Subgroups — C₁₉×#8437 #18014396

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3480	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#559	—	2	1	no	—
9	C₁₉×#559	C₄	1	1	yes	characteristic, complemented
10	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
11	C₁₉×#556	—	2	1	no	—
12	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#553	—	2	1	no	—
15	C₁₉×#550	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#548	—	2	1	no	—
17	C₁₉×#532	—	2	1	no	—
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₁₉×#529	—	2	1	no	—
20	C₁₉×#529	—	2	2	no	—
21	C₄×#41×C₁₉	—	2	1	no	—
22	C₄×#41×C₁₉	—	2	1	no	—
23	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#431	C₂²	1	1	yes	characteristic
26	C₁₉×#423	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#104	—	2	1	no	—
28	C₂×C₁₉×#103	—	2	1	no	—
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#340	—	2	1	no	—
32	C₁₉×#339	—	2	1	no	—
33	C₁₉×#327	—	2	2	no	—
34	C₁₉×Q₈⋊C₈	—	2	1	no	—
35	C₁₉×Q₈⋊C₈	—	2	1	no	—
36	C₁₉×Q₈⋊C₈	—	2	1	no	—
37	C₁₉×D₄⋊C₈	—	2	1	no	—
38	C₁₉×D₄⋊C₈	—	2	2	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
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	1	no	—
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#127	—	2	1	no	—
48	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#126	—	2	2	no	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#125	—	2	2	no	—
53	C₁₉×#125	—	2	1	no	—
54	C₁₉×#124	—	2	2	no	—
55	C₁₉×#124	—	2	1	no	—
56	C₁₉×#124	—	2	1	no	—
57	C₁₉×#124	—	2	1	no	—
58	C₁₉×#124	—	2	1	no	—
59	C₁₉×#123	—	2	2	no	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	—	2	1	no	—
69	C₁₉×#121	D₄	1	2	yes	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
92	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
94	C₄×D₄×C₁₉	D₄	1	2	yes	—
95	C₁₉×#117	—	2	2	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	—	2	2	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
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×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×#104	—	4	2	no	—
112	C₁₉×#103	—	2	4	no	—
113	C₁₉×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₈×C₁₉	—	2	1	no	—
115	C₄×C₈×C₁₉	—	2	1	no	—
116	C₄×C₈×C₁₉	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	#41×C₁₉	—	2	1	no	—
119	#41×C₁₉	—	2	1	no	—
120	#41×C₁₉	—	2	1	no	—
121	#41×C₁₉	—	2	1	no	—
122	#41×C₁₉	—	4	2	no	—
123	#41×C₁₉	—	4	2	no	—
124	#41×C₁₉	—	4	1	no	—
125	#41×C₁₉	—	4	1	no	—
126	#41×C₁₉	—	4	1	no	—
127	#41×C₁₉	—	4	1	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	4	1	no	—
132	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
134	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	4	1	no	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	M₁₆×C₁₉	—	4	1	no	—
156	M₁₆×C₁₉	—	4	1	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	4	1	no	—
159	C₂×C₈×C₁₉	—	4	1	no	—
160	C₂×C₈×C₁₉	—	4	1	no	—
161	C₂×C₈×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	4	1	no	—
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	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
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	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	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	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	2	2	no	—
193	C₄²×C₁₉	—	2	2	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	#8437	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	2	2	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	#120	1	1	yes	characteristic
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	2	1	no	—
214	Q₈×C₁₉	—	2	1	no	—
215	Q₈×C₁₉	—	2	1	no	—
216	Q₈×C₁₉	—	4	2	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	#104	1	2	yes	complemented
220	D₄×C₁₉	—	2	1	no	—
221	D₄×C₁₉	—	2	1	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	4	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	8	2	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
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	2	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	4	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	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	8	1	no	—
254	C₂×C₄×C₁₉	—	8	1	no	—
255	C₂×C₄×C₁₉	—	8	2	no	—
256	C₂×C₄×C₁₉	—	8	1	no	—
257	C₂×C₄×C₁₉	—	8	1	no	—
258	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
266	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
268	C₈×C₁₉	—	4	2	no	—
269	C₈×C₁₉	—	8	1	no	—
270	C₈×C₁₉	—	8	1	no	—
271	#3480	C₂×C₁₉	1	1	yes	characteristic
272	#1806	C₂×C₁₉	1	1	yes	characteristic, complemented
273	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1492	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1487	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1476	C₂×C₁₉	1	1	yes	characteristic, complemented
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	#379	1	1	yes	characteristic
287	C₂²×C₁₉	#449	1	1	yes	characteristic
288	C₂²×C₁₉	#452	1	1	yes	characteristic
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	2	2	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	8	2	no	—
301	C₄×C₁₉	#416	1	1	yes	characteristic
302	C₄×C₁₉	#417	1	1	yes	characteristic
303	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
304	C₄×C₁₉	#421	1	1	yes	characteristic
305	C₄×C₁₉	#449	1	1	yes	characteristic
306	C₄×C₁₉	#452	1	1	yes	characteristic
307	#559	—	2	1	no	—
308	#559	C₄×C₁₉	1	1	yes	characteristic, complemented
309	#557	C₄×C₁₉	1	1	yes	characteristic, complemented
310	#556	—	2	1	no	—
311	#556	C₄×C₁₉	1	1	yes	characteristic, complemented
312	#553	—	2	2	no	—
313	#553	—	2	1	no	—
314	#550	C₄×C₁₉	1	1	yes	characteristic, complemented
315	#548	—	2	1	no	—
316	#532	—	2	1	no	—
317	#532	C₂²×C₁₉	1	1	yes	characteristic
318	#529	—	2	1	no	—
319	#529	—	2	2	no	—
320	C₄×#41	—	2	1	no	—
321	C₄×#41	—	2	1	no	—
322	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
324	#431	C₂²×C₁₉	1	1	yes	characteristic
325	#423	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#104	—	2	1	no	—
327	C₂×#103	—	2	1	no	—
328	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
329	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
330	#340	—	2	1	no	—
331	#339	—	2	1	no	—
332	#327	—	2	2	no	—
333	Q₈⋊C₈	—	2	1	no	—
334	Q₈⋊C₈	—	2	1	no	—
335	Q₈⋊C₈	—	2	1	no	—
336	D₄⋊C₈	—	2	1	no	—
337	D₄⋊C₈	—	2	2	no	—
338	C₂×C₁₉	—	2	1	no	—
339	C₂×C₁₉	—	2	1	no	—
340	C₂×C₁₉	—	8	2	no	—
341	C₂×C₁₉	—	8	1	no	—
342	C₂×C₁₉	#1788	1	1	yes	characteristic
343	C₂×C₁₉	#1789	1	1	yes	characteristic
344	C₂×C₁₉	#1794	1	1	yes	characteristic
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
348	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
349	C₂×M₁₆	—	2	1	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₄⋊Q₈	—	2	1	no	—
352	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
353	#127	—	2	1	no	—
354	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
355	#126	—	2	2	no	—
356	#126	—	2	2	no	—
357	#126	—	2	2	no	—
358	#125	—	2	2	no	—
359	#125	—	2	1	no	—
360	#124	—	2	2	no	—
361	#124	—	2	1	no	—
362	#124	—	2	1	no	—
363	#124	—	2	1	no	—
364	#124	—	2	1	no	—
365	#123	—	2	2	no	—
366	#123	—	2	2	no	—
367	#123	—	2	2	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	—	2	2	no	—
373	#121	—	2	1	no	—
374	#121	—	2	1	no	—
375	#121	D₄×C₁₉	1	2	yes	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
382	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
383	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
384	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
385	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
386	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
399	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
400	C₄×D₄	D₄×C₁₉	1	2	yes	—
401	#117	—	2	2	no	—
402	#117	—	2	2	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	D₄×C₁₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₄²	—	2	2	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	—	2	1	no	—
417	#104	—	4	2	no	—
418	#103	—	2	4	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	#95	—	2	1	no	—
424	C₁₉	#8437	1	1	yes	characteristic, direct product factor, Sylow
425	#41	—	2	1	no	—
426	#41	—	2	1	no	—
427	#41	—	2	1	no	—
428	#41	—	2	1	no	—
429	#41	—	4	2	no	—
430	#41	—	4	2	no	—
431	#41	—	4	1	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
440	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
441	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
449	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	M₁₆	—	4	1	no	—
463	M₁₆	—	4	1	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	4	1	no	—
466	C₂×C₈	—	4	1	no	—
467	C₂×C₈	—	4	1	no	—
468	C₂×C₈	—	4	1	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	—	4	1	no	—
510	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	2	no	—
516	C₂³	C₁₉×#120	1	1	yes	characteristic
517	Q₈	—	2	1	no	—
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	C₁₉×#104	1	2	yes	complemented
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	8	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	8	1	no	—
560	C₂×C₄	—	8	1	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	1	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
567	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
568	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
569	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
570	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
571	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
572	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
573	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
574	C₈	—	4	2	no	—
575	C₈	—	8	1	no	—
576	C₈	—	8	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	1	no	—
585	C₂²	C₁₉×#379	1	1	yes	characteristic
586	C₂²	C₁₉×#449	1	1	yes	characteristic
587	C₂²	C₁₉×#452	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	8	2	no	—
600	C₄	C₁₉×#416	1	1	yes	characteristic
601	C₄	C₁₉×#417	1	1	yes	characteristic
602	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
603	C₄	C₁₉×#421	1	1	yes	characteristic
604	C₄	C₁₉×#449	1	1	yes	characteristic
605	C₄	C₁₉×#452	1	1	yes	characteristic
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	8	1	no	—
609	C₂	—	8	2	no	—
610	C₂	C₁₉×#1788	1	1	yes	characteristic
611	C₂	C₁₉×#1789	1	1	yes	characteristic
612	C₂	C₁₉×#1794	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#379
prime radical	C₁₉×#3480	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1806	C₂	semidirect
3. C₄×C₁₉×#103	C₂	semidirect
4. C₁₉×#1502	C₂	semidirect
5. C₁₉×#1492	C₂	semidirect
6. C₁₉×#1487	C₂	semidirect
7. C₁₉×#1476	C₂	semidirect
9. C₁₉×#559	C₄	semidirect
10. C₁₉×#557	C₄	semidirect
12. C₁₉×#556	C₄	semidirect
15. C₁₉×#550	C₄	semidirect
207. #8437	C₁₉	direct (N × H)
219. Q₈×C₁₉	#104	semidirect
272. #1806	C₂×C₁₉	semidirect
273. C₄×#103	C₂×C₁₉	semidirect
274. #1502	C₂×C₁₉	semidirect
275. #1492	C₂×C₁₉	semidirect
276. #1487	C₂×C₁₉	semidirect
277. #1476	C₂×C₁₉	semidirect
308. #559	C₄×C₁₉	semidirect
309. #557	C₄×C₁₉	semidirect
311. #556	C₄×C₁₉	semidirect
314. #550	C₄×C₁₉	semidirect
424. C₁₉	#8437	direct (N × H)
525. 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×#3480	2
C₁₉×#1806	2
C₄×C₁₉×#103	2
C₁₉×#1502	2
C₁₉×#1492	2
C₁₉×#1487	2
C₁₉×#1476	2
#8437	19

Subgroups — C19×#8437 #18014396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8437 #18014396