Subgroups — C₁₉×#18026 #18023985

Order 4864.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2974	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1496	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#480	C₄	1	1	yes	characteristic
19	C₁₉×#480	C₄	1	1	yes	characteristic
20	C₁₉×#474	C₄	1	1	yes	characteristic
21	C₁₉×#474	C₄	1	1	yes	characteristic
22	C₁₉×#459	C₄	1	1	yes	characteristic
23	C₁₉×#459	C₄	1	1	yes	characteristic
24	C₁₉×#447	C₄	1	1	yes	characteristic
25	C₁₉×#447	C₄	1	1	yes	characteristic
26	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#436	—	2	1	no	—
31	C₁₉×#436	C₂²	1	1	yes	characteristic
32	C₁₉×#436	C₂²	1	1	yes	characteristic
33	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#435	—	2	1	no	—
36	C₁₉×#435	—	2	1	no	—
37	C₈×D₄×C₁₉	—	2	1	no	—
38	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#432	C₂²	1	1	yes	characteristic
43	C₁₉×#431	C₂²	1	1	yes	characteristic
44	C₁₉×#431	C₂²	1	1	yes	characteristic
45	C₁₉×#431	C₂²	1	1	yes	characteristic
46	C₁₉×#431	C₂²	1	1	yes	characteristic
47	C₁₉×#408	—	2	1	no	—
48	C₁₉×#408	—	2	1	no	—
49	C₁₉×#407	—	2	1	no	—
50	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
51	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₉×D₄⋊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, complemented
60	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
73	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	—	2	1	no	—
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×#124	—	2	1	no	—
85	C₁₉×#121	—	2	1	no	—
86	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
87	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
101	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
102	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
103	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
104	C₁₉×C₄⋊C₈	—	2	1	no	—
105	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
114	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
115	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#102	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×C₂²⋊C₈	—	2	1	no	—
122	C₁₉×C₂²⋊C₈	—	2	1	no	—
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	—	2	1	no	—
131	C₁₉×C₂²⋊C₈	—	2	1	no	—
132	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
135	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
136	C₁₉×#97	—	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	C₂⁴×C₁₉	—	2	1	no	—
145	#41×C₁₉	—	8	1	no	—
146	#41×C₁₉	—	8	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	2	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	—	2	1	no	—
154	C₂×D₄×C₁₉	—	4	1	no	—
155	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	8	1	no	—
167	C₂²×C₄×C₁₉	—	8	1	no	—
168	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
171	D₈×C₁₉	—	2	2	no	—
172	D₈×C₁₉	—	2	2	no	—
173	D₈×C₁₉	—	4	1	no	—
174	D₈×C₁₉	—	4	1	no	—
175	M₁₆×C₁₉	—	8	1	no	—
176	M₁₆×C₁₉	—	8	1	no	—
177	M₁₆×C₁₉	—	8	1	no	—
178	M₁₆×C₁₉	—	8	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	8	1	no	—
186	C₂×C₈×C₁₉	—	8	1	no	—
187	C₂×C₈×C₁₉	—	8	1	no	—
188	C₂×C₈×C₁₉	—	8	1	no	—
189	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₉	#41	1	1	yes	characteristic
214	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
215	#18026	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	4	2	no	—
221	C₂³×C₁₉	—	4	2	no	—
222	C₂³×C₁₉	—	8	1	no	—
223	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
224	Q₈×C₁₉	—	8	1	no	—
225	D₄×C₁₉	—	2	1	no	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	2	1	no	—
228	D₄×C₁₉	—	2	1	no	—
229	D₄×C₁₉	—	2	1	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	2	1	no	—
232	D₄×C₁₉	—	4	2	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	8	1	no	—
235	D₄×C₁₉	—	8	1	no	—
236	D₄×C₁₉	—	8	1	no	—
237	D₄×C₁₉	#131	1	2	yes	—
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	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	8	1	no	—
256	C₂×C₄×C₁₉	—	8	1	no	—
257	C₂×C₄×C₁₉	—	8	1	no	—
258	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
264	C₈×C₁₉	—	2	1	no	—
265	C₈×C₁₉	—	2	1	no	—
266	C₈×C₁₉	—	2	1	no	—
267	C₈×C₁₉	—	2	1	no	—
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	1	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	2	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	#3100	C₂×C₁₉	1	1	yes	characteristic
279	#2979	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#2974	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1594	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1589	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1586	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1586	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1580	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1496	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1454	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	8	4	no	—
309	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	C₂×#131	1	1	yes	characteristic
319	C₄×C₁₉	#568	1	1	yes	characteristic
320	C₄×C₁₉	#576	1	1	yes	characteristic
321	C₄×C₁₉	#576	1	1	yes	characteristic
322	#532	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
324	#480	C₄×C₁₉	1	1	yes	characteristic
325	#480	C₄×C₁₉	1	1	yes	characteristic
326	#474	C₄×C₁₉	1	1	yes	characteristic
327	#474	C₄×C₁₉	1	1	yes	characteristic
328	#459	C₄×C₁₉	1	1	yes	characteristic
329	#459	C₄×C₁₉	1	1	yes	characteristic
330	#447	C₄×C₁₉	1	1	yes	characteristic
331	#447	C₄×C₁₉	1	1	yes	characteristic
332	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
333	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
334	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
335	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
336	#436	—	2	1	no	—
337	#436	C₂²×C₁₉	1	1	yes	characteristic
338	#436	C₂²×C₁₉	1	1	yes	characteristic
339	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
340	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#435	—	2	1	no	—
342	#435	—	2	1	no	—
343	C₈×D₄	—	2	1	no	—
344	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
345	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
346	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
347	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#432	C₂²×C₁₉	1	1	yes	characteristic
349	#431	C₂²×C₁₉	1	1	yes	characteristic
350	#431	C₂²×C₁₉	1	1	yes	characteristic
351	#431	C₂²×C₁₉	1	1	yes	characteristic
352	#431	C₂²×C₁₉	1	1	yes	characteristic
353	#408	—	2	1	no	—
354	#408	—	2	1	no	—
355	#407	—	2	1	no	—
356	C₂×C₂²⋊C₈	—	2	1	no	—
357	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
358	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
362	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
363	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
364	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
365	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
372	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	C₂×C₁₉	—	4	1	no	—
374	C₂×C₁₉	—	4	2	no	—
375	C₂×C₁₉	—	8	1	no	—
376	C₂×C₁₉	—	8	1	no	—
377	C₂×C₁₉	—	8	1	no	—
378	C₂×C₁₉	#2933	1	1	yes	characteristic
379	C₂×C₁₉	#2948	1	1	yes	characteristic
380	C₂×C₁₉	#2955	1	1	yes	characteristic
381	C₂×#41	—	2	1	no	—
382	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
385	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
386	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
387	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	2	1	no	—
396	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
397	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
398	#124	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
401	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
406	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
407	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
414	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
415	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
416	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
417	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
421	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
422	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
427	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
428	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
429	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
430	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
431	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
432	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
433	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
434	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	C₂²⋊C₈	—	2	1	no	—
442	C₂²⋊C₈	—	2	1	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	C₂²⋊C₈	—	2	1	no	—
446	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
447	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
448	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
449	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
450	#97	—	2	1	no	—
451	C₄×C₈	—	2	1	no	—
452	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
453	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
454	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
455	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
456	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
457	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
458	C₁₉	#18026	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁴	—	2	1	no	—
460	#41	—	8	1	no	—
461	#41	—	8	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
471	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
472	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
473	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	8	1	no	—
482	C₂²×C₄	—	8	1	no	—
483	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
486	D₈	—	2	2	no	—
487	D₈	—	2	2	no	—
488	D₈	—	4	1	no	—
489	D₈	—	4	1	no	—
490	M₁₆	—	8	1	no	—
491	M₁₆	—	8	1	no	—
492	M₁₆	—	8	1	no	—
493	M₁₆	—	8	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	8	1	no	—
501	C₂×C₈	—	8	1	no	—
502	C₂×C₈	—	8	1	no	—
503	C₂×C₈	—	8	1	no	—
504	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
505	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
506	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
507	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
508	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
527	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄²	#41×C₁₉	1	1	yes	characteristic
529	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	8	1	no	—
537	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
538	Q₈	—	8	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	8	1	no	—
549	D₄	—	8	1	no	—
550	D₄	—	8	1	no	—
551	D₄	C₁₉×#131	1	2	yes	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	8	1	no	—
570	C₂×C₄	—	8	1	no	—
571	C₂×C₄	—	8	1	no	—
572	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
573	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
575	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	8	4	no	—
608	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	C₂×C₁₉×#131	1	1	yes	characteristic
618	C₄	C₁₉×#568	1	1	yes	characteristic
619	C₄	C₁₉×#576	1	1	yes	characteristic
620	C₄	C₁₉×#576	1	1	yes	characteristic
621	C₂	—	4	1	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	1	no	—
624	C₂	—	8	1	no	—
625	C₂	—	8	1	no	—
626	C₂	C₁₉×#2933	1	1	yes	characteristic
627	C₂	C₁₉×#2948	1	1	yes	characteristic
628	C₂	C₁₉×#2955	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×#3100	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×#2979	C₂	semidirect
3. C₁₉×#2974	C₂	semidirect
4. C₁₉×#1594	C₂	semidirect
5. C₁₉×#1589	C₂	semidirect
6. C₁₉×#1586	C₂	semidirect
7. C₁₉×#1586	C₂	semidirect
8. C₁₉×#1581	C₂	semidirect
9. C₁₉×#1581	C₂	semidirect
10. C₁₉×#1580	C₂	semidirect
11. C₈×D₈×C₁₉	C₂	semidirect
12. C₁₉×#1572	C₂	semidirect
13. C₁₉×#1496	C₂	semidirect
14. C₁₉×#1478	C₂	semidirect
15. C₁₉×#1454	C₂	semidirect
33. C₁₉×#436	C₂²	semidirect
34. C₁₉×#436	C₂²	semidirect
40. C₈×D₄×C₁₉	C₂²	semidirect
41. C₈×D₄×C₁₉	C₂²	semidirect
51. C₁₉×#335	C₂²	semidirect
52. C₁₉×#335	C₂²	semidirect
53. C₁₉×#334	C₂²	semidirect
54. C₁₉×#334	C₂²	semidirect
59. C₁₉×D₄⋊C₈	C₂²	semidirect
60. C₁₉×D₄⋊C₈	C₂²	semidirect
61. C₁₉×D₄⋊C₈	C₂²	semidirect
62. C₁₉×D₄⋊C₈	C₂²	semidirect
63. C₁₉×#322	C₂²	semidirect
64. C₁₉×#322	C₂²	semidirect
65. C₁₉×#322	C₂²	semidirect
66. C₈²×C₁₉	C₂²	semidirect
215. #18026	C₁₉	direct (N × H)
279. #2979	C₂×C₁₉	semidirect
280. #2974	C₂×C₁₉	semidirect
281. #1594	C₂×C₁₉	semidirect
282. #1589	C₂×C₁₉	semidirect
283. #1586	C₂×C₁₉	semidirect
284. #1586	C₂×C₁₉	semidirect
285. #1581	C₂×C₁₉	semidirect
286. #1581	C₂×C₁₉	semidirect
287. #1580	C₂×C₁₉	semidirect
288. C₈×D₈	C₂×C₁₉	semidirect
289. #1572	C₂×C₁₉	semidirect
290. #1496	C₂×C₁₉	semidirect
291. #1478	C₂×C₁₉	semidirect
292. #1454	C₂×C₁₉	semidirect
339. #436	C₂²×C₁₉	semidirect
340. #436	C₂²×C₁₉	semidirect
346. C₈×D₄	C₂²×C₁₉	semidirect
347. C₈×D₄	C₂²×C₁₉	semidirect
357. #335	C₂²×C₁₉	semidirect
358. #335	C₂²×C₁₉	semidirect
359. #334	C₂²×C₁₉	semidirect
360. #334	C₂²×C₁₉	semidirect
365. D₄⋊C₈	C₂²×C₁₉	semidirect
366. D₄⋊C₈	C₂²×C₁₉	semidirect
367. D₄⋊C₈	C₂²×C₁₉	semidirect
368. D₄⋊C₈	C₂²×C₁₉	semidirect
369. #322	C₂²×C₁₉	semidirect
370. #322	C₂²×C₁₉	semidirect
371. #322	C₂²×C₁₉	semidirect
372. C₈²	C₂²×C₁₉	semidirect
458. C₁₉	#18026	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×#3100	2
C₁₉×#2979	2
C₁₉×#2974	2
C₁₉×#1594	2
C₁₉×#1589	2
C₁₉×#1586	2
C₁₉×#1581	2
C₁₉×#1580	2
C₈×D₈×C₁₉	2
C₁₉×#1572	2
C₁₉×#1496	2
C₁₉×#1478	2
C₁₉×#1454	2
#18026	19

Subgroups — C19×#18026 #18023985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18026 #18023985