Subgroups — C₁₉×#21413 #18027372

Order 4864.

1070 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×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1894	C₂	1	2	yes	maximal
9	C₁₉×#1892	C₂	1	2	yes	maximal
10	C₁₉×#1763	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#541	—	2	4	no	—
15	C₁₉×#541	C₄	1	8	yes	complemented
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#126	—	2	2	no	—
18	C₂×C₁₉×#125	—	2	2	no	—
19	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₁₉×#405	—	2	4	no	—
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#388	—	2	2	no	—
33	C₁₉×#387	—	2	2	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#382	C₂²	1	1	yes	characteristic
36	C₁₉×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
56	C₁₉×#126	—	2	16	no	—
57	C₁₉×#125	—	2	16	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	C₂×C₄	1	4	yes	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
62	C₄×Q₈×C₁₉	—	2	4	no	—
63	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
64	C₁₉×#117	C₂×C₄	1	4	yes	—
65	C₁₉×#117	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#103	—	2	4	no	—
83	C₁₉×#103	—	2	4	no	—
84	C₁₉×#103	—	2	4	no	—
85	C₁₉×#103	—	2	4	no	—
86	C₁₉×#97	—	2	2	no	—
87	C₁₉×#97	—	2	2	no	—
88	C₄×C₈×C₁₉	—	2	2	no	—
89	C₄×C₈×C₁₉	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₁₉	—	2	8	no	—
115	C₂×C₈×C₁₉	—	2	8	no	—
116	C₂×C₈×C₁₉	—	2	1	no	—
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	#41	1	2	yes	—
125	C₂×C₈×C₁₉	#41	1	2	yes	—
126	C₂×C₈×C₁₉	#41	1	2	yes	—
127	C₂×C₈×C₁₉	#41	1	2	yes	—
128	C₄⋊C₄×C₁₉	—	2	8	no	—
129	C₄⋊C₄×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	8	2	no	—
138	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
139	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
140	C₂²⋊C₄×C₁₉	—	2	8	no	—
141	C₂²⋊C₄×C₁₉	—	8	2	no	—
142	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
143	C₄²×C₁₉	—	2	8	no	—
144	C₄²×C₁₉	—	8	2	no	—
145	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₉	C₂×D₄	1	2	yes	—
148	C₄²×C₁₉	C₂×D₄	1	2	yes	—
149	#21413	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₉	—	2	4	no	—
157	Q₈×C₁₉	—	2	4	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	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	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	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	2	no	—
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₉	—	2	2	no	—
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	2	2	no	—
194	C₈×C₁₉	—	2	2	no	—
195	C₂×#541	C₂×C₁₉	1	1	yes	characteristic
196	C₂×#405	C₂×C₁₉	1	1	yes	characteristic
197	#2314	C₂×C₁₉	1	1	yes	characteristic
198	#1992	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#1991	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#1960	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#1956	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#1894	C₂×C₁₉	1	2	yes	—
203	#1892	C₂×C₁₉	1	2	yes	—
204	#1763	C₂×C₁₉	1	2	yes	complemented
205	C₄×#103	C₂×C₁₉	1	2	yes	complemented
206	C₂²×C₁₉	—	2	4	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₉	#532	1	1	yes	characteristic
213	C₂²×C₁₉	#532	1	1	yes	characteristic
214	C₂²×C₁₉	#577	1	2	yes	—
215	C₂²×C₁₉	#578	1	2	yes	—
216	C₄×C₁₉	—	2	4	no	—
217	C₄×C₁₉	—	2	4	no	—
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
224	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
225	C₄×C₁₉	#525	1	1	yes	characteristic
226	C₄×C₁₉	#525	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
229	#541	—	2	4	no	—
230	#541	C₄×C₁₉	1	8	yes	complemented
231	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#126	—	2	2	no	—
233	C₂×#125	—	2	2	no	—
234	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
236	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
237	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#103	C₂²×C₁₉	1	2	yes	—
239	C₂×#103	C₂²×C₁₉	1	2	yes	—
240	C₂×#103	C₂²×C₁₉	1	2	yes	—
241	C₂×#103	C₂²×C₁₉	1	2	yes	—
242	#405	—	2	4	no	—
243	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
247	#388	—	2	2	no	—
248	#387	—	2	2	no	—
249	#384	C₂²×C₁₉	1	1	yes	characteristic
250	#382	C₂²×C₁₉	1	1	yes	characteristic
251	#380	C₂²×C₁₉	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
253	#340	C₂²×C₁₉	1	2	yes	—
254	#340	C₂²×C₁₉	1	2	yes	—
255	#340	C₂²×C₁₉	1	2	yes	—
256	#340	C₂²×C₁₉	1	2	yes	—
257	C₂×C₁₉	—	4	2	no	—
258	C₂×C₁₉	#2297	1	1	yes	characteristic
259	C₂×C₁₉	#2898	1	2	yes	—
260	C₂×C₁₉	#3174	1	1	yes	characteristic
261	C₂×C₁₉	#3177	1	1	yes	characteristic
262	C₂×C₁₉	#3178	1	2	yes	—
263	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
264	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
277	#126	—	2	16	no	—
278	#125	—	2	16	no	—
279	#125	—	2	2	no	—
280	#125	C₂×C₄×C₁₉	1	4	yes	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
285	#117	C₂×C₄×C₁₉	1	4	yes	—
286	#117	D₄×C₁₉	1	4	yes	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#103	—	2	4	no	—
306	#103	—	2	4	no	—
307	#97	—	2	2	no	—
308	#97	—	2	2	no	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₁₉	#21413	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
336	M₁₆	—	2	8	no	—
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	#41×C₁₉	1	2	yes	—
347	C₂×C₈	#41×C₁₉	1	2	yes	—
348	C₂×C₈	#41×C₁₉	1	2	yes	—
349	C₂×C₈	#41×C₁₉	1	2	yes	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	8	2	no	—
360	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
361	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
365	C₄²	—	2	8	no	—
366	C₄²	—	8	2	no	—
367	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
368	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
369	C₄²	C₂×D₄×C₁₉	1	2	yes	—
370	C₄²	C₂×D₄×C₁₉	1	2	yes	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
376	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	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	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
404	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
405	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
422	C₂²	C₁₉×#532	1	1	yes	characteristic
423	C₂²	C₁₉×#532	1	1	yes	characteristic
424	C₂²	C₁₉×#577	1	2	yes	—
425	C₂²	C₁₉×#578	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	4	no	—
429	C₄	—	4	4	no	—
430	C₄	—	4	4	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
434	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
435	C₄	C₁₉×#525	1	1	yes	characteristic
436	C₄	C₁₉×#525	1	1	yes	characteristic
437	C₂	—	4	2	no	—
438	C₂	C₁₉×#2297	1	1	yes	characteristic
439	C₂	C₁₉×#2898	1	2	yes	—
440	C₂	C₁₉×#3174	1	1	yes	characteristic
441	C₂	C₁₉×#3177	1	1	yes	characteristic
442	C₂	C₁₉×#3178	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1992	C₂	semidirect
5. C₁₉×#1991	C₂	semidirect
6. C₁₉×#1960	C₂	semidirect
7. C₁₉×#1956	C₂	semidirect
10. C₁₉×#1763	C₂	semidirect
11. C₄×C₁₉×#103	C₂	semidirect
15. C₁₉×#541	C₄	semidirect
149. #21413	C₁₉	direct (N × H)
198. #1992	C₂×C₁₉	semidirect
199. #1991	C₂×C₁₉	semidirect
200. #1960	C₂×C₁₉	semidirect
201. #1956	C₂×C₁₉	semidirect
204. #1763	C₂×C₁₉	semidirect
205. C₄×#103	C₂×C₁₉	semidirect
230. #541	C₄×C₁₉	semidirect
314. C₁₉	#21413	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×#541	2
C₂×C₁₉×#405	2
C₁₉×#2314	2
C₁₉×#1992	2
C₁₉×#1991	2
C₁₉×#1960	2
C₁₉×#1956	2
C₁₉×#1894	2
C₁₉×#1892	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#21413	19

Subgroups — C19×#21413 #18027372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21413 #18027372