Subgroups — C₁₉×#23792 #18029751

Order 4864.

656 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2330	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2320	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2095	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2087	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2086	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2068	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2066	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2059	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2026	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#391	C₂²	1	1	yes	characteristic
31	C₁₉×#391	C₂²	1	1	yes	characteristic
32	C₁₉×#389	—	2	1	no	—
33	C₁₉×#389	—	2	1	no	—
34	C₁₉×#389	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#389	C₂²	1	1	yes	characteristic
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#387	—	2	1	no	—
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#384	C₂²	1	1	yes	characteristic
43	C₁₉×#383	—	2	1	no	—
44	C₁₉×#382	—	2	1	no	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#376	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₄×Q₈×C₁₉	Q₈	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#107	—	2	2	no	—
92	C₁₉×#107	—	2	2	no	—
93	C₁₉×#107	—	2	2	no	—
94	C₁₉×#106	—	2	2	no	—
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×C₄⋊C₈	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#97	—	2	2	no	—
102	C₄×C₈×C₁₉	—	2	2	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	1	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	D₄	1	1	yes	characteristic
115	C₁₉×#95	D₄	1	1	yes	characteristic
116	C₁₉×#95	D₄	1	1	yes	characteristic
117	C₁₉×#95	D₄	1	1	yes	characteristic
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	#41	1	2	yes	—
150	C₂×C₈×C₁₉	#41	1	2	yes	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	8	1	no	—
166	C₄⋊C₄×C₁₉	—	8	1	no	—
167	C₄⋊C₄×C₁₉	—	8	1	no	—
168	C₄⋊C₄×C₁₉	—	8	1	no	—
169	C₄⋊C₄×C₁₉	—	8	1	no	—
170	C₄⋊C₄×C₁₉	—	8	1	no	—
171	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
172	C₄⋊C₄×C₁₉	#41	1	2	yes	—
173	C₄⋊C₄×C₁₉	#41	1	2	yes	—
174	C₄²×C₁₉	—	2	4	no	—
175	C₄²×C₁₉	—	2	1	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	C₄²×C₁₉	—	2	1	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	8	1	no	—
180	C₄²×C₁₉	—	8	1	no	—
181	C₄²×C₁₉	—	8	1	no	—
182	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
183	C₄²×C₁₉	#41	1	2	yes	—
184	#23792	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	2	2	no	—
188	Q₈×C₁₉	—	4	1	no	—
189	Q₈×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
231	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
232	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₈×C₁₉	—	2	2	no	—
239	C₈×C₁₉	—	2	2	no	—
240	C₈×C₁₉	—	4	1	no	—
241	C₈×C₁₉	—	4	1	no	—
242	#2330	C₂×C₁₉	1	1	yes	characteristic
243	#2320	C₂×C₁₉	1	1	yes	characteristic
244	#2099	C₂×C₁₉	1	1	yes	characteristic
245	#2095	C₂×C₁₉	1	1	yes	characteristic
246	#2087	C₂×C₁₉	1	1	yes	characteristic
247	#2086	C₂×C₁₉	1	1	yes	characteristic
248	#2068	C₂×C₁₉	1	1	yes	characteristic
249	#2066	C₂×C₁₉	1	1	yes	characteristic
250	#2059	C₂×C₁₉	1	1	yes	characteristic
251	#2026	C₂×C₁₉	1	1	yes	characteristic
252	#1776	C₂×C₁₉	1	1	yes	characteristic
253	C₄×#107	C₂×C₁₉	1	1	yes	characteristic
254	#1768	C₂×C₁₉	1	1	yes	characteristic
255	#1763	C₂×C₁₉	1	1	yes	characteristic
256	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
258	C₂²×C₁₉	#525	1	1	yes	characteristic
259	C₂²×C₁₉	#532	1	1	yes	characteristic
260	C₂²×C₁₉	#576	1	1	yes	characteristic
261	C₂²×C₁₉	#577	1	1	yes	characteristic
262	C₂²×C₁₉	#578	1	1	yes	characteristic
263	C₂²×C₁₉	#578	1	1	yes	characteristic
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	2	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	4	1	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	#529	1	1	yes	characteristic
279	C₄×C₁₉	#529	1	1	yes	characteristic
280	C₄×C₁₉	#533	1	1	yes	characteristic
281	C₄×C₁₉	#533	1	1	yes	characteristic
282	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
296	#391	C₂²×C₁₉	1	1	yes	characteristic
297	#391	C₂²×C₁₉	1	1	yes	characteristic
298	#389	—	2	1	no	—
299	#389	—	2	1	no	—
300	#389	C₂²×C₁₉	1	1	yes	characteristic
301	#389	C₂²×C₁₉	1	1	yes	characteristic
302	#389	C₂²×C₁₉	1	1	yes	characteristic
303	#389	C₂²×C₁₉	1	1	yes	characteristic
304	#387	—	2	1	no	—
305	#387	—	2	1	no	—
306	#387	—	2	1	no	—
307	#387	—	2	1	no	—
308	#384	C₂²×C₁₉	1	1	yes	characteristic
309	#383	—	2	1	no	—
310	#382	—	2	1	no	—
311	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
313	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
314	#376	C₂²×C₁₉	1	1	yes	characteristic
315	#340	C₂²×C₁₉	1	1	yes	characteristic
316	#340	C₂²×C₁₉	1	1	yes	characteristic
317	#340	C₂²×C₁₉	1	1	yes	characteristic
318	#340	C₂²×C₁₉	1	1	yes	characteristic
319	#340	C₂²×C₁₉	1	1	yes	characteristic
320	#340	C₂²×C₁₉	1	1	yes	characteristic
321	#340	C₂²×C₁₉	1	1	yes	characteristic
322	#340	C₂²×C₁₉	1	1	yes	characteristic
323	#336	C₂²×C₁₉	1	1	yes	characteristic
324	#336	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₁₉	#2396	1	1	yes	characteristic
326	C₂×C₁₉	#3082	1	1	yes	characteristic
327	C₂×C₁₉	#3083	1	1	yes	characteristic
328	C₂×C₁₉	#3120	1	1	yes	characteristic
329	C₂×C₁₉	#3124	1	1	yes	characteristic
330	C₂×C₁₉	#3177	1	1	yes	characteristic
331	C₂×C₁₉	#3179	1	1	yes	characteristic
332	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	#125	—	2	2	no	—
338	#125	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	Q₈×C₁₉	1	4	yes	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
364	#107	—	2	2	no	—
365	#107	—	2	2	no	—
366	#107	—	2	2	no	—
367	#106	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	2	no	—
370	#103	—	2	2	no	—
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#97	—	2	2	no	—
375	C₄×C₈	—	2	2	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	D₄×C₁₉	1	1	yes	characteristic
388	#95	D₄×C₁₉	1	1	yes	characteristic
389	#95	D₄×C₁₉	1	1	yes	characteristic
390	#95	D₄×C₁₉	1	1	yes	characteristic
391	C₁₉	#23792	1	1	yes	characteristic, direct product factor, Sylow
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	#41×C₁₉	1	2	yes	—
424	C₂×C₈	#41×C₁₉	1	2	yes	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	8	1	no	—
440	C₄⋊C₄	—	8	1	no	—
441	C₄⋊C₄	—	8	1	no	—
442	C₄⋊C₄	—	8	1	no	—
443	C₄⋊C₄	—	8	1	no	—
444	C₄⋊C₄	—	8	1	no	—
445	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
446	C₄⋊C₄	#41×C₁₉	1	2	yes	—
447	C₄⋊C₄	#41×C₁₉	1	2	yes	—
448	C₄²	—	2	4	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	8	1	no	—
454	C₄²	—	8	1	no	—
455	C₄²	—	8	1	no	—
456	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
457	C₄²	#41×C₁₉	1	2	yes	—
458	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	4	1	no	—
462	Q₈	—	4	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
504	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
505	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
506	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
507	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
511	C₈	—	2	2	no	—
512	C₈	—	2	2	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
516	C₂²	C₁₉×#525	1	1	yes	characteristic
517	C₂²	C₁₉×#532	1	1	yes	characteristic
518	C₂²	C₁₉×#576	1	1	yes	characteristic
519	C₂²	C₁₉×#577	1	1	yes	characteristic
520	C₂²	C₁₉×#578	1	1	yes	characteristic
521	C₂²	C₁₉×#578	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	C₁₉×#529	1	1	yes	characteristic
537	C₄	C₁₉×#529	1	1	yes	characteristic
538	C₄	C₁₉×#533	1	1	yes	characteristic
539	C₄	C₁₉×#533	1	1	yes	characteristic
540	C₂	C₁₉×#2396	1	1	yes	characteristic
541	C₂	C₁₉×#3082	1	1	yes	characteristic
542	C₂	C₁₉×#3083	1	1	yes	characteristic
543	C₂	C₁₉×#3120	1	1	yes	characteristic
544	C₂	C₁₉×#3124	1	1	yes	characteristic
545	C₂	C₁₉×#3177	1	1	yes	characteristic
546	C₂	C₁₉×#3179	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
184. #23792	C₁₉	direct (N × H)
391. C₁₉	#23792	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×#2330	2
C₁₉×#2320	2
C₁₉×#2099	2
C₁₉×#2095	2
C₁₉×#2087	2
C₁₉×#2086	2
C₁₉×#2068	2
C₁₉×#2066	2
C₁₉×#2059	2
C₁₉×#2026	2
C₁₉×#1776	2
C₄×C₁₉×#107	2
C₁₉×#1768	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#23792	19

Subgroups — C19×#23792 #18029751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23792 #18029751