Subgroups — C₁₉×#17523 #18023482

Order 4864.

936 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3482	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1497	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1488	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1481	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1477	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#557	C₄	1	1	yes	characteristic
13	C₁₉×#556	C₄	1	2	yes	—
14	C₁₉×#556	C₄	1	1	yes	characteristic
15	C₁₉×#552	—	2	1	no	—
16	C₁₉×#552	—	2	2	no	—
17	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
18	C₁₉×#548	—	2	1	no	—
19	C₁₉×#547	C₄	1	1	yes	characteristic
20	C₁₉×#547	C₄	1	2	yes	—
21	C₁₉×#533	C₂²	1	2	yes	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₁₉×#529	—	2	1	no	—
24	C₁₉×#529	—	2	2	no	—
25	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×#41×C₁₉	C₂²	1	2	yes	—
27	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
29	C₁₉×#446	—	2	1	no	—
30	C₁₉×#435	—	2	2	no	—
31	C₈×D₄×C₁₉	—	2	1	no	—
32	C₁₉×#433	—	2	2	no	—
33	C₁₉×#432	C₂²	1	2	yes	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	2	yes	—
36	C₁₉×#431	C₂²	1	2	yes	—
37	C₁₉×#424	—	2	1	no	—
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
40	C₁₉×#408	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
47	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	2	no	—
61	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
62	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
64	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
82	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
83	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	2	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
102	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
103	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
105	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₄×D₄×C₁₉	D₄	1	2	yes	—
107	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#117	—	2	2	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	—	2	1	no	—
111	C₁₉×#117	—	2	2	no	—
112	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
113	C₁₉×#117	C₂×C₄	1	2	yes	—
114	C₁₉×#117	D₄	1	1	yes	characteristic
115	C₁₉×#117	D₄	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	—	2	2	no	—
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
122	C₁₉×C₄⋊C₈	—	2	2	no	—
123	C₁₉×C₄⋊C₈	—	2	1	no	—
124	C₁₉×C₄⋊C₈	—	2	2	no	—
125	C₁₉×C₄⋊C₈	—	2	2	no	—
126	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
127	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
128	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
129	C₁₉×C₂²⋊C₈	—	2	2	no	—
130	C₁₉×C₂²⋊C₈	—	2	2	no	—
131	C₁₉×C₂²⋊C₈	—	2	1	no	—
132	C₁₉×C₂²⋊C₈	—	2	2	no	—
133	C₁₉×#97	—	2	1	no	—
134	C₁₉×#97	—	2	2	no	—
135	C₄×C₈×C₁₉	—	2	1	no	—
136	C₄×C₈×C₁₉	—	2	1	no	—
137	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₉	C₂³	1	2	yes	—
140	#41×C₁₉	—	2	2	no	—
141	#41×C₁₉	—	2	4	no	—
142	#41×C₁₉	—	4	1	no	—
143	#41×C₁₉	—	4	2	no	—
144	#41×C₁₉	—	4	2	no	—
145	C₂×Q₈×C₁₉	—	2	2	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	4	4	no	—
148	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
167	M₁₆×C₁₉	—	4	2	no	—
168	M₁₆×C₁₉	—	8	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	4	2	no	—
176	C₂×C₈×C₁₉	—	8	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
193	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
206	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
207	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	2	2	no	—
210	C₄²×C₁₉	—	2	2	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
215	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₉	C₂×D₄	1	2	yes	—
218	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₉	C₂×D₄	1	2	yes	—
220	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
221	#17523	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
225	Q₈×C₁₉	—	2	2	no	—
226	Q₈×C₁₉	—	2	1	no	—
227	Q₈×C₁₉	—	2	2	no	—
228	Q₈×C₁₉	—	2	1	no	—
229	Q₈×C₁₉	—	2	2	no	—
230	Q₈×C₁₉	—	4	4	no	—
231	Q₈×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	2	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	4	2	no	—
236	D₄×C₁₉	—	4	4	no	—
237	D₄×C₁₉	#131	1	2	yes	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	4	no	—
255	C₂×C₄×C₁₉	—	4	4	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	—	4	2	no	—
271	C₈×C₁₉	—	4	1	no	—
272	C₈×C₁₉	—	4	2	no	—
273	C₈×C₁₉	—	4	1	no	—
274	#3482	C₂×C₁₉	1	1	yes	characteristic
275	#2990	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#2922	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1497	C₂×C₁₉	1	2	yes	complemented
278	#1493	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1488	C₂×C₁₉	1	2	yes	complemented
281	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1481	C₂×C₁₉	1	2	yes	complemented
283	#1477	C₂×C₁₉	1	2	yes	complemented
284	#1476	C₂×C₁₉	1	1	yes	characteristic, complemented
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	#421	1	2	yes	—
307	C₄×C₁₉	C₂×#131	1	1	yes	characteristic
308	C₄×C₁₉	#568	1	1	yes	characteristic
309	C₄×C₁₉	#577	1	1	yes	characteristic
310	C₄×C₁₉	#578	1	1	yes	characteristic
311	#557	C₄×C₁₉	1	1	yes	characteristic
312	#556	C₄×C₁₉	1	2	yes	—
313	#556	C₄×C₁₉	1	1	yes	characteristic
314	#552	—	2	1	no	—
315	#552	—	2	2	no	—
316	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
317	#548	—	2	1	no	—
318	#547	C₄×C₁₉	1	1	yes	characteristic
319	#547	C₄×C₁₉	1	2	yes	—
320	#533	C₂²×C₁₉	1	2	yes	—
321	#533	C₂²×C₁₉	1	1	yes	characteristic
322	#529	—	2	1	no	—
323	#529	—	2	2	no	—
324	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
325	C₄×#41	C₂²×C₁₉	1	2	yes	—
326	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×C₄×Q₈	—	2	1	no	—
328	#446	—	2	1	no	—
329	#435	—	2	2	no	—
330	C₈×D₄	—	2	1	no	—
331	#433	—	2	2	no	—
332	#432	C₂²×C₁₉	1	2	yes	—
333	#431	C₂²×C₁₉	1	1	yes	characteristic
334	#431	C₂²×C₁₉	1	2	yes	—
335	#431	C₂²×C₁₉	1	2	yes	—
336	#424	—	2	1	no	—
337	#423	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
339	#408	—	2	1	no	—
340	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
342	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
343	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
344	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
345	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
346	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
347	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
348	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
349	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
350	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
351	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
352	C₂×C₁₉	—	4	1	no	—
353	C₂×C₁₉	—	4	2	no	—
354	C₂×C₁₉	—	4	2	no	—
355	C₂×C₁₉	#2880	1	1	yes	characteristic
356	C₂×C₁₉	#2898	1	1	yes	characteristic
357	C₂×C₁₉	C₂×#421	1	1	yes	characteristic
358	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
359	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
360	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
361	C₂²×Q₈	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	2	no	—
366	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
367	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
368	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
369	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
370	#126	—	2	2	no	—
371	#126	—	2	2	no	—
372	#126	—	2	2	no	—
373	#125	—	2	2	no	—
374	#125	—	2	1	no	—
375	#125	—	2	1	no	—
376	#125	—	2	2	no	—
377	#124	—	2	1	no	—
378	#124	—	2	2	no	—
379	#123	—	2	2	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
387	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
388	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
389	#121	—	2	1	no	—
390	#121	—	2	2	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
397	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
398	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
399	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
400	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
407	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
408	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
409	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
410	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
411	C₄×D₄	D₄×C₁₉	1	2	yes	—
412	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
413	#117	—	2	2	no	—
414	#117	—	2	1	no	—
415	#117	—	2	1	no	—
416	#117	—	2	2	no	—
417	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
418	#117	C₂×C₄×C₁₉	1	2	yes	—
419	#117	D₄×C₁₉	1	1	yes	characteristic
420	#117	D₄×C₁₉	1	2	yes	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	2	no	—
425	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₄⋊C₈	—	2	2	no	—
431	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
433	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
434	C₂²⋊C₈	—	2	2	no	—
435	C₂²⋊C₈	—	2	2	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	#97	—	2	1	no	—
439	#97	—	2	2	no	—
440	C₄×C₈	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₄×C₈	C₂³×C₁₉	1	2	yes	—
445	C₁₉	#17523	1	1	yes	characteristic, direct product factor, Sylow
446	#41	—	2	2	no	—
447	#41	—	2	4	no	—
448	#41	—	4	1	no	—
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	4	4	no	—
454	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
455	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
456	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
460	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
461	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
469	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
473	M₁₆	—	4	2	no	—
474	M₁₆	—	8	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	4	2	no	—
482	C₂×C₈	—	8	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
497	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
499	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
512	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
513	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	2	no	—
520	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
521	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
522	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₄²	C₂×D₄×C₁₉	1	2	yes	—
525	C₄²	C₂×D₄×C₁₉	1	2	yes	—
526	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
527	C₂³	—	2	1	no	—
528	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
529	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	4	no	—
536	Q₈	—	4	2	no	—
537	D₄	—	2	2	no	—
538	D₄	—	2	1	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	4	no	—
542	D₄	C₁₉×#131	1	2	yes	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
565	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
567	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
568	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
569	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	2	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	2	no	—
578	C₈	—	4	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	C₁₉×#421	1	2	yes	—
601	C₄	C₂×C₁₉×#131	1	1	yes	characteristic
602	C₄	C₁₉×#568	1	1	yes	characteristic
603	C₄	C₁₉×#577	1	1	yes	characteristic
604	C₄	C₁₉×#578	1	1	yes	characteristic
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	4	2	no	—
608	C₂	C₁₉×#2880	1	1	yes	characteristic
609	C₂	C₁₉×#2898	1	1	yes	characteristic
610	C₂	C₂×C₁₉×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₁₉×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2990	C₂	semidirect
3. C₁₉×#2922	C₂	semidirect
4. C₁₉×#1497	C₂	semidirect
5. C₁₉×#1493	C₂	semidirect
6. C₁₉×#1489	C₂	semidirect
7. C₁₉×#1488	C₂	semidirect
8. C₁₉×#1485	C₂	semidirect
9. C₁₉×#1481	C₂	semidirect
10. C₁₉×#1477	C₂	semidirect
11. C₁₉×#1476	C₂	semidirect
221. #17523	C₁₉	direct (N × H)
275. #2990	C₂×C₁₉	semidirect
276. #2922	C₂×C₁₉	semidirect
277. #1497	C₂×C₁₉	semidirect
278. #1493	C₂×C₁₉	semidirect
279. #1489	C₂×C₁₉	semidirect
280. #1488	C₂×C₁₉	semidirect
281. #1485	C₂×C₁₉	semidirect
282. #1481	C₂×C₁₉	semidirect
283. #1477	C₂×C₁₉	semidirect
284. #1476	C₂×C₁₉	semidirect
445. C₁₉	#17523	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×#3482	2
C₁₉×#2990	2
C₁₉×#2922	2
C₁₉×#1497	2
C₁₉×#1493	2
C₁₉×#1489	2
C₁₉×#1488	2
C₁₉×#1485	2
C₁₉×#1481	2
C₁₉×#1477	2
C₁₉×#1476	2
#17523	19

Subgroups — C19×#17523 #18023482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17523 #18023482