Subgroups — C₁₉×#19064 #18025023

Order 4864.

834 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3553	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1663	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1534	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#564	C₂²	1	1	yes	characteristic
13	C₁₉×#563	C₂²	1	1	yes	characteristic
14	C₁₉×#563	C₂²	1	1	yes	characteristic
15	C₁₉×#562	C₂²	1	1	yes	characteristic
16	C₁₉×#554	—	2	1	no	—
17	C₁₉×#554	—	2	1	no	—
18	C₁₉×#553	—	2	1	no	—
19	C₁₉×#553	—	2	1	no	—
20	C₁₉×#552	—	2	1	no	—
21	C₁₉×#552	—	2	1	no	—
22	C₁₉×#541	—	2	1	no	—
23	C₁₉×#541	—	2	1	no	—
24	C₁₉×#539	—	2	1	no	—
25	C₁₉×#539	—	2	1	no	—
26	C₁₉×#539	—	2	1	no	—
27	C₁₉×#539	—	2	1	no	—
28	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₉×#529	C₂²	1	1	yes	characteristic
30	C₁₉×#529	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
32	C₁₉×#501	—	2	1	no	—
33	C₁₉×#501	—	2	1	no	—
34	C₁₉×#501	C₂²	1	2	yes	—
35	C₁₉×#501	C₂²	1	2	yes	—
36	C₁₉×#501	C₂²	1	2	yes	—
37	C₁₉×#497	C₂²	1	2	yes	—
38	C₁₉×#491	C₂²	1	2	yes	—
39	C₁₉×#489	C₂²	1	2	yes	—
40	C₁₉×#484	—	2	1	no	—
41	C₁₉×#481	—	2	1	no	—
42	C₁₉×#475	—	2	1	no	—
43	C₁₉×#474	—	2	1	no	—
44	C₁₉×#462	—	2	1	no	—
45	C₁₉×#461	—	2	1	no	—
46	C₁₉×#451	—	2	1	no	—
47	C₁₉×#448	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#432	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#107	—	2	1	no	—
51	C₂×C₁₉×#106	—	2	1	no	—
52	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
53	C₁₉×#330	C₂²	1	2	yes	—
54	C₁₉×#330	C₂²	1	2	yes	—
55	C₁₉×#330	C₂²	1	2	yes	—
56	C₁₉×#330	C₂²	1	2	yes	—
57	C₁₉×#329	C₂²	1	2	yes	—
58	C₁₉×#329	C₂²	1	2	yes	—
59	C₂²×Q₈×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×#126	—	2	1	no	—
70	C₁₉×#126	—	2	1	no	—
71	C₁₉×#126	—	2	1	no	—
72	C₁₉×#126	—	2	1	no	—
73	C₁₉×#126	—	2	1	no	—
74	C₁₉×#126	—	2	1	no	—
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#126	—	2	1	no	—
78	C₁₉×#126	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	—	2	1	no	—
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	—	2	1	no	—
88	C₁₉×#125	—	2	1	no	—
89	C₁₉×#125	—	2	1	no	—
90	C₁₉×#125	—	2	1	no	—
91	C₁₉×#125	D₄	1	1	yes	characteristic
92	C₁₉×#125	D₄	1	1	yes	characteristic
93	C₁₉×#125	C₂³	1	1	yes	characteristic
94	C₁₉×#125	C₂³	1	1	yes	characteristic
95	C₁₉×#125	C₂³	1	1	yes	characteristic
96	C₁₉×#125	C₂³	1	1	yes	characteristic
97	C₁₉×#124	C₂³	1	1	yes	characteristic
98	C₁₉×#124	C₂³	1	1	yes	characteristic
99	C₁₉×#123	—	2	1	no	—
100	C₁₉×#123	—	2	1	no	—
101	C₁₉×#123	—	2	1	no	—
102	C₁₉×#123	—	2	1	no	—
103	C₁₉×#123	—	2	1	no	—
104	C₁₉×#123	—	2	1	no	—
105	C₁₉×#123	—	2	1	no	—
106	C₁₉×#123	—	2	1	no	—
107	C₁₉×#123	—	2	1	no	—
108	C₁₉×#123	—	2	1	no	—
109	C₁₉×C₂²⋊Q₈	—	2	1	no	—
110	C₁₉×C₂²⋊Q₈	—	2	1	no	—
111	C₁₉×C₂²⋊Q₈	—	2	1	no	—
112	C₁₉×C₂²⋊Q₈	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	—	2	1	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×C₂²⋊Q₈	—	2	1	no	—
116	C₁₉×C₂²⋊Q₈	—	2	1	no	—
117	C₁₉×C₂²⋊Q₈	—	2	1	no	—
118	C₁₉×C₂²⋊Q₈	—	2	1	no	—
119	C₁₉×C₂²⋊Q₈	—	2	1	no	—
120	C₁₉×C₂²⋊Q₈	—	2	1	no	—
121	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
122	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₁₉×#121	—	2	1	no	—
124	C₁₉×#121	—	2	1	no	—
125	C₁₉×#121	—	2	1	no	—
126	C₁₉×#121	—	2	1	no	—
127	C₁₉×#121	D₄	1	1	yes	characteristic
128	C₁₉×#121	D₄	1	1	yes	characteristic
129	C₄×Q₈×C₁₉	—	2	1	no	—
130	C₄×Q₈×C₁₉	—	2	1	no	—
131	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
132	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
133	C₄×D₄×C₁₉	—	2	1	no	—
134	C₄×D₄×C₁₉	—	2	1	no	—
135	C₄×D₄×C₁₉	—	2	1	no	—
136	C₄×D₄×C₁₉	—	2	1	no	—
137	C₄×D₄×C₁₉	—	2	1	no	—
138	C₄×D₄×C₁₉	—	2	1	no	—
139	C₄×D₄×C₁₉	—	2	1	no	—
140	C₄×D₄×C₁₉	—	2	1	no	—
141	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
142	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
143	C₁₉×#117	—	2	1	no	—
144	C₁₉×#117	—	2	1	no	—
145	C₁₉×#117	—	2	1	no	—
146	C₁₉×#117	—	2	1	no	—
147	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
155	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
156	C₁₉×#107	—	2	2	no	—
157	C₁₉×#107	—	2	2	no	—
158	C₁₉×#107	—	2	2	no	—
159	C₁₉×#106	—	2	2	no	—
160	C₁₉×#106	—	2	2	no	—
161	C₁₉×#106	—	2	2	no	—
162	C₁₉×C₄⋊C₈	—	2	1	no	—
163	C₁₉×C₄⋊C₈	—	2	1	no	—
164	C₁₉×#103	—	2	2	no	—
165	C₁₉×#103	—	2	2	no	—
166	C₁₉×#103	—	2	2	no	—
167	C₁₉×#102	—	2	2	no	—
168	C₁₉×C₂²⋊C₈	—	2	1	no	—
169	C₁₉×C₂²⋊C₈	—	2	1	no	—
170	C₁₉×#97	—	2	1	no	—
171	C₁₉×#97	C₂³	1	2	yes	—
172	C₁₉×#97	C₂³	1	2	yes	—
173	C₁₉×#97	C₂³	1	2	yes	—
174	C₂×Q₈×C₁₉	—	2	1	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	2	no	—
177	C₂×Q₈×C₁₉	—	4	1	no	—
178	C₂×Q₈×C₁₉	—	8	2	no	—
179	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	4	1	no	—
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	Q₁₆×C₁₉	—	8	2	no	—
200	SD₁₆×C₁₉	—	8	2	no	—
201	C₂×C₈×C₁₉	—	2	4	no	—
202	C₂×C₈×C₁₉	—	2	2	no	—
203	C₂×C₈×C₁₉	—	2	2	no	—
204	C₂×C₈×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	2	1	no	—
233	C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₄⋊C₄×C₁₉	—	2	2	no	—
236	C₄⋊C₄×C₁₉	—	2	2	no	—
237	C₄⋊C₄×C₁₉	—	4	1	no	—
238	C₄⋊C₄×C₁₉	—	4	1	no	—
239	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₂²⋊C₄×C₁₉	—	2	1	no	—
248	C₂²⋊C₄×C₁₉	—	2	1	no	—
249	C₂²⋊C₄×C₁₉	—	2	1	no	—
250	C₂²⋊C₄×C₁₉	—	2	1	no	—
251	C₂²⋊C₄×C₁₉	—	2	1	no	—
252	C₂²⋊C₄×C₁₉	—	2	1	no	—
253	C₂²⋊C₄×C₁₉	—	2	1	no	—
254	C₂²⋊C₄×C₁₉	—	2	1	no	—
255	C₂²⋊C₄×C₁₉	—	2	1	no	—
256	C₂²⋊C₄×C₁₉	—	2	1	no	—
257	C₂²⋊C₄×C₁₉	—	2	1	no	—
258	C₂²⋊C₄×C₁₉	—	2	1	no	—
259	C₂²⋊C₄×C₁₉	—	2	1	no	—
260	C₂²⋊C₄×C₁₉	—	2	1	no	—
261	C₂²⋊C₄×C₁₉	—	2	1	no	—
262	C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₂²⋊C₄×C₁₉	—	2	1	no	—
264	C₂²⋊C₄×C₁₉	—	2	1	no	—
265	C₄²×C₁₉	—	2	1	no	—
266	C₄²×C₁₉	—	2	1	no	—
267	C₄²×C₁₉	—	2	1	no	—
268	C₄²×C₁₉	—	2	1	no	—
269	C₄²×C₁₉	—	2	1	no	—
270	C₄²×C₁₉	—	2	1	no	—
271	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
275	#19064	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₁₉	—	2	1	no	—
277	C₂³×C₁₉	—	2	1	no	—
278	C₂³×C₁₉	#120	1	1	yes	characteristic
279	Q₈×C₁₉	—	4	1	no	—
280	Q₈×C₁₉	—	4	1	no	—
281	Q₈×C₁₉	—	4	2	no	—
282	Q₈×C₁₉	—	4	2	no	—
283	Q₈×C₁₉	—	8	2	no	—
284	Q₈×C₁₉	—	8	1	no	—
285	Q₈×C₁₉	—	8	1	no	—
286	D₄×C₁₉	—	4	1	no	—
287	D₄×C₁₉	—	4	1	no	—
288	D₄×C₁₉	—	4	2	no	—
289	D₄×C₁₉	—	4	2	no	—
290	D₄×C₁₉	—	8	1	no	—
291	D₄×C₁₉	—	8	1	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	1	no	—
296	C₂×C₄×C₁₉	—	2	1	no	—
297	C₂×C₄×C₁₉	—	2	1	no	—
298	C₂×C₄×C₁₉	—	2	1	no	—
299	C₂×C₄×C₁₉	—	2	1	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	2	no	—
306	C₂×C₄×C₁₉	—	8	1	no	—
307	C₂×C₄×C₁₉	—	8	1	no	—
308	C₂×C₄×C₁₉	—	8	1	no	—
309	C₂×C₄×C₁₉	—	8	1	no	—
310	C₂×C₄×C₁₉	—	8	1	no	—
311	C₂×C₄×C₁₉	—	8	1	no	—
312	C₂×C₄×C₁₉	—	8	1	no	—
313	C₂×C₄×C₁₉	—	8	1	no	—
314	C₂×C₄×C₁₉	—	8	2	no	—
315	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
316	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
317	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
318	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
321	C₈×C₁₉	—	2	4	no	—
322	C₈×C₁₉	—	4	2	no	—
323	C₈×C₁₉	—	4	2	no	—
324	#3553	C₂×C₁₉	1	1	yes	characteristic
325	#3239	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
327	C₂×#501	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#1664	C₂×C₁₉	1	2	yes	complemented
329	#1663	C₂×C₁₉	1	2	yes	complemented
330	#1661	C₂×C₁₉	1	2	yes	complemented
331	#1660	C₂×C₁₉	1	2	yes	complemented
332	#1534	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
335	C₂²×C₁₉	—	2	1	no	—
336	C₂²×C₁₉	—	2	1	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	1	no	—
343	C₂²×C₁₉	#456	1	2	yes	—
344	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
345	C₄×C₁₉	—	2	1	no	—
346	C₄×C₁₉	—	2	1	no	—
347	C₄×C₁₉	—	2	1	no	—
348	C₄×C₁₉	—	2	1	no	—
349	C₄×C₁₉	—	2	1	no	—
350	C₄×C₁₉	—	2	1	no	—
351	C₄×C₁₉	—	4	1	no	—
352	C₄×C₁₉	—	4	1	no	—
353	C₄×C₁₉	—	4	1	no	—
354	C₄×C₁₉	—	4	1	no	—
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	1	no	—
360	C₄×C₁₉	—	4	1	no	—
361	C₄×C₁₉	—	8	2	no	—
362	#564	C₂²×C₁₉	1	1	yes	characteristic
363	#563	C₂²×C₁₉	1	1	yes	characteristic
364	#563	C₂²×C₁₉	1	1	yes	characteristic
365	#562	C₂²×C₁₉	1	1	yes	characteristic
366	#554	—	2	1	no	—
367	#554	—	2	1	no	—
368	#553	—	2	1	no	—
369	#553	—	2	1	no	—
370	#552	—	2	1	no	—
371	#552	—	2	1	no	—
372	#541	—	2	1	no	—
373	#541	—	2	1	no	—
374	#539	—	2	1	no	—
375	#539	—	2	1	no	—
376	#539	—	2	1	no	—
377	#539	—	2	1	no	—
378	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
379	#529	C₂²×C₁₉	1	1	yes	characteristic
380	#529	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
382	#501	—	2	1	no	—
383	#501	—	2	1	no	—
384	#501	C₂²×C₁₉	1	2	yes	—
385	#501	C₂²×C₁₉	1	2	yes	—
386	#501	C₂²×C₁₉	1	2	yes	—
387	#497	C₂²×C₁₉	1	2	yes	—
388	#491	C₂²×C₁₉	1	2	yes	—
389	#489	C₂²×C₁₉	1	2	yes	—
390	#484	—	2	1	no	—
391	#481	—	2	1	no	—
392	#475	—	2	1	no	—
393	#474	—	2	1	no	—
394	#462	—	2	1	no	—
395	#461	—	2	1	no	—
396	#451	—	2	1	no	—
397	#448	—	2	1	no	—
398	#432	C₂²×C₁₉	1	1	yes	characteristic
399	#432	C₂²×C₁₉	1	1	yes	characteristic
400	C₂×#107	—	2	1	no	—
401	C₂×#106	—	2	1	no	—
402	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
403	#330	C₂²×C₁₉	1	2	yes	—
404	#330	C₂²×C₁₉	1	2	yes	—
405	#330	C₂²×C₁₉	1	2	yes	—
406	#330	C₂²×C₁₉	1	2	yes	—
407	#329	C₂²×C₁₉	1	2	yes	—
408	#329	C₂²×C₁₉	1	2	yes	—
409	C₂×C₁₉	—	2	2	no	—
410	C₂×C₁₉	—	8	1	no	—
411	C₂×C₁₉	—	8	1	no	—
412	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
413	C₂×C₁₉	#3021	1	1	yes	characteristic
414	C₂×C₁₉	#3022	1	1	yes	characteristic
415	C₂²×Q₈	—	2	1	no	—
416	C₂×Q₁₆	—	2	2	no	—
417	C₂×SD₁₆	—	2	2	no	—
418	C₂²×C₈	—	2	1	no	—
419	C₄⋊Q₈	—	2	1	no	—
420	C₄⋊Q₈	—	2	1	no	—
421	C₄⋊Q₈	—	2	1	no	—
422	C₄⋊Q₈	—	2	1	no	—
423	C₄⋊Q₈	—	2	1	no	—
424	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
425	#126	—	2	1	no	—
426	#126	—	2	1	no	—
427	#126	—	2	1	no	—
428	#126	—	2	1	no	—
429	#126	—	2	1	no	—
430	#126	—	2	1	no	—
431	#126	—	2	1	no	—
432	#126	—	2	1	no	—
433	#126	—	2	1	no	—
434	#126	—	2	1	no	—
435	#125	—	2	1	no	—
436	#125	—	2	1	no	—
437	#125	—	2	1	no	—
438	#125	—	2	1	no	—
439	#125	—	2	1	no	—
440	#125	—	2	1	no	—
441	#125	—	2	1	no	—
442	#125	—	2	1	no	—
443	#125	—	2	1	no	—
444	#125	—	2	1	no	—
445	#125	—	2	1	no	—
446	#125	—	2	1	no	—
447	#125	D₄×C₁₉	1	1	yes	characteristic
448	#125	D₄×C₁₉	1	1	yes	characteristic
449	#125	C₂³×C₁₉	1	1	yes	characteristic
450	#125	C₂³×C₁₉	1	1	yes	characteristic
451	#125	C₂³×C₁₉	1	1	yes	characteristic
452	#125	C₂³×C₁₉	1	1	yes	characteristic
453	#124	C₂³×C₁₉	1	1	yes	characteristic
454	#124	C₂³×C₁₉	1	1	yes	characteristic
455	#123	—	2	1	no	—
456	#123	—	2	1	no	—
457	#123	—	2	1	no	—
458	#123	—	2	1	no	—
459	#123	—	2	1	no	—
460	#123	—	2	1	no	—
461	#123	—	2	1	no	—
462	#123	—	2	1	no	—
463	#123	—	2	1	no	—
464	#123	—	2	1	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
478	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	—	2	1	no	—
483	#121	D₄×C₁₉	1	1	yes	characteristic
484	#121	D₄×C₁₉	1	1	yes	characteristic
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
488	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	—	2	1	no	—
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
498	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
499	#117	—	2	1	no	—
500	#117	—	2	1	no	—
501	#117	—	2	1	no	—
502	#117	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
512	#107	—	2	2	no	—
513	#107	—	2	2	no	—
514	#107	—	2	2	no	—
515	#106	—	2	2	no	—
516	#106	—	2	2	no	—
517	#106	—	2	2	no	—
518	C₄⋊C₈	—	2	1	no	—
519	C₄⋊C₈	—	2	1	no	—
520	#103	—	2	2	no	—
521	#103	—	2	2	no	—
522	#103	—	2	2	no	—
523	#102	—	2	2	no	—
524	C₂²⋊C₈	—	2	1	no	—
525	C₂²⋊C₈	—	2	1	no	—
526	#97	—	2	1	no	—
527	#97	C₂³×C₁₉	1	2	yes	—
528	#97	C₂³×C₁₉	1	2	yes	—
529	#97	C₂³×C₁₉	1	2	yes	—
530	C₁₉	#19064	1	1	yes	characteristic, direct product factor, Sylow
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	4	1	no	—
535	C₂×Q₈	—	8	2	no	—
536	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
556	Q₁₆	—	8	2	no	—
557	SD₁₆	—	8	2	no	—
558	C₂×C₈	—	2	4	no	—
559	C₂×C₈	—	2	2	no	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	2	2	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	4	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
597	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
600	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
601	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
602	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
603	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	C₁₉×#120	1	1	yes	characteristic
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	4	2	no	—
638	Q₈	—	4	2	no	—
639	Q₈	—	8	2	no	—
640	Q₈	—	8	1	no	—
641	Q₈	—	8	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	2	no	—
646	D₄	—	8	1	no	—
647	D₄	—	8	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	—	8	1	no	—
664	C₂×C₄	—	8	1	no	—
665	C₂×C₄	—	8	1	no	—
666	C₂×C₄	—	8	1	no	—
667	C₂×C₄	—	8	1	no	—
668	C₂×C₄	—	8	1	no	—
669	C₂×C₄	—	8	1	no	—
670	C₂×C₄	—	8	2	no	—
671	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
672	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
673	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
675	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
676	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
677	C₈	—	2	4	no	—
678	C₈	—	4	2	no	—
679	C₈	—	4	2	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	C₁₉×#456	1	2	yes	—
689	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	8	2	no	—
707	C₂	—	2	2	no	—
708	C₂	—	8	1	no	—
709	C₂	—	8	1	no	—
710	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
711	C₂	C₁₉×#3021	1	1	yes	characteristic
712	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3553	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3239	C₂	semidirect
3. C₁₉×#3218	C₂	semidirect
4. C₂×C₁₉×#501	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1663	C₂	semidirect
7. C₁₉×#1661	C₂	semidirect
8. C₁₉×#1660	C₂	semidirect
9. C₁₉×#1534	C₂	semidirect
10. C₁₉×#1532	C₂	semidirect
11. C₁₉×#1532	C₂	semidirect
275. #19064	C₁₉	direct (N × H)
325. #3239	C₂×C₁₉	semidirect
326. #3218	C₂×C₁₉	semidirect
327. C₂×#501	C₂×C₁₉	semidirect
328. #1664	C₂×C₁₉	semidirect
329. #1663	C₂×C₁₉	semidirect
330. #1661	C₂×C₁₉	semidirect
331. #1660	C₂×C₁₉	semidirect
332. #1534	C₂×C₁₉	semidirect
333. #1532	C₂×C₁₉	semidirect
334. #1532	C₂×C₁₉	semidirect
530. C₁₉	#19064	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×#3553	2
C₁₉×#3239	2
C₁₉×#3218	2
C₂×C₁₉×#501	2
C₁₉×#1664	2
C₁₉×#1663	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1534	2
C₁₉×#1532	2
#19064	19

Subgroups — C19×#19064 #18025023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19064 #18025023