Subgroups — C₁₉×#22543 #18028502

Order 4864.

1138 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1983	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1958	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₉×#102	C₂	1	2	yes	maximal, complemented
12	C₁₉×#559	—	2	4	no	—
13	C₁₉×#559	C₄	1	8	yes	complemented
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#124	—	2	1	no	—
16	C₂×C₁₉×#124	C₂²	1	2	yes	—
17	C₂×C₁₉×#123	—	2	2	no	—
18	C₂×C₄×Q₈×C₁₉	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	2	yes	—
22	C₈×Q₈×C₁₉	—	2	4	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#391	—	2	1	no	—
35	C₁₉×#387	—	2	2	no	—
36	C₁₉×#384	C₂²	1	1	yes	characteristic
37	C₁₉×#382	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	1	yes	characteristic
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#340	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#127	—	2	2	no	—
54	C₁₉×#127	C₂×C₄	1	4	yes	—
55	C₁₉×#124	—	2	8	no	—
56	C₁₉×#124	—	2	4	no	—
57	C₁₉×#124	C₂×C₄	1	8	yes	—
58	C₁₉×#123	—	2	16	no	—
59	C₄×Q₈×C₁₉	—	2	2	no	—
60	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
62	C₄×Q₈×C₁₉	D₄	1	4	yes	—
63	C₄×D₄×C₁₉	—	2	8	no	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	—	2	4	no	—
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×#103	—	2	2	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×#102	—	2	4	no	—
90	C₁₉×#102	—	4	2	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₄×C₈×C₁₉	—	2	4	no	—
93	C₄×C₈×C₁₉	—	2	2	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₁₉×#95	—	2	2	no	—
97	C₁₉×#95	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
107	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	8	1	no	—
118	C₂×D₄×C₁₉	—	8	1	no	—
119	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	8	2	no	—
127	C₂²×C₄×C₁₉	—	8	2	no	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	#41	1	2	yes	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	4	2	no	—
150	C₄⋊C₄×C₁₉	—	8	1	no	—
151	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
152	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
153	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
154	C₄⋊C₄×C₁₉	#41	1	2	yes	—
155	C₂²⋊C₄×C₁₉	—	2	8	no	—
156	C₂²⋊C₄×C₁₉	—	2	8	no	—
157	C₂²⋊C₄×C₁₉	—	2	8	no	—
158	C₄²×C₁₉	—	2	4	no	—
159	C₄²×C₁₉	—	4	2	no	—
160	C₄²×C₁₉	—	8	2	no	—
161	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
162	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
163	C₄²×C₁₉	C₂×D₄	1	4	yes	—
164	C₄²×C₁₉	C₂×D₄	1	2	yes	—
165	#22543	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	4	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	8	no	—
175	Q₈×C₁₉	—	2	2	no	—
176	Q₈×C₁₉	—	2	2	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	Q₈×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	8	no	—
184	D₄×C₁₉	—	8	4	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	8	8	no	—
207	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
209	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂×C₄×C₁₉	#135	1	2	yes	—
212	C₂×C₄×C₁₉	#135	1	2	yes	—
213	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₁₉	—	2	2	no	—
220	C₈×C₁₉	—	4	2	no	—
221	C₈×C₁₉	—	4	1	no	—
222	C₂×#559	C₂×C₁₉	1	1	yes	characteristic
223	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2355	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#1983	C₂×C₁₉	1	2	yes	complemented
226	#1982	C₂×C₁₉	1	1	yes	characteristic
227	#1958	C₂×C₁₉	1	2	yes	complemented
228	#1957	C₂×C₁₉	1	1	yes	characteristic
229	#1804	C₂×C₁₉	1	2	yes	complemented
230	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₄×#102	C₂×C₁₉	1	2	yes	complemented
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	4	no	—
235	C₂²×C₁₉	—	4	4	no	—
236	C₂²×C₁₉	—	8	2	no	—
237	C₂²×C₁₉	—	8	2	no	—
238	C₂²×C₁₉	—	8	2	no	—
239	C₂²×C₁₉	—	8	2	no	—
240	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₁₉	#548	1	1	yes	characteristic
242	C₂²×C₁₉	#550	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
244	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
245	C₂²×C₁₉	#576	1	1	yes	characteristic
246	C₂²×C₁₉	#577	1	1	yes	characteristic
247	C₄×C₁₉	—	2	4	no	—
248	C₄×C₁₉	—	2	4	no	—
249	C₄×C₁₉	—	2	2	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	4	2	no	—
253	C₄×C₁₉	—	8	1	no	—
254	C₄×C₁₉	—	8	2	no	—
255	C₄×C₁₉	#416	1	4	yes	—
256	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
257	C₄×C₁₉	#520	1	1	yes	characteristic
258	C₄×C₁₉	#548	1	1	yes	characteristic
259	C₄×C₁₉	#550	1	1	yes	characteristic
260	#559	—	2	4	no	—
261	#559	C₄×C₁₉	1	8	yes	complemented
262	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#124	—	2	1	no	—
264	C₂×#124	C₂²×C₁₉	1	2	yes	—
265	C₂×#123	—	2	2	no	—
266	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×C₄×D₄	—	2	1	no	—
269	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
270	C₈×Q₈	—	2	4	no	—
271	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
273	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×#103	C₂²×C₁₉	1	2	yes	—
276	C₂×#102	C₂²×C₁₉	1	2	yes	—
277	C₂×#102	C₂²×C₁₉	1	2	yes	—
278	C₂×#102	C₂²×C₁₉	1	2	yes	—
279	C₂×#102	C₂²×C₁₉	1	2	yes	—
280	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
282	#391	—	2	1	no	—
283	#387	—	2	2	no	—
284	#384	C₂²×C₁₉	1	1	yes	characteristic
285	#382	C₂²×C₁₉	1	2	yes	—
286	C₄×C₄⋊C₄	—	2	1	no	—
287	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
289	#340	C₂²×C₁₉	1	2	yes	—
290	#340	C₂²×C₁₉	1	1	yes	characteristic
291	#340	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×C₁₉	—	8	4	no	—
293	C₂×C₁₉	#2341	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#416	1	1	yes	characteristic
295	C₂×C₁₉	#2897	1	1	yes	characteristic
296	C₂×C₁₉	#3361	1	1	yes	characteristic
297	C₂×C₁₉	#3365	1	1	yes	characteristic
298	C₂×C₁₉	#3394	1	1	yes	characteristic
299	C₂×C₁₉	#3396	1	1	yes	characteristic
300	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
301	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
305	C₂³×C₄	—	2	2	no	—
306	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
307	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
309	#127	—	2	2	no	—
310	#127	C₂×C₄×C₁₉	1	4	yes	—
311	#124	—	2	8	no	—
312	#124	—	2	4	no	—
313	#124	C₂×C₄×C₁₉	1	8	yes	—
314	#123	—	2	16	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
317	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
318	C₄×Q₈	D₄×C₁₉	1	4	yes	—
319	C₄×D₄	—	2	8	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
338	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
339	C₄⋊C₈	—	2	4	no	—
340	C₄⋊C₈	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	2	2	no	—
343	#103	—	4	2	no	—
344	#102	—	2	4	no	—
345	#102	—	2	4	no	—
346	#102	—	4	2	no	—
347	#102	—	4	2	no	—
348	C₄×C₈	—	2	4	no	—
349	C₄×C₈	—	2	2	no	—
350	#95	—	2	2	no	—
351	#95	—	2	1	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	C₁₉	#22543	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
364	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	8	1	no	—
375	C₂×D₄	—	8	1	no	—
376	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	8	2	no	—
384	C₂²×C₄	—	8	2	no	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	#41×C₁₉	1	2	yes	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	8	1	no	—
408	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
409	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
410	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
411	C₄⋊C₄	#41×C₁₉	1	2	yes	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₄²	—	2	4	no	—
416	C₄²	—	4	2	no	—
417	C₄²	—	8	2	no	—
418	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
419	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
420	C₄²	C₂×D₄×C₁₉	1	4	yes	—
421	C₄²	C₂×D₄×C₁₉	1	2	yes	—
422	C₂³	—	2	4	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
430	Q₈	—	2	8	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	4	8	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	8	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	8	8	no	—
463	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
464	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
466	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
467	C₂×C₄	C₁₉×#135	1	2	yes	—
468	C₂×C₄	C₁₉×#135	1	2	yes	—
469	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	1	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
486	C₂²	C₁₉×#548	1	1	yes	characteristic
487	C₂²	C₁₉×#550	1	1	yes	characteristic
488	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
489	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
490	C₂²	C₁₉×#576	1	1	yes	characteristic
491	C₂²	C₁₉×#577	1	1	yes	characteristic
492	C₄	—	2	4	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	2	no	—
500	C₄	C₁₉×#416	1	4	yes	—
501	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
502	C₄	C₁₉×#520	1	1	yes	characteristic
503	C₄	C₁₉×#548	1	1	yes	characteristic
504	C₄	C₁₉×#550	1	1	yes	characteristic
505	C₂	—	8	4	no	—
506	C₂	C₁₉×#2341	1	1	yes	characteristic
507	C₂	C₂×C₁₉×#416	1	1	yes	characteristic
508	C₂	C₁₉×#2897	1	1	yes	characteristic
509	C₂	C₁₉×#3361	1	1	yes	characteristic
510	C₂	C₁₉×#3365	1	1	yes	characteristic
511	C₂	C₁₉×#3394	1	1	yes	characteristic
512	C₂	C₁₉×#3396	1	1	yes	characteristic

	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×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₁₉	C₂	semidirect
3. C₁₉×#2355	C₂	semidirect
4. C₁₉×#1983	C₂	semidirect
6. C₁₉×#1958	C₂	semidirect
8. C₁₉×#1804	C₂	semidirect
9. C₁₉×#1803	C₂	semidirect
10. C₄×C₁₉×#103	C₂	semidirect
11. C₄×C₁₉×#102	C₂	semidirect
13. C₁₉×#559	C₄	semidirect
165. #22543	C₁₉	direct (N × H)
223. C₂×C₈×Q₈	C₂×C₁₉	semidirect
224. #2355	C₂×C₁₉	semidirect
225. #1983	C₂×C₁₉	semidirect
227. #1958	C₂×C₁₉	semidirect
229. #1804	C₂×C₁₉	semidirect
230. #1803	C₂×C₁₉	semidirect
231. C₄×#103	C₂×C₁₉	semidirect
232. C₄×#102	C₂×C₁₉	semidirect
261. #559	C₄×C₁₉	semidirect
354. C₁₉	#22543	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×#559	2
C₂×C₈×Q₈×C₁₉	2
C₁₉×#2355	2
C₁₉×#1983	2
C₁₉×#1982	2
C₁₉×#1958	2
C₁₉×#1957	2
C₁₉×#1804	2
C₁₉×#1803	2
C₄×C₁₉×#103	2
C₄×C₁₉×#102	2
#22543	19

Subgroups — C19×#22543 #18028502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22543 #18028502