Subgroups — C₁₉×#8329 #18014288

Order 4864.

1276 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#328	C₂	1	4	yes	maximal, complemented
4	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
8	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
9	C₂×C₁₉×C₂²⋊Q₈	—	2	8	no	—
10	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	complemented
11	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
15	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
16	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#95	—	2	1	no	—
20	C₂×C₁₉×#95	C₂²	1	2	yes	—
21	C₁₉×#328	—	2	8	no	—
22	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×Q₈×C₁₉	—	2	4	no	—
24	C₂²×Q₈×C₁₉	—	2	1	no	—
25	C₂²×Q₈×C₁₉	—	4	2	no	—
26	C₂²×Q₈×C₁₉	—	4	2	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	—	2	4	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	—	4	2	no	—
33	C₂³×C₄×C₁₉	—	4	2	no	—
34	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₁₉×C₂²⋊Q₈	—	2	8	no	—
42	C₁₉×C₂²⋊Q₈	—	2	8	no	—
43	C₁₉×C₂²⋊Q₈	—	2	4	no	—
44	C₁₉×C₂²⋊Q₈	—	2	4	no	—
45	C₁₉×C₂²⋊Q₈	—	2	4	no	—
46	C₁₉×C₂²⋊Q₈	D₄	1	8	yes	—
47	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
59	C₁₉×C₂²⋊C₈	—	2	4	no	—
60	C₁₉×C₂²⋊C₈	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	—	4	2	no	—
62	C₁₉×#95	—	2	4	no	—
63	C₁₉×#95	—	4	2	no	—
64	C₂⁴×C₁₉	—	2	2	no	—
65	C₂⁴×C₁₉	—	2	2	no	—
66	C₂⁴×C₁₉	—	2	2	no	—
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂⁴×C₁₉	—	4	1	no	—
69	C₂⁴×C₁₉	—	4	1	no	—
70	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₁₉	SD₁₆	1	2	yes	—
73	C₂⁴×C₁₉	Q₁₆	1	2	yes	—
74	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×Q₈×C₁₉	—	2	4	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	4	16	no	—
78	C₂×Q₈×C₁₉	—	4	2	no	—
79	C₂×Q₈×C₁₉	—	4	2	no	—
80	C₂×Q₈×C₁₉	—	4	2	no	—
81	C₂×Q₈×C₁₉	—	4	2	no	—
82	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	16	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₁₉	—	4	2	no	—
122	C₂×C₈×C₁₉	—	4	2	no	—
123	C₂×C₈×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	8	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	8	no	—
128	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	complemented
129	C₂²⋊C₄×C₁₉	—	2	8	no	—
130	C₂²⋊C₄×C₁₉	—	2	8	no	—
131	C₂²⋊C₄×C₁₉	—	4	8	no	—
132	#8329	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	2	1	no	—
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	—	2	4	no	—
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	—	4	4	no	—
154	C₂³×C₁₉	—	4	4	no	—
155	C₂³×C₁₉	—	4	4	no	—
156	C₂³×C₁₉	—	4	4	no	—
157	C₂³×C₁₉	#99	1	2	yes	—
158	C₂³×C₁₉	#103	1	2	yes	—
159	C₂³×C₁₉	#103	1	2	yes	—
160	C₂³×C₁₉	#104	1	2	yes	—
161	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂³×C₁₉	#120	1	2	yes	—
163	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
165	C₂³×C₁₉	#137	1	2	yes	—
166	Q₈×C₁₉	—	4	4	no	—
167	Q₈×C₁₉	—	4	8	no	—
168	Q₈×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	2	8	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	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	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	8	no	—
187	C₂×C₄×C₁₉	—	4	8	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	—	8	2	no	—
198	C₂×C₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	#99	1	2	yes	—
200	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₉	#120	1	2	yes	—
202	C₈×C₁₉	—	8	2	no	—
203	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
204	#1779	C₂×C₁₉	1	1	yes	characteristic
205	C₂×#328	C₂×C₁₉	1	4	yes	complemented
206	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	4	8	no	—
225	C₂²×C₁₉	—	4	8	no	—
226	C₂²×C₁₉	—	4	1	no	—
227	C₂²×C₁₉	—	4	1	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	#328	1	4	yes	complemented
231	C₂²×C₁₉	#379	1	1	yes	characteristic
232	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
233	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
234	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
235	C₂²×C₁₉	#419	1	1	yes	characteristic
236	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
237	C₂²×C₁₉	#421	1	1	yes	characteristic
238	C₂²×C₁₉	#448	1	2	yes	—
239	C₂²×C₁₉	#451	1	2	yes	—
240	C₄×C₁₉	—	2	2	no	—
241	C₄×C₁₉	—	2	2	no	—
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	4	1	no	—
244	C₄×C₁₉	—	4	4	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	8	4	no	—
247	C₂³×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
248	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×C₂²⋊Q₈	—	2	8	no	—
252	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	complemented
253	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
254	C₂²×C₄⋊C₄	—	2	1	no	—
255	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
256	C₂²×C₂²⋊C₄	—	2	1	no	—
257	C₂²×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₈	—	2	1	no	—
259	C₂×C₂²⋊C₈	—	2	1	no	—
260	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
261	C₂×#95	—	2	1	no	—
262	C₂×#95	C₂²×C₁₉	1	2	yes	—
263	#328	—	2	8	no	—
264	C₂×C₁₉	—	2	2	no	—
265	C₂×C₁₉	—	2	4	no	—
266	C₂×C₁₉	—	2	2	no	—
267	C₂×C₁₉	—	4	2	no	—
268	C₂×C₁₉	C₂×#328	1	1	yes	characteristic
269	C₂×C₁₉	#1508	1	1	yes	characteristic
270	C₂×C₁₉	#1511	1	1	yes	characteristic
271	C₂×C₁₉	#1520	1	1	yes	characteristic
272	C₂×C₁₉	#1781	1	1	yes	characteristic
273	C₂×C₁₉	#1787	1	1	yes	characteristic
274	C₂×C₁₉	#1789	1	1	yes	characteristic
275	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
276	C₂²×Q₈	—	2	4	no	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	4	2	no	—
279	C₂²×Q₈	—	4	2	no	—
280	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	—	4	2	no	—
286	C₂³×C₄	—	4	2	no	—
287	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
289	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
290	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₂²×C₈	—	2	2	no	—
294	C₂²⋊Q₈	—	2	8	no	—
295	C₂²⋊Q₈	—	2	8	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	C₂²⋊Q₈	—	2	4	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	D₄×C₁₉	1	8	yes	—
300	C₂×C₄⋊C₄	—	2	8	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	8	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₂²⋊C₄	—	4	2	no	—
311	C₂×C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	C₂²⋊C₈	—	4	2	no	—
314	C₂²⋊C₈	—	4	2	no	—
315	#95	—	2	4	no	—
316	#95	—	4	2	no	—
317	C₁₉	#8329	1	1	yes	characteristic, direct product factor, Sylow
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	4	1	no	—
323	C₂⁴	—	4	1	no	—
324	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
325	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
326	C₂⁴	SD₁₆×C₁₉	1	2	yes	—
327	C₂⁴	Q₁₆×C₁₉	1	2	yes	—
328	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	16	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	16	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	complemented
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	4	8	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	4	4	no	—
410	C₂³	C₁₉×#99	1	2	yes	—
411	C₂³	C₁₉×#103	1	2	yes	—
412	C₂³	C₁₉×#103	1	2	yes	—
413	C₂³	C₁₉×#104	1	2	yes	—
414	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
415	C₂³	C₁₉×#120	1	2	yes	—
416	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
417	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
418	C₂³	C₁₉×#137	1	2	yes	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	4	no	—
421	Q₈	—	4	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	—	4	8	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	—	8	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	C₁₉×#99	1	2	yes	—
453	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
454	C₂×C₄	C₁₉×#120	1	2	yes	—
455	C₈	—	8	2	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	C₁₉×#328	1	4	yes	complemented
480	C₂²	C₁₉×#379	1	1	yes	characteristic
481	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
482	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
483	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
484	C₂²	C₁₉×#419	1	1	yes	characteristic
485	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
486	C₂²	C₁₉×#421	1	1	yes	characteristic
487	C₂²	C₁₉×#448	1	2	yes	—
488	C₂²	C₁₉×#451	1	2	yes	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	4	no	—
495	C₄	—	8	4	no	—
496	C₂	—	2	2	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	4	no	—
499	C₂	—	4	2	no	—
500	C₂	C₂×C₁₉×#328	1	1	yes	characteristic
501	C₂	C₁₉×#1508	1	1	yes	characteristic
502	C₂	C₁₉×#1511	1	1	yes	characteristic
503	C₂	C₁₉×#1520	1	1	yes	characteristic
504	C₂	C₁₉×#1781	1	1	yes	characteristic
505	C₂	C₁₉×#1787	1	1	yes	characteristic
506	C₂	C₁₉×#1789	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#328	C₂	semidirect
5. C₂³×Q₈×C₁₉	C₄	semidirect
10. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
13. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
82. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
128. C₄⋊C₄×C₁₉	C₂²⋊C₄	semidirect
132. #8329	C₁₉	direct (N × H)
205. C₂×#328	C₂×C₁₉	semidirect
230. C₂²×C₁₉	#328	semidirect
247. C₂³×Q₈	C₄×C₁₉	semidirect
252. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
255. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
317. C₁₉	#8329	direct (N × H)
336. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
382. C₄⋊C₄	C₂²⋊C₄×C₁₉	semidirect
479. C₂²	C₁₉×#328	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₁₉×#1779	2
C₂×C₁₉×#328	2
C₁₉×C₂²⋊#95	2
#8329	19

Subgroups — C19×#8329 #18014288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8329 #18014288