Subgroups — C₁₉×#11082 #18017041

Order 4864.

898 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#423	—	2	2	no	—
16	C₁₉×#423	—	2	2	no	—
17	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
18	C₂×C₁₉×#104	—	2	2	no	—
19	C₂×C₁₉×#104	—	2	1	no	—
20	C₂×C₁₉×#104	—	2	1	no	—
21	C₂×C₁₉×#104	C₄	1	4	yes	complemented
22	C₁₉×#419	—	2	1	no	—
23	C₁₉×#418	—	2	1	no	—
24	C₁₉×#417	—	2	2	no	—
25	C₁₉×#416	—	2	2	no	—
26	C₁₉×#413	—	2	2	no	—
27	C₁₉×#413	—	2	2	no	—
28	C₂×C₁₉×#101	—	2	1	no	—
29	C₂×C₁₉×#100	—	2	1	no	—
30	C₁₉×#343	—	2	2	no	—
31	C₁₉×#339	—	2	1	no	—
32	C₁₉×#339	—	2	1	no	—
33	C₁₉×#338	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×#41×C₁₉	Q₈	1	2	yes	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₂×M₁₆×C₁₉	—	2	1	no	—
64	C₂×M₁₆×C₁₉	—	2	1	no	—
65	C₂×M₁₆×C₁₉	—	2	1	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₂×M₁₆×C₁₉	—	2	1	no	—
68	C₂×M₁₆×C₁₉	—	2	1	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
75	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
76	C₂²×C₈×C₁₉	—	2	1	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	D₄	1	2	yes	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	—	2	1	no	—
82	C₁₉×#117	—	2	1	no	—
83	C₁₉×#117	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₁₉	D₄	1	2	yes	—
92	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
94	C₁₉×C₄⋊C₈	—	2	8	no	—
95	C₁₉×#104	—	2	4	no	—
96	C₁₉×#104	—	2	4	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×#101	—	2	4	no	—
100	C₁₉×#100	—	2	4	no	—
101	C₂⁴×C₁₉	—	2	1	no	—
102	C₂⁴×C₁₉	#41	1	1	yes	characteristic
103	#41×C₁₉	—	2	2	no	—
104	#41×C₁₉	—	2	2	no	—
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	—	4	1	no	—
113	#41×C₁₉	—	4	1	no	—
114	#41×C₁₉	—	4	1	no	—
115	#41×C₁₉	—	4	1	no	—
116	#41×C₁₉	—	4	1	no	—
117	#41×C₁₉	—	4	1	no	—
118	#41×C₁₉	—	4	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	—	2	1	no	—
124	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	4	1	no	—
147	C₂²×C₄×C₁₉	—	4	1	no	—
148	C₂²×C₄×C₁₉	—	4	1	no	—
149	C₂²×C₄×C₁₉	—	4	1	no	—
150	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	2	2	no	—
168	M₁₆×C₁₉	—	2	2	no	—
169	M₁₆×C₁₉	—	2	2	no	—
170	M₁₆×C₁₉	—	4	1	no	—
171	M₁₆×C₁₉	—	4	1	no	—
172	M₁₆×C₁₉	—	4	1	no	—
173	M₁₆×C₁₉	—	4	1	no	—
174	M₁₆×C₁₉	—	4	1	no	—
175	M₁₆×C₁₉	—	4	1	no	—
176	M₁₆×C₁₉	—	4	1	no	—
177	M₁₆×C₁₉	—	4	1	no	—
178	M₁₆×C₁₉	—	4	1	no	—
179	M₁₆×C₁₉	—	4	1	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	2	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	4	1	no	—
187	C₂×C₈×C₁₉	—	4	1	no	—
188	C₂×C₈×C₁₉	—	4	1	no	—
189	C₂×C₈×C₁₉	—	4	1	no	—
190	C₂×C₈×C₁₉	—	4	1	no	—
191	C₂×C₈×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	4	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
203	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
204	#11082	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	—	8	2	no	—
210	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
211	C₂³×C₁₉	#121	1	1	yes	characteristic
212	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₁₉	#123	1	1	yes	characteristic
214	C₂³×C₁₉	#123	1	1	yes	characteristic
215	C₂³×C₁₉	#123	1	1	yes	characteristic
216	C₂³×C₁₉	#126	1	1	yes	characteristic
217	Q₈×C₁₉	—	2	2	no	—
218	Q₈×C₁₉	—	2	2	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	D₄×C₁₉	—	2	2	no	—
222	D₄×C₁₉	—	2	2	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	4	2	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	4	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
272	C₈×C₁₉	—	4	2	no	—
273	C₈×C₁₉	—	4	2	no	—
274	C₈×C₁₉	—	4	2	no	—
275	C₈×C₁₉	—	4	2	no	—
276	C₂×#423	C₂×C₁₉	1	1	yes	characteristic, complemented
277	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic
278	#2896	C₂×C₁₉	1	1	yes	characteristic
279	C₂×#413	C₂×C₁₉	1	1	yes	characteristic
280	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
281	C₂×#339	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂×#338	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	8	2	no	—
292	C₂²×C₁₉	—	8	2	no	—
293	C₂²×C₁₉	—	8	2	no	—
294	C₂²×C₁₉	#385	1	1	yes	characteristic
295	C₂²×C₁₉	#386	1	1	yes	characteristic
296	C₂²×C₁₉	#388	1	1	yes	characteristic
297	C₂²×C₁₉	#394	1	1	yes	characteristic
298	C₂²×C₁₉	#396	1	1	yes	characteristic
299	C₂²×C₁₉	#397	1	1	yes	characteristic
300	C₂²×C₁₉	#399	1	1	yes	characteristic
301	C₄×C₁₉	—	2	4	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	8	2	no	—
305	C₄×C₁₉	#380	1	1	yes	characteristic
306	C₄×C₁₉	#385	1	1	yes	characteristic
307	C₄×C₁₉	#388	1	1	yes	characteristic
308	C₄×C₁₉	#390	1	1	yes	characteristic
309	C₄×C₁₉	#392	1	1	yes	characteristic
310	C₄×C₁₉	#393	1	1	yes	characteristic
311	C₄×C₁₉	#394	1	1	yes	characteristic
312	C₄×C₁₉	#396	1	1	yes	characteristic
313	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
314	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
317	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
319	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
320	#423	—	2	2	no	—
321	#423	—	2	2	no	—
322	C₂×C₄⋊C₈	—	2	2	no	—
323	C₂×#104	—	2	1	no	—
324	C₂×#104	—	2	1	no	—
325	C₂×#104	—	2	2	no	—
326	C₂×#104	C₄×C₁₉	1	4	yes	complemented
327	#419	—	2	1	no	—
328	#418	—	2	1	no	—
329	#417	—	2	2	no	—
330	#416	—	2	2	no	—
331	#413	—	2	2	no	—
332	#413	—	2	2	no	—
333	C₂×#101	—	2	1	no	—
334	C₂×#100	—	2	1	no	—
335	#343	—	2	2	no	—
336	#339	—	2	1	no	—
337	#339	—	2	1	no	—
338	#338	—	2	2	no	—
339	C₂×C₁₉	—	2	1	no	—
340	C₂×C₁₉	—	2	1	no	—
341	C₂×C₁₉	—	2	1	no	—
342	C₂×C₁₉	—	2	1	no	—
343	C₂×C₁₉	—	2	1	no	—
344	C₂×C₁₉	—	2	1	no	—
345	C₂×C₁₉	—	8	2	no	—
346	C₂×C₁₉	#1439	1	1	yes	characteristic
347	C₂×C₁₉	#2050	1	2	yes	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
359	C₂×#41	Q₈×C₁₉	1	2	yes	—
360	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
388	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
389	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	D₄×C₁₉	1	2	yes	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
405	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
406	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
407	C₂×C₄²	D₄×C₁₉	1	2	yes	—
408	C₄⋊C₈	—	2	8	no	—
409	#104	—	2	4	no	—
410	#104	—	2	4	no	—
411	#103	—	2	4	no	—
412	#102	—	2	4	no	—
413	#101	—	2	4	no	—
414	#100	—	2	4	no	—
415	C₁₉	#11082	1	1	yes	characteristic, direct product factor, Sylow
416	C₂⁴	—	2	1	no	—
417	C₂⁴	#41×C₁₉	1	1	yes	characteristic
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	4	1	no	—
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	1	no	—
430	#41	—	4	1	no	—
431	#41	—	4	1	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	yes	characteristic
473	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	4	1	no	—
486	M₁₆	—	4	1	no	—
487	M₁₆	—	4	1	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	4	1	no	—
490	M₁₆	—	4	1	no	—
491	M₁₆	—	4	1	no	—
492	M₁₆	—	4	1	no	—
493	M₁₆	—	4	1	no	—
494	M₁₆	—	4	1	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	4	1	no	—
502	C₂×C₈	—	4	1	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	4	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	4	1	no	—
516	C₄²	—	4	1	no	—
517	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
518	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	8	2	no	—
524	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
525	C₂³	C₁₉×#121	1	1	yes	characteristic
526	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
527	C₂³	C₁₉×#123	1	1	yes	characteristic
528	C₂³	C₁₉×#123	1	1	yes	characteristic
529	C₂³	C₁₉×#123	1	1	yes	characteristic
530	C₂³	C₁₉×#126	1	1	yes	characteristic
531	Q₈	—	2	2	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	1	no	—
535	D₄	—	2	2	no	—
536	D₄	—	2	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
559	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
560	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
561	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
562	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
563	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
565	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
566	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
567	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
568	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
569	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
570	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
571	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
572	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
573	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
574	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
575	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
576	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
577	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
578	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
579	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
580	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
581	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
582	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
583	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
584	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
585	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
586	C₈	—	4	2	no	—
587	C₈	—	4	2	no	—
588	C₈	—	4	2	no	—
589	C₈	—	4	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	8	2	no	—
599	C₂²	—	8	2	no	—
600	C₂²	—	8	2	no	—
601	C₂²	C₁₉×#385	1	1	yes	characteristic
602	C₂²	C₁₉×#386	1	1	yes	characteristic
603	C₂²	C₁₉×#388	1	1	yes	characteristic
604	C₂²	C₁₉×#394	1	1	yes	characteristic
605	C₂²	C₁₉×#396	1	1	yes	characteristic
606	C₂²	C₁₉×#397	1	1	yes	characteristic
607	C₂²	C₁₉×#399	1	1	yes	characteristic
608	C₄	—	2	4	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	8	2	no	—
612	C₄	C₁₉×#380	1	1	yes	characteristic
613	C₄	C₁₉×#385	1	1	yes	characteristic
614	C₄	C₁₉×#388	1	1	yes	characteristic
615	C₄	C₁₉×#390	1	1	yes	characteristic
616	C₄	C₁₉×#392	1	1	yes	characteristic
617	C₄	C₁₉×#393	1	1	yes	characteristic
618	C₄	C₁₉×#394	1	1	yes	characteristic
619	C₄	C₁₉×#396	1	1	yes	characteristic
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	8	2	no	—
627	C₂	C₁₉×#1439	1	1	yes	characteristic
628	C₂	C₁₉×#2050	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#124
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#394
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#423	C₂	semidirect
5. C₁₉×#1742	C₂	semidirect
6. C₂×C₁₉×#339	C₂	semidirect
7. C₂×C₁₉×#338	C₂	semidirect
21. C₂×C₁₉×#104	C₄	semidirect
204. #11082	C₁₉	direct (N × H)
276. C₂×#423	C₂×C₁₉	semidirect
280. #1742	C₂×C₁₉	semidirect
281. C₂×#339	C₂×C₁₉	semidirect
282. C₂×#338	C₂×C₁₉	semidirect
326. C₂×#104	C₄×C₁₉	semidirect
415. C₁₉	#11082	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#423	2
C₂²×C₁₉×#104	2
C₁₉×#2896	2
C₂×C₁₉×#413	2
C₁₉×#1742	2
C₂×C₁₉×#339	2
C₂×C₁₉×#338	2
#11082	19

Subgroups — C19×#11082 #18017041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11082 #18017041