Subgroups — C₁₉×#26285 #18032244

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2584	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2101	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2100	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2085	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1991	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#398	—	2	1	no	—
25	C₁₉×#395	—	2	1	no	—
26	C₁₉×#391	—	2	1	no	—
27	C₁₉×#389	—	2	1	no	—
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	C₂²	1	1	yes	characteristic
30	C₁₉×#389	C₂²	1	1	yes	characteristic
31	C₁₉×#389	C₂²	1	1	yes	characteristic
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#387	—	2	1	no	—
34	C₁₉×#387	—	2	1	no	—
35	C₁₉×#384	C₂²	1	1	yes	characteristic
36	C₁₉×#382	C₂²	1	1	yes	characteristic
37	C₁₉×#382	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#340	C₂²	1	1	yes	characteristic
44	C₁₉×#340	C₂²	1	1	yes	characteristic
45	C₁₉×#340	C₂²	1	1	yes	characteristic
46	C₁₉×#340	C₂²	1	1	yes	characteristic
47	C₁₉×#340	C₂²	1	1	yes	characteristic
48	C₁₉×#340	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₄×Q₈×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#107	—	2	2	no	—
95	C₁₉×#106	—	2	2	no	—
96	C₁₉×#106	—	2	2	no	—
97	C₁₉×#106	Q₈	1	4	yes	complemented
98	C₁₉×C₄⋊C₈	—	2	2	no	—
99	C₄×C₈×C₁₉	—	2	2	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	1	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	2	1	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	4	2	no	—
159	C₄⋊C₄×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	4	2	no	—
161	C₄⋊C₄×C₁₉	—	4	2	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	—	8	1	no	—
164	C₄⋊C₄×C₁₉	—	8	1	no	—
165	C₄⋊C₄×C₁₉	—	8	1	no	—
166	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
168	C₄⋊C₄×C₁₉	#41	1	2	yes	—
169	C₄²×C₁₉	—	2	1	no	—
170	C₄²×C₁₉	—	2	1	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	2	1	no	—
173	C₄²×C₁₉	—	4	2	no	—
174	C₄²×C₁₉	—	8	1	no	—
175	C₄²×C₁₉	—	8	1	no	—
176	C₄²×C₁₉	—	8	1	no	—
177	C₄²×C₁₉	#41	1	2	yes	—
178	C₄²×C₁₉	#41	1	2	yes	—
179	#26285	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	#123	1	2	yes	—
222	C₂×C₄×C₁₉	#123	1	2	yes	—
223	C₂×C₄×C₁₉	#135	1	2	yes	—
224	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
229	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
230	C₈×C₁₉	—	2	2	no	—
231	C₈×C₁₉	—	4	1	no	—
232	C₈×C₁₉	—	4	1	no	—
233	C₈×C₁₉	—	4	1	no	—
234	#2584	C₂×C₁₉	1	1	yes	characteristic
235	#2355	C₂×C₁₉	1	1	yes	characteristic
236	#2101	C₂×C₁₉	1	1	yes	characteristic
237	#2100	C₂×C₁₉	1	1	yes	characteristic
238	#2085	C₂×C₁₉	1	1	yes	characteristic
239	#2084	C₂×C₁₉	1	1	yes	characteristic
240	#1991	C₂×C₁₉	1	1	yes	characteristic
241	#1989	C₂×C₁₉	1	1	yes	characteristic
242	#1984	C₂×C₁₉	1	1	yes	characteristic
243	#1949	C₂×C₁₉	1	1	yes	characteristic
244	#1920	C₂×C₁₉	1	1	yes	characteristic
245	#1920	C₂×C₁₉	1	1	yes	characteristic
246	#1919	C₂×C₁₉	1	1	yes	characteristic
247	#1918	C₂×C₁₉	1	1	yes	characteristic
248	C₄×#106	C₂×C₁₉	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
250	C₂²×C₁₉	#548	1	1	yes	characteristic
251	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
252	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
253	C₂²×C₁₉	#575	1	1	yes	characteristic
254	C₂²×C₁₉	#577	1	1	yes	characteristic
255	C₂²×C₁₉	#577	1	1	yes	characteristic
256	C₄×C₁₉	—	2	2	no	—
257	C₄×C₁₉	—	2	2	no	—
258	C₄×C₁₉	—	2	2	no	—
259	C₄×C₁₉	—	4	1	no	—
260	C₄×C₁₉	—	4	1	no	—
261	C₄×C₁₉	—	4	1	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	—	8	1	no	—
267	C₄×C₁₉	—	8	1	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	—	8	1	no	—
270	C₄×C₁₉	#533	1	1	yes	characteristic
271	C₄×C₁₉	#541	1	1	yes	characteristic
272	C₄×C₁₉	#556	1	1	yes	characteristic
273	C₄×C₁₉	#557	1	1	yes	characteristic
274	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
282	#398	—	2	1	no	—
283	#395	—	2	1	no	—
284	#391	—	2	1	no	—
285	#389	—	2	1	no	—
286	#389	—	2	1	no	—
287	#389	C₂²×C₁₉	1	1	yes	characteristic
288	#389	C₂²×C₁₉	1	1	yes	characteristic
289	#389	C₂²×C₁₉	1	1	yes	characteristic
290	#389	C₂²×C₁₉	1	1	yes	characteristic
291	#387	—	2	1	no	—
292	#387	—	2	1	no	—
293	#384	C₂²×C₁₉	1	1	yes	characteristic
294	#382	C₂²×C₁₉	1	1	yes	characteristic
295	#382	C₂²×C₁₉	1	1	yes	characteristic
296	C₄×C₄⋊C₄	—	2	1	no	—
297	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
301	#340	C₂²×C₁₉	1	1	yes	characteristic
302	#340	C₂²×C₁₉	1	1	yes	characteristic
303	#340	C₂²×C₁₉	1	1	yes	characteristic
304	#340	C₂²×C₁₉	1	1	yes	characteristic
305	#340	C₂²×C₁₉	1	1	yes	characteristic
306	#340	C₂²×C₁₉	1	1	yes	characteristic
307	#340	C₂²×C₁₉	1	1	yes	characteristic
308	#340	C₂²×C₁₉	1	1	yes	characteristic
309	#340	C₂²×C₁₉	1	1	yes	characteristic
310	#340	C₂²×C₁₉	1	1	yes	characteristic
311	#340	C₂²×C₁₉	1	1	yes	characteristic
312	#340	C₂²×C₁₉	1	1	yes	characteristic
313	#336	C₂²×C₁₉	1	1	yes	characteristic
314	#336	C₂²×C₁₉	1	1	yes	characteristic
315	#336	C₂²×C₁₉	1	1	yes	characteristic
316	#336	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₁₉	#2446	1	1	yes	characteristic
318	C₂×C₁₉	#3091	1	1	yes	characteristic
319	C₂×C₁₉	#3099	1	1	yes	characteristic
320	C₂×C₁₉	#3360	1	1	yes	characteristic
321	C₂×C₁₉	#3371	1	1	yes	characteristic
322	C₂×C₁₉	#3381	1	1	yes	characteristic
323	C₂×C₁₉	#3388	1	1	yes	characteristic
324	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
329	#125	—	2	2	no	—
330	#125	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
359	#107	—	2	2	no	—
360	#106	—	2	2	no	—
361	#106	—	2	2	no	—
362	#106	Q₈×C₁₉	1	4	yes	complemented
363	C₄⋊C₈	—	2	2	no	—
364	C₄×C₈	—	2	2	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	C₁₉	#26285	1	1	yes	characteristic, direct product factor, Sylow
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	4	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
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	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	4	2	no	—
428	C₄⋊C₄	—	4	2	no	—
429	C₄⋊C₄	—	8	1	no	—
430	C₄⋊C₄	—	8	1	no	—
431	C₄⋊C₄	—	8	1	no	—
432	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
433	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
434	C₄⋊C₄	#41×C₁₉	1	2	yes	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	4	2	no	—
440	C₄²	—	8	1	no	—
441	C₄²	—	8	1	no	—
442	C₄²	—	8	1	no	—
443	C₄²	#41×C₁₉	1	2	yes	—
444	C₄²	#41×C₁₉	1	2	yes	—
445	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
446	Q₈	—	4	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	C₁₉×#123	1	2	yes	—
487	C₂×C₄	C₁₉×#123	1	2	yes	—
488	C₂×C₄	C₁₉×#135	1	2	yes	—
489	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
492	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
493	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
494	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	4	1	no	—
497	C₈	—	4	1	no	—
498	C₈	—	4	1	no	—
499	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
500	C₂²	C₁₉×#548	1	1	yes	characteristic
501	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
502	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
503	C₂²	C₁₉×#575	1	1	yes	characteristic
504	C₂²	C₁₉×#577	1	1	yes	characteristic
505	C₂²	C₁₉×#577	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	—	8	1	no	—
520	C₄	C₁₉×#533	1	1	yes	characteristic
521	C₄	C₁₉×#541	1	1	yes	characteristic
522	C₄	C₁₉×#556	1	1	yes	characteristic
523	C₄	C₁₉×#557	1	1	yes	characteristic
524	C₂	C₁₉×#2446	1	1	yes	characteristic
525	C₂	C₁₉×#3091	1	1	yes	characteristic
526	C₂	C₁₉×#3099	1	1	yes	characteristic
527	C₂	C₁₉×#3360	1	1	yes	characteristic
528	C₂	C₁₉×#3371	1	1	yes	characteristic
529	C₂	C₁₉×#3381	1	1	yes	characteristic
530	C₂	C₁₉×#3388	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×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
97. C₁₉×#106	Q₈	semidirect
179. #26285	C₁₉	direct (N × H)
362. #106	Q₈×C₁₉	semidirect
377. C₁₉	#26285	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2584	2
C₁₉×#2355	2
C₁₉×#2101	2
C₁₉×#2100	2
C₁₉×#2085	2
C₁₉×#2084	2
C₁₉×#1991	2
C₁₉×#1989	2
C₁₉×#1984	2
C₁₉×#1949	2
C₁₉×#1920	2
C₁₉×#1919	2
C₁₉×#1918	2
C₄×C₁₉×#106	2
#26285	19

Subgroups — C19×#26285 #18032244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26285 #18032244