Subgroups — C₁₉×#17987 #18023946

Order 4864.

606 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3171	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1588	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1586	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1585	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₁₉×#529	C₂²	1	1	yes	characteristic
18	C₁₉×#501	C₄	1	1	yes	characteristic
19	C₁₉×#496	C₄	1	1	yes	characteristic
20	C₁₉×#490	C₄	1	1	yes	characteristic
21	C₁₉×#489	C₄	1	1	yes	characteristic
22	C₁₉×#469	C₄	1	1	yes	characteristic
23	C₁₉×#469	C₄	1	1	yes	characteristic
24	C₁₉×#468	C₄	1	1	yes	characteristic
25	C₁₉×#468	C₄	1	1	yes	characteristic
26	C₁₉×#446	C₂²	1	1	yes	characteristic
27	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#436	—	2	1	no	—
33	C₁₉×#436	C₂²	1	1	yes	characteristic
34	C₁₉×#436	C₂²	1	1	yes	characteristic
35	C₁₉×#436	C₂²	1	1	yes	characteristic
36	C₁₉×#435	—	2	1	no	—
37	C₁₉×#435	—	2	1	no	—
38	C₁₉×#435	—	2	1	no	—
39	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#433	—	2	1	no	—
43	C₁₉×#432	C₂²	1	1	yes	characteristic
44	C₁₉×#431	C₂²	1	1	yes	characteristic
45	C₁₉×#424	—	2	1	no	—
46	C₁₉×#423	C₂²	1	1	yes	characteristic
47	C₁₉×#408	—	2	1	no	—
48	C₁₉×#408	—	2	1	no	—
49	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#335	C₂²	1	1	yes	characteristic
52	C₁₉×#335	C₂²	1	1	yes	characteristic
53	C₁₉×#334	C₂²	1	1	yes	characteristic
54	C₁₉×#334	C₂²	1	1	yes	characteristic
55	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×#322	C₂²	1	1	yes	characteristic
64	C₁₉×#322	C₂²	1	1	yes	characteristic
65	C₁₉×#322	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
70	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
84	C₁₉×#126	—	2	1	no	—
85	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
88	C₁₉×#123	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
92	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
93	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#117	—	2	1	no	—
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
103	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
104	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
105	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
111	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
118	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
119	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
120	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
121	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
122	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
123	C₁₉×C₂²⋊C₈	—	2	1	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×C₂²⋊C₈	—	2	1	no	—
126	C₁₉×C₂²⋊C₈	—	2	1	no	—
127	C₁₉×C₂²⋊C₈	—	2	1	no	—
128	C₁₉×C₂²⋊C₈	—	2	1	no	—
129	C₁₉×C₂²⋊C₈	—	2	1	no	—
130	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
131	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
132	C₁₉×#97	—	2	1	no	—
133	C₁₉×#97	—	2	1	no	—
134	C₁₉×#97	C₂×C₄	1	1	yes	characteristic
135	C₁₉×#97	C₂×C₄	1	1	yes	characteristic
136	C₄×C₈×C₁₉	—	2	1	no	—
137	C₄×C₈×C₁₉	—	2	1	no	—
138	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	8	1	no	—
145	#41×C₁₉	—	8	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
162	SD₁₆×C₁₉	—	4	1	no	—
163	SD₁₆×C₁₉	—	4	1	no	—
164	D₈×C₁₉	—	4	1	no	—
165	D₈×C₁₉	—	4	1	no	—
166	M₁₆×C₁₉	—	4	1	no	—
167	M₁₆×C₁₉	—	4	1	no	—
168	M₁₆×C₁₉	—	8	1	no	—
169	M₁₆×C₁₉	—	8	1	no	—
170	M₁₆×C₁₉	—	8	1	no	—
171	M₁₆×C₁₉	—	8	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	4	2	no	—
179	C₂×C₈×C₁₉	—	8	1	no	—
180	C₂×C₈×C₁₉	—	8	1	no	—
181	C₂×C₈×C₁₉	—	8	1	no	—
182	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₉	#41	1	1	yes	characteristic
212	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
213	#17987	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
218	Q₈×C₁₉	—	2	1	no	—
219	Q₈×C₁₉	—	2	1	no	—
220	Q₈×C₁₉	—	8	1	no	—
221	D₄×C₁₉	—	2	1	no	—
222	D₄×C₁₉	—	2	1	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	2	1	no	—
225	D₄×C₁₉	—	2	1	no	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	8	1	no	—
228	D₄×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	8	1	no	—
230	D₄×C₁₉	—	8	1	no	—
231	D₄×C₁₉	—	8	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
254	C₈×C₁₉	—	2	2	no	—
255	C₈×C₁₉	—	2	1	no	—
256	C₈×C₁₉	—	2	1	no	—
257	C₈×C₁₉	—	2	1	no	—
258	C₈×C₁₉	—	2	1	no	—
259	C₈×C₁₉	—	2	1	no	—
260	C₈×C₁₉	—	2	1	no	—
261	C₈×C₁₉	—	2	1	no	—
262	C₈×C₁₉	—	2	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	#3171	C₂×C₁₉	1	1	yes	characteristic
269	#2993	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#2981	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1588	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1586	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1586	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1585	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1583	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1492	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1451	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	#568	1	1	yes	characteristic
306	C₄×C₁₉	#568	1	1	yes	characteristic
307	C₄×C₁₉	#576	1	1	yes	characteristic
308	C₄×C₁₉	#577	1	1	yes	characteristic
309	#532	C₂²×C₁₉	1	1	yes	characteristic
310	#529	C₂²×C₁₉	1	1	yes	characteristic
311	#501	C₄×C₁₉	1	1	yes	characteristic
312	#496	C₄×C₁₉	1	1	yes	characteristic
313	#490	C₄×C₁₉	1	1	yes	characteristic
314	#489	C₄×C₁₉	1	1	yes	characteristic
315	#469	C₄×C₁₉	1	1	yes	characteristic
316	#469	C₄×C₁₉	1	1	yes	characteristic
317	#468	C₄×C₁₉	1	1	yes	characteristic
318	#468	C₄×C₁₉	1	1	yes	characteristic
319	#446	C₂²×C₁₉	1	1	yes	characteristic
320	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
322	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
323	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
324	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
325	#436	—	2	1	no	—
326	#436	C₂²×C₁₉	1	1	yes	characteristic
327	#436	C₂²×C₁₉	1	1	yes	characteristic
328	#436	C₂²×C₁₉	1	1	yes	characteristic
329	#435	—	2	1	no	—
330	#435	—	2	1	no	—
331	#435	—	2	1	no	—
332	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
333	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
334	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
335	#433	—	2	1	no	—
336	#432	C₂²×C₁₉	1	1	yes	characteristic
337	#431	C₂²×C₁₉	1	1	yes	characteristic
338	#424	—	2	1	no	—
339	#423	C₂²×C₁₉	1	1	yes	characteristic
340	#408	—	2	1	no	—
341	#408	—	2	1	no	—
342	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
344	#335	C₂²×C₁₉	1	1	yes	characteristic
345	#335	C₂²×C₁₉	1	1	yes	characteristic
346	#334	C₂²×C₁₉	1	1	yes	characteristic
347	#334	C₂²×C₁₉	1	1	yes	characteristic
348	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
349	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
350	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
351	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
352	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
353	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
354	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
355	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
356	#322	C₂²×C₁₉	1	1	yes	characteristic
357	#322	C₂²×C₁₉	1	1	yes	characteristic
358	#322	C₂²×C₁₉	1	1	yes	characteristic
359	#322	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₁₉	—	4	1	no	—
361	C₂×C₁₉	—	8	1	no	—
362	C₂×C₁₉	—	8	1	no	—
363	C₂×C₁₉	—	8	1	no	—
364	C₂×C₁₉	#2932	1	1	yes	characteristic
365	C₂×C₁₉	#2946	1	1	yes	characteristic
366	C₂×C₁₉	#2956	1	1	yes	characteristic
367	C₂×#41	—	2	1	no	—
368	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
369	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
370	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
371	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
377	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
383	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
384	#126	—	2	1	no	—
385	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
386	#124	—	2	1	no	—
387	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
388	#123	—	2	1	no	—
389	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
390	#121	—	2	1	no	—
391	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
392	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
393	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
398	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
399	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
400	#117	—	2	1	no	—
401	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
402	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
403	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
404	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
405	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
410	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
415	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
416	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
417	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
418	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
419	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
420	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
421	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
422	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
423	C₂²⋊C₈	—	2	1	no	—
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
431	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
432	#97	—	2	1	no	—
433	#97	—	2	1	no	—
434	#97	C₂×C₄×C₁₉	1	1	yes	characteristic
435	#97	C₂×C₄×C₁₉	1	1	yes	characteristic
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	—	2	1	no	—
438	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₁₉	#17987	1	1	yes	characteristic, direct product factor, Sylow
445	#41	—	8	1	no	—
446	#41	—	8	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
455	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
456	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
463	SD₁₆	—	4	1	no	—
464	SD₁₆	—	4	1	no	—
465	D₈	—	4	1	no	—
466	D₈	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	8	1	no	—
470	M₁₆	—	8	1	no	—
471	M₁₆	—	8	1	no	—
472	M₁₆	—	8	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	4	2	no	—
480	C₂×C₈	—	8	1	no	—
481	C₂×C₈	—	8	1	no	—
482	C₂×C₈	—	8	1	no	—
483	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
484	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
485	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
486	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄²	#41×C₁₉	1	1	yes	characteristic
513	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	8	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	8	1	no	—
531	D₄	—	8	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
549	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
550	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
551	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
554	C₈	—	2	2	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	C₁₉×#568	1	1	yes	characteristic
591	C₄	C₁₉×#568	1	1	yes	characteristic
592	C₄	C₁₉×#576	1	1	yes	characteristic
593	C₄	C₁₉×#577	1	1	yes	characteristic
594	C₂	—	4	1	no	—
595	C₂	—	8	1	no	—
596	C₂	—	8	1	no	—
597	C₂	—	8	1	no	—
598	C₂	C₁₉×#2932	1	1	yes	characteristic
599	C₂	C₁₉×#2946	1	1	yes	characteristic
600	C₂	C₁₉×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₁₉×#3171	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2993	C₂	semidirect
3. C₁₉×#2981	C₂	semidirect
4. C₁₉×#1588	C₂	semidirect
5. C₁₉×#1586	C₂	semidirect
6. C₁₉×#1586	C₂	semidirect
7. C₁₉×#1585	C₂	semidirect
8. C₁₉×#1583	C₂	semidirect
9. C₁₉×#1582	C₂	semidirect
10. C₁₉×#1581	C₂	semidirect
11. C₁₉×#1581	C₂	semidirect
12. C₁₉×#1569	C₂	semidirect
13. C₁₉×#1494	C₂	semidirect
14. C₁₉×#1492	C₂	semidirect
15. C₁₉×#1451	C₂	semidirect
213. #17987	C₁₉	direct (N × H)
269. #2993	C₂×C₁₉	semidirect
270. #2981	C₂×C₁₉	semidirect
271. #1588	C₂×C₁₉	semidirect
272. #1586	C₂×C₁₉	semidirect
273. #1586	C₂×C₁₉	semidirect
274. #1585	C₂×C₁₉	semidirect
275. #1583	C₂×C₁₉	semidirect
276. #1582	C₂×C₁₉	semidirect
277. #1581	C₂×C₁₉	semidirect
278. #1581	C₂×C₁₉	semidirect
279. #1569	C₂×C₁₉	semidirect
280. #1494	C₂×C₁₉	semidirect
281. #1492	C₂×C₁₉	semidirect
282. #1451	C₂×C₁₉	semidirect
444. C₁₉	#17987	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×#3171	2
C₁₉×#2993	2
C₁₉×#2981	2
C₁₉×#1588	2
C₁₉×#1586	2
C₁₉×#1585	2
C₁₉×#1583	2
C₁₉×#1582	2
C₁₉×#1581	2
C₁₉×#1569	2
C₁₉×#1494	2
C₁₉×#1492	2
C₁₉×#1451	2
#17987	19

Subgroups — C19×#17987 #18023946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17987 #18023946