Subgroups — C₁₉×#8419 #18014378

Order 4864.

778 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3522	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1509	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#559	—	2	1	no	—
9	C₁₉×#559	C₄	1	1	yes	characteristic, complemented
10	Q₈²×C₁₉	C₄	1	1	yes	characteristic, complemented
11	C₁₉×#554	—	2	1	no	—
12	C₁₉×#554	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#550	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#548	—	2	1	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#547	—	2	1	no	—
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#532	—	2	1	no	—
20	C₁₉×#532	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	1	no	—
22	C₁₉×#529	C₂²	1	1	yes	characteristic
23	C₁₉×#520	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#432	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#104	—	2	2	no	—
27	C₂×C₁₉×#103	—	2	1	no	—
28	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#340	—	2	1	no	—
32	C₁₉×#330	—	2	1	no	—
33	C₁₉×#329	—	2	1	no	—
34	C₁₉×#329	—	2	2	no	—
35	C₁₉×#328	—	2	1	no	—
36	C₁₉×#327	—	2	1	no	—
37	C₁₉×Q₈⋊C₈	—	2	1	no	—
38	C₁₉×Q₈⋊C₈	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	D₄	1	2	yes	—
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	—	2	2	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#127	—	2	1	no	—
50	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	1	no	—
53	C₁₉×#125	—	2	1	no	—
54	C₁₉×#125	D₄	1	1	yes	characteristic
55	C₁₉×#124	—	2	2	no	—
56	C₁₉×#124	—	2	2	no	—
57	C₁₉×#124	—	2	1	no	—
58	C₁₉×#124	—	2	1	no	—
59	C₁₉×#124	D₄	1	1	yes	characteristic
60	C₁₉×#124	D₄	1	2	yes	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×#123	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	—	2	1	no	—
77	C₁₉×#121	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
98	C₁₉×#117	—	2	2	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×#104	—	4	4	no	—
110	C₁₉×#103	—	2	4	no	—
111	C₁₉×C₂²⋊C₈	—	2	1	no	—
112	C₁₉×#97	—	2	1	no	—
113	C₁₉×#97	—	2	1	no	—
114	C₁₉×#97	—	2	1	no	—
115	C₁₉×#97	—	2	1	no	—
116	C₄×C₈×C₁₉	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	#41×C₁₉	—	4	2	no	—
119	#41×C₁₉	—	4	2	no	—
120	#41×C₁₉	—	4	2	no	—
121	#41×C₁₉	—	4	2	no	—
122	#41×C₁₉	—	8	2	no	—
123	#41×C₁₉	—	8	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	4	1	no	—
128	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	4	1	no	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	M₁₆×C₁₉	—	2	2	no	—
152	M₁₆×C₁₉	—	4	1	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	4	1	no	—
155	C₂×C₈×C₁₉	—	4	1	no	—
156	C₂×C₈×C₁₉	—	4	1	no	—
157	C₂×C₈×C₁₉	—	4	1	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	4	1	no	—
175	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
176	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
178	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	1	no	—
188	C₂²⋊C₄×C₁₉	—	2	1	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	4	2	no	—
198	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
199	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
202	#8419	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	#120	1	1	yes	characteristic
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	Q₈×C₁₉	—	8	2	no	—
213	Q₈×C₁₉	#104	1	2	yes	complemented
214	D₄×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	1	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	1	no	—
222	D₄×C₁₉	—	4	1	no	—
223	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	4	no	—
240	C₂×C₄×C₁₉	—	4	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	2	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	—	8	2	no	—
247	C₂×C₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	8	1	no	—
249	C₂×C₄×C₁₉	—	8	1	no	—
250	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₈×C₁₉	—	4	2	no	—
257	C₈×C₁₉	—	4	2	no	—
258	C₈×C₁₉	—	8	1	no	—
259	#3522	C₂×C₁₉	1	1	yes	characteristic
260	#1980	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1763	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1509	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
266	C₂²×C₁₉	—	2	1	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	#379	1	1	yes	characteristic
275	C₂²×C₁₉	#453	1	1	yes	characteristic
276	C₂²×C₁₉	#455	1	1	yes	characteristic
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	2	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	8	2	no	—
291	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
292	C₄×C₁₉	#421	1	1	yes	characteristic
293	#559	—	2	1	no	—
294	#559	C₄×C₁₉	1	1	yes	characteristic, complemented
295	Q₈²	C₄×C₁₉	1	1	yes	characteristic, complemented
296	#554	—	2	1	no	—
297	#554	C₄×C₁₉	1	1	yes	characteristic, complemented
298	#550	C₄×C₁₉	1	1	yes	characteristic, complemented
299	#548	—	2	1	no	—
300	#547	—	2	2	no	—
301	#547	—	2	1	no	—
302	#542	—	2	2	no	—
303	#542	—	2	1	no	—
304	#532	—	2	1	no	—
305	#532	C₂²×C₁₉	1	1	yes	characteristic
306	#529	—	2	1	no	—
307	#529	C₂²×C₁₉	1	1	yes	characteristic
308	#520	—	2	1	no	—
309	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
310	#432	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#104	—	2	2	no	—
312	C₂×#103	—	2	1	no	—
313	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
316	#340	—	2	1	no	—
317	#330	—	2	1	no	—
318	#329	—	2	1	no	—
319	#329	—	2	2	no	—
320	#328	—	2	1	no	—
321	#327	—	2	1	no	—
322	Q₈⋊C₈	—	2	1	no	—
323	Q₈⋊C₈	—	2	1	no	—
324	C₂×C₁₉	—	2	1	no	—
325	C₂×C₁₉	—	2	1	no	—
326	C₂×C₁₉	—	8	2	no	—
327	C₂×C₁₉	—	8	1	no	—
328	C₂×C₁₉	#1789	1	1	yes	characteristic
329	C₂×C₁₉	#1792	1	1	yes	characteristic
330	C₂×C₁₉	#1796	1	1	yes	characteristic
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	D₄×C₁₉	1	2	yes	—
334	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
335	C₂×M₁₆	—	2	1	no	—
336	C₂²×C₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
341	#127	—	2	1	no	—
342	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
343	#126	—	2	2	no	—
344	#126	—	2	1	no	—
345	#125	—	2	1	no	—
346	#125	D₄×C₁₉	1	1	yes	characteristic
347	#124	—	2	2	no	—
348	#124	—	2	2	no	—
349	#124	—	2	1	no	—
350	#124	—	2	1	no	—
351	#124	D₄×C₁₉	1	1	yes	characteristic
352	#124	D₄×C₁₉	1	2	yes	—
353	#123	—	2	2	no	—
354	#123	—	2	2	no	—
355	#123	—	2	2	no	—
356	#123	—	2	2	no	—
357	#123	—	2	1	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
364	#121	—	2	2	no	—
365	#121	—	2	2	no	—
366	#121	—	2	1	no	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	D₄×C₁₉	1	1	yes	characteristic
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
376	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
377	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
378	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
390	#117	—	2	2	no	—
391	#117	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
400	C₄⋊C₈	—	2	1	no	—
401	#104	—	4	4	no	—
402	#103	—	2	4	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	#97	—	2	1	no	—
405	#97	—	2	1	no	—
406	#97	—	2	1	no	—
407	#97	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	#95	—	2	1	no	—
410	C₁₉	#8419	1	1	yes	characteristic, direct product factor, Sylow
411	#41	—	4	2	no	—
412	#41	—	4	2	no	—
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	#41	—	8	2	no	—
416	#41	—	8	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
422	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
423	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
424	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
432	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
444	M₁₆	—	2	2	no	—
445	M₁₆	—	4	1	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	4	1	no	—
448	C₂×C₈	—	4	1	no	—
449	C₂×C₈	—	4	1	no	—
450	C₂×C₈	—	4	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	2	no	—
491	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂³	—	2	2	no	—
496	C₂³	—	2	1	no	—
497	C₂³	C₁₉×#120	1	1	yes	characteristic
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	8	2	no	—
505	Q₈	C₁₉×#104	1	2	yes	complemented
506	D₄	—	4	2	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	1	no	—
516	D₄	—	8	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	8	1	no	—
541	C₂×C₄	—	8	1	no	—
542	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
546	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
547	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
548	C₈	—	4	2	no	—
549	C₈	—	4	2	no	—
550	C₈	—	8	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	C₁₉×#379	1	1	yes	characteristic
560	C₂²	C₁₉×#453	1	1	yes	characteristic
561	C₂²	C₁₉×#455	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	8	2	no	—
576	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
577	C₄	C₁₉×#421	1	1	yes	characteristic
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	8	2	no	—
581	C₂	—	8	1	no	—
582	C₂	C₁₉×#1789	1	1	yes	characteristic
583	C₂	C₁₉×#1792	1	1	yes	characteristic
584	C₂	C₁₉×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3522	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×#1980	C₂	semidirect
3. C₁₉×#1763	C₂	semidirect
4. C₁₉×#1530	C₂	semidirect
5. C₁₉×#1524	C₂	semidirect
6. C₁₉×#1509	C₂	semidirect
7. C₁₉×#1491	C₂	semidirect
9. C₁₉×#559	C₄	semidirect
10. Q₈²×C₁₉	C₄	semidirect
12. C₁₉×#554	C₄	semidirect
13. C₁₉×#550	C₄	semidirect
202. #8419	C₁₉	direct (N × H)
213. Q₈×C₁₉	#104	semidirect
260. #1980	C₂×C₁₉	semidirect
261. #1763	C₂×C₁₉	semidirect
262. #1530	C₂×C₁₉	semidirect
263. #1524	C₂×C₁₉	semidirect
264. #1509	C₂×C₁₉	semidirect
265. #1491	C₂×C₁₉	semidirect
294. #559	C₄×C₁₉	semidirect
295. Q₈²	C₄×C₁₉	semidirect
297. #554	C₄×C₁₉	semidirect
298. #550	C₄×C₁₉	semidirect
410. C₁₉	#8419	direct (N × H)
505. Q₈	C₁₉×#104	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3522	2
C₁₉×#1980	2
C₁₉×#1763	2
C₁₉×#1530	2
C₁₉×#1524	2
C₁₉×#1509	2
C₁₉×#1491	2
#8419	19

Subgroups — C19×#8419 #18014378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8419 #18014378