Subgroups — C₁₉×#18465 #18024424

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3564	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2821	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1606	C₂	1	2	yes	maximal
6	C₁₉×#1605	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1603	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1602	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1521	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1515	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1473	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	1	no	—
13	C₁₉×#563	—	2	1	no	—
14	C₁₉×#556	—	2	1	no	—
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#552	—	2	1	no	—
18	C₁₉×#551	—	2	1	no	—
19	C₁₉×#551	—	2	1	no	—
20	C₁₉×#544	C₂²	1	1	yes	characteristic
21	C₁₉×#543	C₂²	1	1	yes	characteristic
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#541	—	2	1	no	—
24	C₁₉×#541	—	2	1	no	—
25	C₁₉×#539	—	2	1	no	—
26	C₁₉×#539	C₂²	1	1	yes	characteristic
27	C₁₉×#538	C₂²	1	1	yes	characteristic
28	C₁₉×#533	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₁₉×#529	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#126	C₂²	1	1	yes	characteristic
32	C₁₉×#497	—	2	1	no	—
33	C₁₉×#494	—	2	1	no	—
34	C₁₉×#491	—	2	1	no	—
35	C₁₉×#487	—	2	1	no	—
36	C₁₉×#462	—	2	1	no	—
37	C₁₉×#462	—	2	1	no	—
38	C₁₉×#462	—	2	1	no	—
39	C₁₉×#461	—	2	1	no	—
40	C₁₉×#451	C₂²	1	2	yes	—
41	C₁₉×#451	C₂²	1	2	yes	—
42	C₁₉×#451	C₂²	1	2	yes	—
43	C₁₉×#448	C₂²	1	2	yes	—
44	C₁₉×#432	C₂²	1	1	yes	characteristic
45	C₁₉×#431	C₂²	1	1	yes	characteristic
46	C₁₉×#400	—	2	1	no	—
47	C₁₉×#399	—	2	1	no	—
48	C₁₉×#398	—	2	1	no	—
49	C₁₉×#397	—	2	1	no	—
50	C₁₉×#395	C₂²	1	2	yes	—
51	C₁₉×#393	C₂²	1	2	yes	—
52	C₁₉×#383	C₂²	1	1	yes	characteristic
53	C₁₉×#328	C₂²	1	2	yes	—
54	C₁₉×#328	C₂²	1	2	yes	—
55	C₁₉×#328	C₂²	1	2	yes	—
56	C₁₉×#327	C₂²	1	2	yes	—
57	C₁₉×#324	C₂²	1	2	yes	—
58	C₁₉×#323	C₂²	1	2	yes	—
59	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
60	C₂×Q₁₆×C₁₉	—	2	2	no	—
61	C₂×Q₁₆×C₁₉	—	2	2	no	—
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	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	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
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×#126	—	2	1	no	—
80	C₁₉×#126	—	2	1	no	—
81	C₁₉×#126	—	2	1	no	—
82	C₁₉×#126	—	2	1	no	—
83	C₁₉×#126	—	2	1	no	—
84	C₁₉×#126	—	2	1	no	—
85	C₁₉×#126	—	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	—	2	1	no	—
92	C₁₉×#125	—	2	1	no	—
93	C₁₉×#125	—	2	1	no	—
94	C₁₉×#125	—	2	1	no	—
95	C₁₉×#125	D₄	1	1	yes	characteristic
96	C₁₉×#124	—	2	1	no	—
97	C₁₉×#124	—	2	1	no	—
98	C₁₉×#124	—	2	1	no	—
99	C₁₉×#124	D₄	1	1	yes	characteristic
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×C₂²⋊Q₈	—	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	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
124	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₉×#121	—	2	1	no	—
126	C₁₉×#121	C₂³	1	1	yes	characteristic
127	C₁₉×#120	—	2	1	no	—
128	C₄×Q₈×C₁₉	—	2	1	no	—
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×Q₈×C₁₉	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
140	C₁₉×#117	—	2	1	no	—
141	C₁₉×#117	—	2	1	no	—
142	C₁₉×#117	—	2	1	no	—
143	C₁₉×#117	—	2	1	no	—
144	C₁₉×#117	—	2	1	no	—
145	C₁₉×#117	—	2	1	no	—
146	C₂×C₄⋊C₄×C₁₉	—	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	2	no	—
150	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
159	C₁₉×C₄⋊C₈	—	2	1	no	—
160	C₁₉×C₄⋊C₈	—	2	1	no	—
161	C₁₉×#103	—	2	2	no	—
162	C₁₉×#103	—	2	2	no	—
163	C₁₉×#103	—	2	2	no	—
164	C₁₉×#103	—	2	2	no	—
165	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
166	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
167	C₁₉×#97	—	2	1	no	—
168	C₄×C₈×C₁₉	—	2	1	no	—
169	C₁₉×#95	—	2	1	no	—
170	C₁₉×#95	—	2	1	no	—
171	C₁₉×#95	—	2	2	no	—
172	C₁₉×#95	—	2	2	no	—
173	C₁₉×#95	C₂³	1	2	yes	—
174	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	1	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	—	2	2	no	—
179	C₂×Q₈×C₁₉	—	2	2	no	—
180	C₂×Q₈×C₁₉	—	8	2	no	—
181	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
194	C₂²×C₄×C₁₉	—	2	2	no	—
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
201	Q₁₆×C₁₉	—	8	2	no	—
202	Q₁₆×C₁₉	—	8	2	no	—
203	Q₁₆×C₁₉	—	8	2	no	—
204	SD₁₆×C₁₉	—	8	2	no	—
205	C₂×C₈×C₁₉	—	2	2	no	—
206	C₂×C₈×C₁₉	—	2	2	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	1	no	—
236	C₄⋊C₄×C₁₉	—	4	1	no	—
237	C₄⋊C₄×C₁₉	—	4	1	no	—
238	C₄⋊C₄×C₁₉	—	4	1	no	—
239	C₄⋊C₄×C₁₉	—	4	1	no	—
240	C₄⋊C₄×C₁₉	—	8	2	no	—
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
246	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
266	C₂²⋊C₄×C₁₉	—	8	2	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	—	2	1	no	—
272	C₄²×C₁₉	—	2	1	no	—
273	C₄²×C₁₉	—	2	1	no	—
274	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
278	#18465	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂³×C₁₉	—	2	1	no	—
280	C₂³×C₁₉	—	2	1	no	—
281	C₂³×C₁₉	—	2	2	no	—
282	C₂³×C₁₉	—	4	1	no	—
283	C₂³×C₁₉	—	4	1	no	—
284	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₁₉	—	4	1	no	—
286	Q₈×C₁₉	—	4	1	no	—
287	Q₈×C₁₉	—	4	1	no	—
288	Q₈×C₁₉	—	4	2	no	—
289	Q₈×C₁₉	—	4	2	no	—
290	Q₈×C₁₉	—	4	2	no	—
291	Q₈×C₁₉	—	4	2	no	—
292	Q₈×C₁₉	—	8	1	no	—
293	Q₈×C₁₉	—	8	1	no	—
294	Q₈×C₁₉	—	8	1	no	—
295	D₄×C₁₉	—	4	1	no	—
296	D₄×C₁₉	—	4	2	no	—
297	D₄×C₁₉	—	8	1	no	—
298	D₄×C₁₉	—	8	1	no	—
299	C₂×C₄×C₁₉	—	2	2	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	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	2	1	no	—
310	C₂×C₄×C₁₉	—	2	2	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	no	—
315	C₂×C₄×C₁₉	—	4	2	no	—
316	C₂×C₄×C₁₉	—	4	2	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	—	4	2	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	8	1	no	—
322	C₂×C₄×C₁₉	—	8	1	no	—
323	C₂×C₄×C₁₉	—	8	1	no	—
324	C₂×C₄×C₁₉	—	8	1	no	—
325	C₂×C₄×C₁₉	—	8	1	no	—
326	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
327	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
328	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
329	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
330	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
332	C₈×C₁₉	—	4	2	no	—
333	C₈×C₁₉	—	4	2	no	—
334	#3564	C₂×C₁₉	1	1	yes	characteristic
335	#3218	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#2821	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#1606	C₂×C₁₉	1	2	yes	—
339	#1605	C₂×C₁₉	1	2	yes	complemented
340	#1603	C₂×C₁₉	1	2	yes	complemented
341	#1602	C₂×C₁₉	1	2	yes	complemented
342	#1521	C₂×C₁₉	1	1	yes	characteristic, complemented
343	#1515	C₂×C₁₉	1	1	yes	characteristic, complemented
344	#1473	C₂×C₁₉	1	1	yes	characteristic, complemented
345	C₂²×C₁₉	—	2	1	no	—
346	C₂²×C₁₉	—	2	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	1	no	—
349	C₂²×C₁₉	—	4	1	no	—
350	C₂²×C₁₉	—	4	1	no	—
351	C₂²×C₁₉	—	4	1	no	—
352	C₂²×C₁₉	—	4	1	no	—
353	C₂²×C₁₉	—	8	2	no	—
354	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
355	C₂²×C₁₉	#578	1	2	yes	—
356	C₄×C₁₉	—	2	1	no	—
357	C₄×C₁₉	—	2	1	no	—
358	C₄×C₁₉	—	2	1	no	—
359	C₄×C₁₉	—	2	1	no	—
360	C₄×C₁₉	—	2	1	no	—
361	C₄×C₁₉	—	2	1	no	—
362	C₄×C₁₉	—	4	1	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	4	1	no	—
366	C₄×C₁₉	—	4	1	no	—
367	C₄×C₁₉	—	4	1	no	—
368	C₄×C₁₉	—	4	1	no	—
369	C₄×C₁₉	—	4	1	no	—
370	C₄×C₁₉	—	4	1	no	—
371	C₄×C₁₉	—	4	1	no	—
372	C₄×C₁₉	—	8	2	no	—
373	C₄×C₁₉	—	8	2	no	—
374	#563	—	2	1	no	—
375	#563	—	2	1	no	—
376	#556	—	2	1	no	—
377	#554	—	2	1	no	—
378	#552	—	2	1	no	—
379	#552	—	2	1	no	—
380	#551	—	2	1	no	—
381	#551	—	2	1	no	—
382	#544	C₂²×C₁₉	1	1	yes	characteristic
383	#543	C₂²×C₁₉	1	1	yes	characteristic
384	#542	—	2	1	no	—
385	#541	—	2	1	no	—
386	#541	—	2	1	no	—
387	#539	—	2	1	no	—
388	#539	C₂²×C₁₉	1	1	yes	characteristic
389	#538	C₂²×C₁₉	1	1	yes	characteristic
390	#533	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
392	#529	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#126	C₂²×C₁₉	1	1	yes	characteristic
394	#497	—	2	1	no	—
395	#494	—	2	1	no	—
396	#491	—	2	1	no	—
397	#487	—	2	1	no	—
398	#462	—	2	1	no	—
399	#462	—	2	1	no	—
400	#462	—	2	1	no	—
401	#461	—	2	1	no	—
402	#451	C₂²×C₁₉	1	2	yes	—
403	#451	C₂²×C₁₉	1	2	yes	—
404	#451	C₂²×C₁₉	1	2	yes	—
405	#448	C₂²×C₁₉	1	2	yes	—
406	#432	C₂²×C₁₉	1	1	yes	characteristic
407	#431	C₂²×C₁₉	1	1	yes	characteristic
408	#400	—	2	1	no	—
409	#399	—	2	1	no	—
410	#398	—	2	1	no	—
411	#397	—	2	1	no	—
412	#395	C₂²×C₁₉	1	2	yes	—
413	#393	C₂²×C₁₉	1	2	yes	—
414	#383	C₂²×C₁₉	1	1	yes	characteristic
415	#328	C₂²×C₁₉	1	2	yes	—
416	#328	C₂²×C₁₉	1	2	yes	—
417	#328	C₂²×C₁₉	1	2	yes	—
418	#327	C₂²×C₁₉	1	2	yes	—
419	#324	C₂²×C₁₉	1	2	yes	—
420	#323	C₂²×C₁₉	1	2	yes	—
421	C₂×C₁₉	—	2	2	no	—
422	C₂×C₁₉	—	8	1	no	—
423	C₂×C₁₉	—	8	1	no	—
424	C₂×C₁₉	#3011	1	1	yes	characteristic
425	C₂×C₁₉	#3022	1	1	yes	characteristic
426	C₂×C₁₉	#3027	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
428	C₂×Q₁₆	—	2	2	no	—
429	C₂×Q₁₆	—	2	2	no	—
430	C₂×Q₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	—	2	1	no	—
434	C₄⋊Q₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	—	2	1	no	—
438	C₄⋊Q₈	—	2	1	no	—
439	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
440	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
441	#126	—	2	1	no	—
442	#126	—	2	1	no	—
443	#126	—	2	1	no	—
444	#126	—	2	1	no	—
445	#126	—	2	1	no	—
446	#126	—	2	1	no	—
447	#126	—	2	1	no	—
448	#126	—	2	1	no	—
449	#126	—	2	1	no	—
450	#126	—	2	1	no	—
451	#126	—	2	1	no	—
452	#126	—	2	1	no	—
453	#126	—	2	1	no	—
454	#125	—	2	1	no	—
455	#125	—	2	1	no	—
456	#125	—	2	1	no	—
457	#125	—	2	1	no	—
458	#125	—	2	1	no	—
459	#125	—	2	1	no	—
460	#125	—	2	1	no	—
461	#125	—	2	1	no	—
462	#125	—	2	1	no	—
463	#125	D₄×C₁₉	1	1	yes	characteristic
464	#124	—	2	1	no	—
465	#124	—	2	1	no	—
466	#124	—	2	1	no	—
467	#124	D₄×C₁₉	1	1	yes	characteristic
468	#123	—	2	1	no	—
469	#123	—	2	1	no	—
470	#123	—	2	1	no	—
471	#123	—	2	1	no	—
472	#123	—	2	1	no	—
473	#123	—	2	1	no	—
474	#123	—	2	1	no	—
475	#123	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	C₂²⋊Q₈	—	2	1	no	—
480	C₂²⋊Q₈	—	2	1	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
491	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
492	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
493	#121	—	2	1	no	—
494	#121	C₂³×C₁₉	1	1	yes	characteristic
495	#120	—	2	1	no	—
496	C₄×Q₈	—	2	1	no	—
497	C₄×Q₈	—	2	1	no	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
500	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
501	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
508	#117	—	2	1	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	—	2	1	no	—
513	#117	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	2	no	—
518	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	2	no	—
523	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
527	C₄⋊C₈	—	2	1	no	—
528	C₄⋊C₈	—	2	1	no	—
529	#103	—	2	2	no	—
530	#103	—	2	2	no	—
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
534	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
535	#97	—	2	1	no	—
536	C₄×C₈	—	2	1	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	#95	—	2	2	no	—
540	#95	—	2	2	no	—
541	#95	C₂³×C₁₉	1	2	yes	—
542	C₁₉	#18465	1	1	yes	characteristic, direct product factor, Sylow
543	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	8	2	no	—
550	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
570	Q₁₆	—	8	2	no	—
571	Q₁₆	—	8	2	no	—
572	Q₁₆	—	8	2	no	—
573	SD₁₆	—	8	2	no	—
574	C₂×C₈	—	2	2	no	—
575	C₂×C₈	—	2	2	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	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	4	1	no	—
606	C₄⋊C₄	—	4	1	no	—
607	C₄⋊C₄	—	4	1	no	—
608	C₄⋊C₄	—	4	1	no	—
609	C₄⋊C₄	—	8	2	no	—
610	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
612	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	8	2	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
646	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	8	1	no	—
661	Q₈	—	8	1	no	—
662	Q₈	—	8	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	2	no	—
665	D₄	—	8	1	no	—
666	D₄	—	8	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	8	1	no	—
690	C₂×C₄	—	8	1	no	—
691	C₂×C₄	—	8	1	no	—
692	C₂×C₄	—	8	1	no	—
693	C₂×C₄	—	8	1	no	—
694	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
695	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
696	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
697	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
700	C₈	—	4	2	no	—
701	C₈	—	4	2	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	8	2	no	—
711	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
712	C₂²	C₁₉×#578	1	2	yes	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	8	2	no	—
730	C₄	—	8	2	no	—
731	C₂	—	2	2	no	—
732	C₂	—	8	1	no	—
733	C₂	—	8	1	no	—
734	C₂	C₁₉×#3011	1	1	yes	characteristic
735	C₂	C₁₉×#3022	1	1	yes	characteristic
736	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#538	C₂²
LCS	G ▷ C₂²×C₄ ▷ 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×#3218	C₂	semidirect
3. C₁₉×#3209	C₂	semidirect
4. C₁₉×#2821	C₂	semidirect
6. C₁₉×#1605	C₂	semidirect
7. C₁₉×#1603	C₂	semidirect
8. C₁₉×#1602	C₂	semidirect
9. C₁₉×#1521	C₂	semidirect
10. C₁₉×#1515	C₂	semidirect
11. C₁₉×#1473	C₂	semidirect
278. #18465	C₁₉	direct (N × H)
335. #3218	C₂×C₁₉	semidirect
336. #3209	C₂×C₁₉	semidirect
337. #2821	C₂×C₁₉	semidirect
339. #1605	C₂×C₁₉	semidirect
340. #1603	C₂×C₁₉	semidirect
341. #1602	C₂×C₁₉	semidirect
342. #1521	C₂×C₁₉	semidirect
343. #1515	C₂×C₁₉	semidirect
344. #1473	C₂×C₁₉	semidirect
542. C₁₉	#18465	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×#3564	2
C₁₉×#3218	2
C₁₉×#3209	2
C₁₉×#2821	2
C₁₉×#1606	2
C₁₉×#1605	2
C₁₉×#1603	2
C₁₉×#1602	2
C₁₉×#1521	2
C₁₉×#1515	2
C₁₉×#1473	2
#18465	19

Subgroups — C19×#18465 #18024424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18465 #18024424