Subgroups — C₁₉×#11022 #18016981

Order 4864.

1822 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#102	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#390	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
7	C₂²×D₈×C₁₉	—	2	4	no	—
8	C₂²×D₈×C₁₉	—	2	4	no	—
9	C₂²×D₈×C₁₉	—	2	2	no	—
10	C₂²×D₈×C₁₉	—	2	2	no	—
11	C₂²×D₈×C₁₉	C₄	1	4	yes	complemented
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	—	2	4	no	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#102	—	2	4	no	—
18	C₂×C₁₉×#102	—	2	4	no	—
19	C₂×C₁₉×#102	—	2	4	no	—
20	C₁₉×#390	—	2	4	no	—
21	C₁₉×#390	—	2	4	no	—
22	C₁₉×#340	—	2	2	no	—
23	C₁₉×#336	—	2	2	no	—
24	C₂⁵×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	2	no	—
30	C₂²×D₄×C₁₉	—	2	2	no	—
31	C₂²×D₄×C₁₉	—	2	2	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	2	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₁₉	D₄	1	4	yes	—
38	C₂²×D₄×C₁₉	D₄	1	4	yes	—
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	D₄	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×D₈×C₁₉	—	2	8	no	—
43	C₂×D₈×C₁₉	—	2	8	no	—
44	C₂×D₈×C₁₉	—	2	16	no	—
45	C₂×D₈×C₁₉	—	2	16	no	—
46	C₂×D₈×C₁₉	—	2	8	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	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	1	no	—
52	C₂²×C₈×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₉	D₄	1	2	yes	—
55	C₂²×C₈×C₁₉	D₄	1	2	yes	—
56	C₂²×C₈×C₁₉	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
66	C₂×C₄²×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₁₉×#102	—	2	16	no	—
71	C₂⁴×C₁₉	—	2	4	no	—
72	C₂⁴×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	4	2	no	—
75	C₂⁴×C₁₉	—	4	2	no	—
76	C₂⁴×C₁₉	—	4	2	no	—
77	C₂⁴×C₁₉	—	4	2	no	—
78	C₂⁴×C₁₉	—	4	4	no	—
79	C₂⁴×C₁₉	—	4	4	no	—
80	C₂⁴×C₁₉	—	4	4	no	—
81	C₂⁴×C₁₉	—	4	4	no	—
82	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	4	2	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	4	2	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	2	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	4	no	—
119	C₂²×C₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
121	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
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	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
131	D₈×C₁₉	—	2	32	no	—
132	C₂×C₈×C₁₉	—	2	4	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	4	no	—
136	C₂×C₈×C₁₉	—	2	4	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	4	1	no	—
139	C₂×C₈×C₁₉	—	4	2	no	—
140	C₂×C₈×C₁₉	—	4	1	no	—
141	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₂²⋊C₄×C₁₉	—	4	32	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	4	2	no	—
149	C₄²×C₁₉	—	4	1	no	—
150	#11022	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	8	no	—
152	C₂³×C₁₉	—	4	4	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	—	4	4	no	—
158	C₂³×C₁₉	—	4	8	no	—
159	C₂³×C₁₉	—	4	8	no	—
160	C₂³×C₁₉	—	4	8	no	—
161	C₂³×C₁₉	—	4	8	no	—
162	C₂³×C₁₉	—	4	8	no	—
163	C₂³×C₁₉	—	4	8	no	—
164	C₂³×C₁₉	—	8	4	no	—
165	C₂³×C₁₉	—	8	4	no	—
166	C₂³×C₁₉	—	8	4	no	—
167	C₂³×C₁₉	—	8	4	no	—
168	C₂³×C₁₉	—	8	4	no	—
169	C₂³×C₁₉	—	8	4	no	—
170	C₂³×C₁₉	—	8	2	no	—
171	C₂³×C₁₉	—	8	2	no	—
172	C₂³×C₁₉	—	8	2	no	—
173	C₂³×C₁₉	—	8	2	no	—
174	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₉	#120	1	2	yes	—
176	C₂³×C₁₉	#121	1	2	yes	—
177	C₂³×C₁₉	#121	1	1	yes	characteristic
178	C₂³×C₁₉	#127	1	1	yes	characteristic
179	C₂³×C₁₉	C₂×D₈	1	2	yes	—
180	C₂³×C₁₉	#135	1	2	yes	—
181	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
182	D₄×C₁₉	—	2	8	no	—
183	D₄×C₁₉	—	2	8	no	—
184	D₄×C₁₉	—	4	4	no	—
185	D₄×C₁₉	—	4	4	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	4	4	no	—
189	D₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	2	8	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	—	4	8	no	—
197	C₂×C₄×C₁₉	—	8	4	no	—
198	C₂×C₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#120	1	2	yes	—
207	C₂×C₄×C₁₉	#120	1	2	yes	—
208	C₂×C₄×C₁₉	#121	1	2	yes	—
209	C₂×C₄×C₁₉	#121	1	2	yes	—
210	C₂×C₄×C₁₉	#121	1	2	yes	—
211	C₂×C₄×C₁₉	#121	1	2	yes	—
212	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#123	1	2	yes	—
214	C₂×C₄×C₁₉	#123	1	2	yes	—
215	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
218	C₈×C₁₉	—	2	4	no	—
219	C₈×C₁₉	—	4	2	no	—
220	C₂³×D₈	C₂×C₁₉	1	1	yes	characteristic
221	C₂²×#102	C₂×C₁₉	1	2	yes	complemented
222	C₂×#390	C₂×C₁₉	1	2	yes	complemented
223	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂×#336	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂²×C₁₉	—	4	16	no	—
226	C₂²×C₁₉	—	4	8	no	—
227	C₂²×C₁₉	—	8	8	no	—
228	C₂²×C₁₉	—	8	8	no	—
229	C₂²×C₁₉	—	8	4	no	—
230	C₂²×C₁₉	—	8	4	no	—
231	C₂²×C₁₉	—	8	8	no	—
232	C₂²×C₁₉	—	8	4	no	—
233	C₂²×C₁₉	—	8	4	no	—
234	C₂²×C₁₉	—	8	4	no	—
235	C₂²×C₁₉	—	8	4	no	—
236	C₂²×C₁₉	#386	1	2	yes	—
237	C₂²×C₁₉	#390	1	1	yes	characteristic
238	C₂²×C₁₉	#392	1	1	yes	characteristic
239	C₂²×C₁₉	#392	1	2	yes	—
240	C₂²×C₁₉	#394	1	1	yes	characteristic
241	C₂²×C₁₉	C₄×D₈	1	2	yes	—
242	C₂²×C₁₉	#442	1	2	yes	—
243	C₂²×C₁₉	#447	1	4	yes	—
244	C₂²×C₁₉	#449	1	4	yes	—
245	C₂²×C₁₉	#459	1	4	yes	—
246	C₂²×C₁₉	#463	1	4	yes	—
247	C₂²×C₁₉	#466	1	2	yes	—
248	C₂²×C₁₉	#469	1	2	yes	—
249	C₂²×C₁₉	#493	1	1	yes	characteristic
250	C₂²×C₁₉	#495	1	1	yes	characteristic
251	C₂²×C₁₉	#496	1	2	yes	—
252	C₄×C₁₉	—	4	4	no	—
253	C₄×C₁₉	—	8	4	no	—
254	C₄×C₁₉	#379	1	1	yes	characteristic
255	C₄×C₁₉	#386	1	2	yes	—
256	C₄×C₁₉	#390	1	1	yes	characteristic
257	C₄×C₁₉	#392	1	1	yes	characteristic
258	C₄×C₁₉	#394	1	1	yes	characteristic
259	C₄×C₁₉	#394	1	2	yes	—
260	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
261	C₂²×D₈	—	2	4	no	—
262	C₂²×D₈	—	2	4	no	—
263	C₂²×D₈	—	2	2	no	—
264	C₂²×D₈	—	2	2	no	—
265	C₂²×D₈	C₄×C₁₉	1	4	yes	complemented
266	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
267	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
269	C₂²×C₂²⋊C₄	—	2	4	no	—
270	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×#102	—	2	4	no	—
272	C₂×#102	—	2	4	no	—
273	C₂×#102	—	2	4	no	—
274	#390	—	2	4	no	—
275	#390	—	2	4	no	—
276	#340	—	2	2	no	—
277	#336	—	2	2	no	—
278	C₂×C₁₉	—	8	8	no	—
279	C₂×C₁₉	#1438	1	1	yes	characteristic
280	C₂×C₁₉	#1879	1	4	yes	—
281	C₂×C₁₉	#1970	1	1	yes	characteristic
282	C₂×C₁₉	#1972	1	1	yes	characteristic
283	C₂×C₁₉	#1999	1	2	yes	—
284	C₂×C₁₉	#2011	1	2	yes	—
285	C₂×C₁₉	#2012	1	2	yes	—
286	C₂×C₁₉	#2054	1	2	yes	—
287	C₂⁵	—	2	2	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
300	C₂²×D₄	D₄×C₁₉	1	4	yes	—
301	C₂²×D₄	D₄×C₁₉	1	4	yes	—
302	C₂³×C₄	—	2	2	no	—
303	C₂³×C₄	D₄×C₁₉	1	2	yes	—
304	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×D₈	—	2	8	no	—
306	C₂×D₈	—	2	8	no	—
307	C₂×D₈	—	2	16	no	—
308	C₂×D₈	—	2	16	no	—
309	C₂×D₈	—	2	8	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
317	C₂²×C₈	D₄×C₁₉	1	2	yes	—
318	C₂²×C₈	D₄×C₁₉	1	2	yes	—
319	C₂²×C₈	D₄×C₁₉	1	2	yes	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
326	C₂×C₂²⋊C₄	—	2	16	no	—
327	C₂×C₂²⋊C₄	—	4	8	no	—
328	C₂×C₂²⋊C₄	—	4	8	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	—	2	1	no	—
333	#102	—	2	16	no	—
334	C₁₉	#11022	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	4	2	no	—
339	C₂⁴	—	4	2	no	—
340	C₂⁴	—	4	2	no	—
341	C₂⁴	—	4	2	no	—
342	C₂⁴	—	4	4	no	—
343	C₂⁴	—	4	4	no	—
344	C₂⁴	—	4	4	no	—
345	C₂⁴	—	4	4	no	—
346	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	4	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
385	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
392	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	#41×C₁₉	1	2	yes	—
394	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
395	D₈	—	2	32	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	4	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂×C₈	—	4	1	no	—
405	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₂²⋊C₄	—	4	32	no	—
411	C₄²	—	4	1	no	—
412	C₄²	—	4	2	no	—
413	C₄²	—	4	1	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	8	4	no	—
428	C₂³	—	8	4	no	—
429	C₂³	—	8	4	no	—
430	C₂³	—	8	4	no	—
431	C₂³	—	8	4	no	—
432	C₂³	—	8	4	no	—
433	C₂³	—	8	2	no	—
434	C₂³	—	8	2	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
438	C₂³	C₁₉×#120	1	2	yes	—
439	C₂³	C₁₉×#121	1	2	yes	—
440	C₂³	C₁₉×#121	1	1	yes	characteristic
441	C₂³	C₁₉×#127	1	1	yes	characteristic
442	C₂³	C₂×D₈×C₁₉	1	2	yes	—
443	C₂³	C₁₉×#135	1	2	yes	—
444	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
445	D₄	—	2	8	no	—
446	D₄	—	2	8	no	—
447	D₄	—	4	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	4	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
464	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
467	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
468	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
469	C₂×C₄	C₁₉×#120	1	2	yes	—
470	C₂×C₄	C₁₉×#120	1	2	yes	—
471	C₂×C₄	C₁₉×#121	1	2	yes	—
472	C₂×C₄	C₁₉×#121	1	2	yes	—
473	C₂×C₄	C₁₉×#121	1	2	yes	—
474	C₂×C₄	C₁₉×#121	1	2	yes	—
475	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
476	C₂×C₄	C₁₉×#123	1	2	yes	—
477	C₂×C₄	C₁₉×#123	1	2	yes	—
478	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
479	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
480	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
481	C₈	—	2	4	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	4	8	no	—
484	C₂²	—	4	16	no	—
485	C₂²	—	8	4	no	—
486	C₂²	—	8	4	no	—
487	C₂²	—	8	8	no	—
488	C₂²	—	8	4	no	—
489	C₂²	—	8	4	no	—
490	C₂²	—	8	4	no	—
491	C₂²	—	8	4	no	—
492	C₂²	—	8	8	no	—
493	C₂²	—	8	8	no	—
494	C₂²	C₁₉×#386	1	2	yes	—
495	C₂²	C₁₉×#390	1	1	yes	characteristic
496	C₂²	C₁₉×#392	1	1	yes	characteristic
497	C₂²	C₁₉×#392	1	2	yes	—
498	C₂²	C₁₉×#394	1	1	yes	characteristic
499	C₂²	C₄×D₈×C₁₉	1	2	yes	—
500	C₂²	C₁₉×#442	1	2	yes	—
501	C₂²	C₁₉×#447	1	4	yes	—
502	C₂²	C₁₉×#449	1	4	yes	—
503	C₂²	C₁₉×#459	1	4	yes	—
504	C₂²	C₁₉×#463	1	4	yes	—
505	C₂²	C₁₉×#466	1	2	yes	—
506	C₂²	C₁₉×#469	1	2	yes	—
507	C₂²	C₁₉×#493	1	1	yes	characteristic
508	C₂²	C₁₉×#495	1	1	yes	characteristic
509	C₂²	C₁₉×#496	1	2	yes	—
510	C₄	—	4	4	no	—
511	C₄	—	8	4	no	—
512	C₄	C₁₉×#379	1	1	yes	characteristic
513	C₄	C₁₉×#386	1	2	yes	—
514	C₄	C₁₉×#390	1	1	yes	characteristic
515	C₄	C₁₉×#392	1	1	yes	characteristic
516	C₄	C₁₉×#394	1	1	yes	characteristic
517	C₄	C₁₉×#394	1	2	yes	—
518	C₂	—	8	8	no	—
519	C₂	C₁₉×#1438	1	1	yes	characteristic
520	C₂	C₁₉×#1879	1	4	yes	—
521	C₂	C₁₉×#1970	1	1	yes	characteristic
522	C₂	C₁₉×#1972	1	1	yes	characteristic
523	C₂	C₁₉×#1999	1	2	yes	—
524	C₂	C₁₉×#2011	1	2	yes	—
525	C₂	C₁₉×#2012	1	2	yes	—
526	C₂	C₁₉×#2054	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₈×C₁₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#102	C₂	semidirect
3. C₂×C₁₉×#390	C₂	semidirect
4. C₂×C₁₉×#340	C₂	semidirect
5. C₂×C₁₉×#336	C₂	semidirect
11. C₂²×D₈×C₁₉	C₄	semidirect
110. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
120. C₂²×C₄×C₁₉	D₈	semidirect
141. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
150. #11022	C₁₉	direct (N × H)
221. C₂²×#102	C₂×C₁₉	semidirect
222. C₂×#390	C₂×C₁₉	semidirect
223. C₂×#340	C₂×C₁₉	semidirect
224. C₂×#336	C₂×C₁₉	semidirect
265. C₂²×D₈	C₄×C₁₉	semidirect
334. C₁₉	#11022	direct (N × H)
374. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
384. C₂²×C₄	D₈×C₁₉	semidirect
405. C₂×C₈	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₁₉	2
C₂²×C₁₉×#102	2
C₂×C₁₉×#390	2
C₂×C₁₉×#340	2
C₂×C₁₉×#336	2
#11022	19

Subgroups — C19×#11022 #18016981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11022 #18016981