	semidirect
197. #1958	C₂×C₁₉	semidirect
199. #1894	C₂×C₁₉	semidirect
200. #1763	C₂×C₁₉	semidirect
201. #1762	C₂×C₁₉	semidirect
227. #529	C₄×C₁₉	semidirect
314. C₁₉	#21411	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×#529	2
C₂×C₄×M₁₆×C₁₉	2
C₁₉×#2283	2
C₁₉×#1991	2
C₁₉×#1958	2
C₁₉×#1895	2
C₁₉×#1894	2
C₁₉×#1763	2
C₁₉×#1762	2
#21411	19

Subgroups — C19×#21411 #18027370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21411 #18027370