Subgroups — C₁₉×#34912 #18040871

Order 4864.

1750 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2608	C₂	1	2	yes	maximal
2	C₁₉×#2607	C₂	1	2	yes	maximal
3	C₁₉×#2606	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2605	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2570	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2550	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2441	C₂	1	2	yes	maximal
8	C₁₉×#2439	C₂	1	2	yes	maximal
9	C₁₉×#2396	C₂	1	4	yes	maximal
10	C₄×C₁₉×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#125	C₂	1	2	yes	maximal, complemented
12	C₁₉×#2295	C₂	1	4	yes	maximal, complemented
13	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
19	C₂×C₁₉×#117	C₂²	1	2	yes	—
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#400	C₂²	1	4	yes	—
23	C₁₉×#399	C₂²	1	4	yes	—
24	C₁₉×#398	C₂²	1	4	yes	—
25	C₁₉×#398	C₂²	1	4	yes	—
26	C₁₉×#396	C₂²	1	4	yes	—
27	C₁₉×#396	C₂²	1	4	yes	—
28	C₁₉×#395	C₂²	1	4	yes	—
29	C₁₉×#393	C₂²	1	4	yes	—
30	C₁₉×#391	C₂²	1	4	yes	—
31	C₁₉×#391	C₂²	1	4	yes	—
32	C₁₉×#391	C₂²	1	4	yes	—
33	C₁₉×#389	C₂²	1	2	yes	—
34	C₁₉×#389	C₂²	1	2	yes	—
35	C₁₉×#389	C₂²	1	2	yes	—
36	C₁₉×#389	C₂²	1	4	yes	—
37	C₁₉×#389	C₂²	1	2	yes	—
38	C₁₉×#389	C₂²	1	4	yes	—
39	C₁₉×#389	C₂²	1	4	yes	—
40	C₁₉×#387	C₂²	1	4	yes	—
41	C₁₉×#387	C₂²	1	4	yes	—
42	C₁₉×#387	C₂²	1	4	yes	—
43	C₁₉×#387	C₂²	1	4	yes	—
44	C₁₉×#387	C₂²	1	4	yes	—
45	C₁₉×#387	C₂²	1	4	yes	—
46	C₁₉×#384	C₂²	1	2	yes	—
47	C₁₉×#383	C₂²	1	2	yes	—
48	C₁₉×#382	C₂²	1	2	yes	—
49	C₁₉×#382	C₂²	1	2	yes	—
50	C₁₉×#381	C₂²	1	2	yes	—
51	C₁₉×#380	C₂²	1	1	yes	characteristic
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
55	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
56	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
61	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
68	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
69	C₁₉×#376	C₂²	1	2	yes	—
70	C₁₉×#376	C₂²	1	2	yes	—
71	C₁₉×#376	C₂²	1	2	yes	—
72	C₄³×C₁₉	C₂²	1	2	yes	—
73	C₄³×C₁₉	C₂²	1	1	yes	characteristic
74	C₄³×C₁₉	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	—	2	8	no	—
80	C₁₉×#125	—	2	8	no	—
81	C₄×Q₈×C₁₉	—	2	16	no	—
82	C₁₉×#117	—	2	8	no	—
83	C₁₉×#117	—	2	8	no	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₁₉	Q₈	1	8	yes	complemented
105	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
106	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
122	C₁₉×#95	C₂³	1	2	yes	—
123	C₁₉×#95	C₂³	1	2	yes	—
124	C₁₉×#95	C₂³	1	4	yes	—
125	C₁₉×#95	C₂³	1	2	yes	—
126	C₁₉×#95	C₂³	1	2	yes	—
127	C₁₉×#95	C₂³	1	2	yes	—
128	C₁₉×#95	C₂³	1	2	yes	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₁₉×#95	C₂³	1	2	yes	—
131	C₁₉×#95	C₂³	1	4	yes	—
132	C₁₉×#95	C₂³	1	4	yes	—
133	C₁₉×#95	C₂³	1	4	yes	—
134	C₁₉×#95	C₂³	1	4	yes	—
135	C₁₉×#95	C₂³	1	4	yes	—
136	C₁₉×#95	C₂³	1	4	yes	—
137	C₁₉×#95	C₂³	1	4	yes	—
138	C₁₉×#95	C₂³	1	4	yes	—
139	C₁₉×#95	C₂³	1	4	yes	—
140	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₂×Q₈×C₁₉	—	2	8	no	—
142	C₂×Q₈×C₁₉	—	2	8	no	—
143	C₂×Q₈×C₁₉	—	4	4	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	4	1	no	—
147	C₂²×C₄×C₁₉	—	4	1	no	—
148	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
150	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₄⋊C₄×C₁₉	—	2	4	no	—
166	C₄⋊C₄×C₁₉	—	2	4	no	—
167	C₄⋊C₄×C₁₉	—	2	4	no	—
168	C₄⋊C₄×C₁₉	—	2	8	no	—
169	C₄⋊C₄×C₁₉	—	2	8	no	—
170	C₄⋊C₄×C₁₉	—	2	8	no	—
171	C₄⋊C₄×C₁₉	—	2	8	no	—
172	C₄⋊C₄×C₁₉	—	2	8	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	8	no	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	4	4	no	—
177	C₄⋊C₄×C₁₉	—	4	4	no	—
178	C₄⋊C₄×C₁₉	—	4	4	no	—
179	C₄⋊C₄×C₁₉	#41	1	8	yes	—
180	C₂²⋊C₄×C₁₉	—	2	8	no	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₉	—	4	2	no	—
184	C₂²⋊C₄×C₁₉	—	4	2	no	—
185	C₄²×C₁₉	—	2	8	no	—
186	C₄²×C₁₉	—	2	4	no	—
187	C₄²×C₁₉	—	2	8	no	—
188	C₄²×C₁₉	—	2	8	no	—
189	C₄²×C₁₉	—	2	4	no	—
190	C₄²×C₁₉	—	2	4	no	—
191	C₄²×C₁₉	—	4	1	no	—
192	C₄²×C₁₉	—	4	2	no	—
193	C₄²×C₁₉	—	4	1	no	—
194	C₄²×C₁₉	—	4	1	no	—
195	C₄²×C₁₉	—	4	2	no	—
196	C₄²×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
198	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
199	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
200	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
201	C₄²×C₁₉	#41	1	8	yes	—
202	#34912	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
208	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
209	Q₈×C₁₉	—	4	16	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	8	no	—
223	C₂×C₄×C₁₉	—	2	8	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	4	4	no	—
240	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
241	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
242	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
243	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
244	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
245	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
246	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
247	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
248	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
251	#2608	C₂×C₁₉	1	2	yes	—
252	#2607	C₂×C₁₉	1	2	yes	—
253	#2606	C₂×C₁₉	1	2	yes	complemented
254	#2605	C₂×C₁₉	1	2	yes	complemented
255	#2570	C₂×C₁₉	1	2	yes	complemented
256	#2550	C₂×C₁₉	1	2	yes	complemented
257	#2441	C₂×C₁₉	1	2	yes	—
258	#2439	C₂×C₁₉	1	2	yes	—
259	#2396	C₂×C₁₉	1	4	yes	—
260	C₄×C₄⋊Q₈	C₂×C₁₉	1	2	yes	complemented
261	C₄×#125	C₂×C₁₉	1	2	yes	complemented
262	#2295	C₂×C₁₉	1	4	yes	complemented
263	#2283	C₂×C₁₉	1	1	yes	characteristic
264	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
265	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
272	C₂²×C₁₉	C₂²×#41	1	2	yes	—
273	C₂²×C₁₉	C₂²×#41	1	2	yes	—
274	C₂²×C₁₉	#585	1	1	yes	characteristic
275	C₂²×C₁₉	#585	1	1	yes	characteristic
276	C₄×C₁₉	—	2	2	no	—
277	C₄×C₁₉	—	2	2	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	2	8	no	—
281	C₄×C₁₉	—	2	4	no	—
282	C₄×C₁₉	—	2	4	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	4	no	—
285	C₄×C₁₉	—	4	4	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	4	no	—
288	C₄×C₁₉	#533	1	4	yes	—
289	C₄×C₁₉	#533	1	4	yes	—
290	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
291	C₂×#125	C₂²×C₁₉	1	2	yes	—
292	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
293	C₂×#117	C₂²×C₁₉	1	2	yes	—
294	C₂×#117	C₂²×C₁₉	1	2	yes	—
295	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
296	#400	C₂²×C₁₉	1	4	yes	—
297	#399	C₂²×C₁₉	1	4	yes	—
298	#398	C₂²×C₁₉	1	4	yes	—
299	#398	C₂²×C₁₉	1	4	yes	—
300	#396	C₂²×C₁₉	1	4	yes	—
301	#396	C₂²×C₁₉	1	4	yes	—
302	#395	C₂²×C₁₉	1	4	yes	—
303	#393	C₂²×C₁₉	1	4	yes	—
304	#391	C₂²×C₁₉	1	4	yes	—
305	#391	C₂²×C₁₉	1	4	yes	—
306	#391	C₂²×C₁₉	1	4	yes	—
307	#389	C₂²×C₁₉	1	2	yes	—
308	#389	C₂²×C₁₉	1	2	yes	—
309	#389	C₂²×C₁₉	1	2	yes	—
310	#389	C₂²×C₁₉	1	4	yes	—
311	#389	C₂²×C₁₉	1	2	yes	—
312	#389	C₂²×C₁₉	1	4	yes	—
313	#389	C₂²×C₁₉	1	4	yes	—
314	#387	C₂²×C₁₉	1	4	yes	—
315	#387	C₂²×C₁₉	1	4	yes	—
316	#387	C₂²×C₁₉	1	4	yes	—
317	#387	C₂²×C₁₉	1	4	yes	—
318	#387	C₂²×C₁₉	1	4	yes	—
319	#387	C₂²×C₁₉	1	4	yes	—
320	#384	C₂²×C₁₉	1	2	yes	—
321	#383	C₂²×C₁₉	1	2	yes	—
322	#382	C₂²×C₁₉	1	2	yes	—
323	#382	C₂²×C₁₉	1	2	yes	—
324	#381	C₂²×C₁₉	1	2	yes	—
325	#380	C₂²×C₁₉	1	1	yes	characteristic
326	#380	C₂²×C₁₉	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
330	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
331	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
332	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
333	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
334	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
337	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
339	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
340	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
341	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
342	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
343	#376	C₂²×C₁₉	1	2	yes	—
344	#376	C₂²×C₁₉	1	2	yes	—
345	#376	C₂²×C₁₉	1	2	yes	—
346	C₄³	C₂²×C₁₉	1	1	yes	characteristic
347	C₄³	C₂²×C₁₉	1	1	yes	characteristic
348	C₄³	C₂²×C₁₉	1	2	yes	—
349	C₂×C₁₉	—	4	2	no	—
350	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
351	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
352	C₂×C₁₉	#3458	1	1	yes	characteristic
353	C₂×C₁₉	#3475	1	2	yes	—
354	C₂×C₁₉	#3480	1	2	yes	—
355	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
356	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₄⋊Q₈	—	2	8	no	—
360	#125	—	2	8	no	—
361	C₄×Q₈	—	2	16	no	—
362	#117	—	2	8	no	—
363	#117	—	2	8	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
384	C₂×C₄²	Q₈×C₁₉	1	8	yes	complemented
385	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
386	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
387	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
388	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
389	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
391	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
402	#95	C₂³×C₁₉	1	2	yes	—
403	#95	C₂³×C₁₉	1	2	yes	—
404	#95	C₂³×C₁₉	1	4	yes	—
405	#95	C₂³×C₁₉	1	2	yes	—
406	#95	C₂³×C₁₉	1	2	yes	—
407	#95	C₂³×C₁₉	1	2	yes	—
408	#95	C₂³×C₁₉	1	2	yes	—
409	#95	C₂³×C₁₉	1	2	yes	—
410	#95	C₂³×C₁₉	1	2	yes	—
411	#95	C₂³×C₁₉	1	4	yes	—
412	#95	C₂³×C₁₉	1	4	yes	—
413	#95	C₂³×C₁₉	1	4	yes	—
414	#95	C₂³×C₁₉	1	4	yes	—
415	#95	C₂³×C₁₉	1	4	yes	—
416	#95	C₂³×C₁₉	1	4	yes	—
417	#95	C₂³×C₁₉	1	4	yes	—
418	#95	C₂³×C₁₉	1	4	yes	—
419	#95	C₂³×C₁₉	1	4	yes	—
420	C₁₉	#34912	1	1	yes	characteristic, direct product factor, Sylow
421	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
422	C₂×Q₈	—	2	8	no	—
423	C₂×Q₈	—	2	8	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
430	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
431	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₄⋊C₄	—	4	4	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₄⋊C₄	#41×C₁₉	1	8	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₄²	—	2	8	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	8	no	—
469	C₄²	—	2	8	no	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	4	1	no	—
473	C₄²	—	4	2	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	2	no	—
478	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
479	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
480	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
481	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
482	C₄²	#41×C₁₉	1	8	yes	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
488	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
489	Q₈	—	4	16	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
521	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
522	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
523	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
524	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
525	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
526	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
527	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
528	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
529	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
530	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
537	C₂²	C₂²×#41×C₁₉	1	2	yes	—
538	C₂²	C₂²×#41×C₁₉	1	2	yes	—
539	C₂²	C₁₉×#585	1	1	yes	characteristic
540	C₂²	C₁₉×#585	1	1	yes	characteristic
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	4	no	—
546	C₄	—	2	8	no	—
547	C₄	—	2	4	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	4	no	—
553	C₄	C₁₉×#533	1	4	yes	—
554	C₄	C₁₉×#533	1	4	yes	—
555	C₂	—	4	2	no	—
556	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
557	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
558	C₂	C₁₉×#3458	1	1	yes	characteristic
559	C₂	C₁₉×#3475	1	2	yes	—
560	C₂	C₁₉×#3480	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2606	C₂	semidirect
4. C₁₉×#2605	C₂	semidirect
5. C₁₉×#2570	C₂	semidirect
6. C₁₉×#2550	C₂	semidirect
10. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
11. C₄×C₁₉×#125	C₂	semidirect
12. C₁₉×#2295	C₂	semidirect
104. C₂×C₄²×C₁₉	Q₈	semidirect
202. #34912	C₁₉	direct (N × H)
253. #2606	C₂×C₁₉	semidirect
254. #2605	C₂×C₁₉	semidirect
255. #2570	C₂×C₁₉	semidirect
256. #2550	C₂×C₁₉	semidirect
260. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
261. C₄×#125	C₂×C₁₉	semidirect
262. #2295	C₂×C₁₉	semidirect
384. C₂×C₄²	Q₈×C₁₉	semidirect
420. C₁₉	#34912	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×#2608	2
C₁₉×#2607	2
C₁₉×#2606	2
C₁₉×#2605	2
C₁₉×#2570	2
C₁₉×#2550	2
C₁₉×#2441	2
C₁₉×#2439	2
C₁₉×#2396	2
C₄×C₁₉×C₄⋊Q₈	2
C₄×C₁₉×#125	2
C₁₉×#2295	2
C₁₉×#2283	2
C₄×C₁₉×#117	2
#34912	19

Subgroups — C19×#34912 #18040871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34912 #18040871