Subgroups — C₁₉×#11199 #18017158

Order 4864.

1186 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#340	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#340	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
12	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
14	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
15	C₁₉×#380	—	2	2	no	—
16	C₁₉×#380	—	2	4	no	—
17	C₁₉×#380	C₄	1	4	yes	complemented
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₂×C₁₉×#95	—	2	1	no	—
20	C₁₉×#340	—	2	4	no	—
21	C₁₉×#340	—	2	4	no	—
22	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	—	2	2	no	—
24	C₂³×C₄×C₁₉	—	2	2	no	—
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂³×C₄×C₁₉	—	2	2	no	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	2	2	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	D₄	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	—	2	2	no	—
37	C₂²×C₈×C₁₉	—	2	2	no	—
38	C₂²×C₈×C₁₉	—	2	2	no	—
39	C₂²×C₈×C₁₉	—	2	2	no	—
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	D₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
63	C₁₉×C₂²⋊C₈	—	2	8	no	—
64	C₁₉×#95	—	2	4	no	—
65	C₁₉×#95	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	1	no	—
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	1	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	2	1	no	—
72	C₂⁴×C₁₉	—	2	1	no	—
73	C₂⁴×C₁₉	—	2	2	no	—
74	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
75	C₂⁴×C₁₉	D₈	1	2	yes	—
76	C₂⁴×C₁₉	SD₁₆	1	2	yes	—
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	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	4	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	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	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	#41	1	2	yes	—
123	C₂²×C₄×C₁₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₉	#41	1	2	yes	—
125	C₂²×C₄×C₁₉	#41	1	2	yes	—
126	C₂×C₈×C₁₉	—	2	4	no	—
127	C₂×C₈×C₁₉	—	2	4	no	—
128	C₂×C₈×C₁₉	—	2	4	no	—
129	C₂×C₈×C₁₉	—	4	2	no	—
130	C₂×C₈×C₁₉	—	4	2	no	—
131	C₂×C₈×C₁₉	—	4	2	no	—
132	C₂×C₈×C₁₉	—	4	2	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	4	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₂²⋊C₄×C₁₉	—	4	8	no	—
143	C₂²⋊C₄×C₁₉	—	4	8	no	—
144	#11199	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	2	4	no	—
155	C₂³×C₁₉	—	2	4	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	4	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	#102	1	4	yes	—
168	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂³×C₁₉	#120	1	1	yes	characteristic
170	C₂³×C₁₉	#121	1	2	yes	—
171	C₂³×C₁₉	#123	1	2	yes	—
172	C₂³×C₁₉	#123	1	1	yes	characteristic
173	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
174	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
175	C₂³×C₁₉	#135	1	2	yes	—
176	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂³×C₁₉	#137	1	1	yes	characteristic
178	C₂³×C₁₉	#137	1	2	yes	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	—	4	4	no	—
197	C₂×C₄×C₁₉	—	8	1	no	—
198	C₂×C₄×C₁₉	—	8	1	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	—	8	2	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	—	8	1	no	—
204	C₂×C₄×C₁₉	—	8	2	no	—
205	C₂×C₄×C₁₉	—	8	1	no	—
206	C₂×C₄×C₁₉	—	8	2	no	—
207	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#121	1	2	yes	—
213	C₂×C₄×C₁₉	#121	1	2	yes	—
214	C₂×C₄×C₁₉	#121	1	2	yes	—
215	C₂×C₄×C₁₉	#123	1	2	yes	—
216	C₂×C₄×C₁₉	#123	1	2	yes	—
217	C₂×C₄×C₁₉	#123	1	2	yes	—
218	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#124	1	2	yes	—
220	C₂×C₄×C₁₉	#124	1	2	yes	—
221	C₂×C₄×C₁₉	#126	1	2	yes	—
222	C₂×C₄×C₁₉	#126	1	2	yes	—
223	C₈×C₁₉	—	4	4	no	—
224	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
225	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
226	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
227	C₂×#340	C₂×C₁₉	1	2	yes	complemented
228	C₂×#340	C₂×C₁₉	1	2	yes	complemented
229	C₂²×C₁₉	—	2	4	no	—
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	2	4	no	—
232	C₂²×C₁₉	—	4	4	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	#381	1	1	yes	characteristic
241	C₂²×C₁₉	#386	1	1	yes	characteristic
242	C₂²×C₁₉	#386	1	1	yes	characteristic
243	C₂²×C₁₉	#394	1	2	yes	—
244	C₂²×C₁₉	#397	1	2	yes	—
245	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
246	C₂²×C₁₉	#416	1	1	yes	characteristic
247	C₂²×C₁₉	#417	1	1	yes	characteristic
248	C₂²×C₁₉	#419	1	1	yes	characteristic
249	C₂²×C₁₉	#447	1	1	yes	characteristic
250	C₂²×C₁₉	#448	1	1	yes	characteristic
251	C₂²×C₁₉	#452	1	2	yes	—
252	C₂²×C₁₉	#465	1	2	yes	—
253	C₂²×C₁₉	#466	1	2	yes	—
254	C₂²×C₁₉	#468	1	2	yes	—
255	C₂²×C₁₉	#470	1	2	yes	—
256	C₂²×C₁₉	#480	1	1	yes	characteristic
257	C₂²×C₁₉	#480	1	2	yes	—
258	C₂²×C₁₉	#481	1	1	yes	characteristic
259	C₂²×C₁₉	#482	1	2	yes	—
260	C₂²×C₁₉	#483	1	2	yes	—
261	C₂²×C₁₉	#485	1	2	yes	—
262	C₂²×C₁₉	#485	1	2	yes	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	8	2	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₄×C₁₉	—	8	4	no	—
267	C₄×C₁₉	#388	1	2	yes	—
268	C₄×C₁₉	#388	1	2	yes	—
269	C₄×C₁₉	#394	1	2	yes	—
270	C₄×C₁₉	#397	1	2	yes	—
271	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
273	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
276	C₂²×C₂²⋊C₄	—	2	1	no	—
277	C₂²×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₈	—	2	2	no	—
279	C₂×C₂²⋊C₈	—	2	4	no	—
280	#380	—	2	2	no	—
281	#380	—	2	4	no	—
282	#380	C₄×C₁₉	1	4	yes	complemented
283	C₂×#95	—	2	1	no	—
284	C₂×#95	—	2	1	no	—
285	#340	—	2	4	no	—
286	#340	—	2	4	no	—
287	C₂×C₁₉	—	4	4	no	—
288	C₂×C₁₉	#1440	1	1	yes	characteristic
289	C₂×C₁₉	#1823	1	1	yes	characteristic
290	C₂×C₁₉	#1825	1	1	yes	characteristic
291	C₂×C₁₉	#1873	1	1	yes	characteristic
292	C₂×C₁₉	#1874	1	1	yes	characteristic
293	C₂×C₁₉	#1893	1	1	yes	characteristic
294	C₂×C₁₉	#1894	1	1	yes	characteristic
295	C₂×C₁₉	#2033	1	2	yes	—
296	C₂×C₁₉	#2035	1	2	yes	—
297	C₂×C₁₉	#2075	1	2	yes	—
298	C₂×C₁₉	#2077	1	2	yes	—
299	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	—	2	2	no	—
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
310	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂³×C₄	D₄×C₁₉	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	2	2	no	—
318	C₂²×C₈	—	2	2	no	—
319	C₂²×C₈	D₄×C₁₉	1	4	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	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
332	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
333	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
334	C₂×C₂²⋊C₄	—	2	4	no	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	4	2	no	—
337	C₂×C₂²⋊C₄	—	4	2	no	—
338	C₂×C₂²⋊C₄	—	4	2	no	—
339	C₂×C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₈	—	2	8	no	—
341	#95	—	2	4	no	—
342	#95	—	2	4	no	—
343	C₁₉	#11199	1	1	yes	characteristic, direct product factor, Sylow
344	C₂⁴	—	2	1	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	—	2	2	no	—
349	C₂⁴	—	2	1	no	—
350	C₂⁴	—	2	1	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
353	C₂⁴	D₈×C₁₉	1	2	yes	—
354	C₂⁴	SD₁₆×C₁₉	1	2	yes	—
355	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	#41×C₁₉	1	2	yes	—
401	C₂²×C₄	#41×C₁₉	1	2	yes	—
402	C₂²×C₄	#41×C₁₉	1	2	yes	—
403	C₂²×C₄	#41×C₁₉	1	2	yes	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	4	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	—	4	2	no	—
410	C₂×C₈	—	4	2	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	8	no	—
421	C₂²⋊C₄	—	4	8	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	C₁₉×#102	1	4	yes	—
445	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
446	C₂³	C₁₉×#120	1	1	yes	characteristic
447	C₂³	C₁₉×#121	1	2	yes	—
448	C₂³	C₁₉×#123	1	2	yes	—
449	C₂³	C₁₉×#123	1	1	yes	characteristic
450	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
451	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
452	C₂³	C₁₉×#135	1	2	yes	—
453	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
454	C₂³	C₁₉×#137	1	1	yes	characteristic
455	C₂³	C₁₉×#137	1	2	yes	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	—	8	1	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	1	no	—
482	C₂×C₄	—	8	1	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
485	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
486	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
487	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
488	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
489	C₂×C₄	C₁₉×#121	1	2	yes	—
490	C₂×C₄	C₁₉×#121	1	2	yes	—
491	C₂×C₄	C₁₉×#121	1	2	yes	—
492	C₂×C₄	C₁₉×#123	1	2	yes	—
493	C₂×C₄	C₁₉×#123	1	2	yes	—
494	C₂×C₄	C₁₉×#123	1	2	yes	—
495	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
496	C₂×C₄	C₁₉×#124	1	2	yes	—
497	C₂×C₄	C₁₉×#124	1	2	yes	—
498	C₂×C₄	C₁₉×#126	1	2	yes	—
499	C₂×C₄	C₁₉×#126	1	2	yes	—
500	C₈	—	4	4	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	C₁₉×#381	1	1	yes	characteristic
513	C₂²	C₁₉×#386	1	1	yes	characteristic
514	C₂²	C₁₉×#386	1	1	yes	characteristic
515	C₂²	C₁₉×#394	1	2	yes	—
516	C₂²	C₁₉×#397	1	2	yes	—
517	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
518	C₂²	C₁₉×#416	1	1	yes	characteristic
519	C₂²	C₁₉×#417	1	1	yes	characteristic
520	C₂²	C₁₉×#419	1	1	yes	characteristic
521	C₂²	C₁₉×#447	1	1	yes	characteristic
522	C₂²	C₁₉×#448	1	1	yes	characteristic
523	C₂²	C₁₉×#452	1	2	yes	—
524	C₂²	C₁₉×#465	1	2	yes	—
525	C₂²	C₁₉×#466	1	2	yes	—
526	C₂²	C₁₉×#468	1	2	yes	—
527	C₂²	C₁₉×#470	1	2	yes	—
528	C₂²	C₁₉×#480	1	2	yes	—
529	C₂²	C₁₉×#480	1	1	yes	characteristic
530	C₂²	C₁₉×#481	1	1	yes	characteristic
531	C₂²	C₁₉×#482	1	2	yes	—
532	C₂²	C₁₉×#483	1	2	yes	—
533	C₂²	C₁₉×#485	1	2	yes	—
534	C₂²	C₁₉×#485	1	2	yes	—
535	C₄	—	4	2	no	—
536	C₄	—	8	2	no	—
537	C₄	—	8	4	no	—
538	C₄	—	8	2	no	—
539	C₄	C₁₉×#388	1	2	yes	—
540	C₄	C₁₉×#388	1	2	yes	—
541	C₄	C₁₉×#394	1	2	yes	—
542	C₄	C₁₉×#397	1	2	yes	—
543	C₂	—	4	4	no	—
544	C₂	C₁₉×#1440	1	1	yes	characteristic
545	C₂	C₁₉×#1823	1	1	yes	characteristic
546	C₂	C₁₉×#1825	1	1	yes	characteristic
547	C₂	C₁₉×#1873	1	1	yes	characteristic
548	C₂	C₁₉×#1874	1	1	yes	characteristic
549	C₂	C₁₉×#1893	1	1	yes	characteristic
550	C₂	C₁₉×#1894	1	1	yes	characteristic
551	C₂	C₁₉×#2033	1	2	yes	—
552	C₂	C₁₉×#2035	1	2	yes	—
553	C₂	C₁₉×#2075	1	2	yes	—
554	C₂	C₁₉×#2077	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	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#340	C₂	semidirect
5. C₂×C₁₉×#340	C₂	semidirect
17. C₁₉×#380	C₄	semidirect
144. #11199	C₁₉	direct (N × H)
227. C₂×#340	C₂×C₁₉	semidirect
228. C₂×#340	C₂×C₁₉	semidirect
282. #380	C₄×C₁₉	semidirect
343. C₁₉	#11199	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#380	2
C₂×C₁₉×#340	2
#11199	19

Subgroups — C19×#11199 #18017158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11199 #18017158