Subgroups — C₂×C₁₉×#2082 #18029610

Order 4864.

878 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2082	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×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	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₁₉×#430	—	2	2	no	—
17	C₁₉×#430	C₂²	1	4	yes	—
18	C₂×C₁₉×#108	—	2	2	no	—
19	C₁₉×#419	—	2	2	no	—
20	C₁₉×#419	—	2	2	no	—
21	C₁₉×#419	C₂²	1	4	yes	—
22	C₁₉×#419	C₂²	1	4	yes	—
23	C₂×C₁₉×#103	—	2	2	no	—
24	C₂×C₁₉×#103	—	2	2	no	—
25	C₂×C₁₉×#101	—	2	2	no	—
26	C₂×C₁₉×#101	—	2	2	no	—
27	C₂×C₁₉×#101	C₂²	1	4	yes	—
28	C₁₉×#344	C₂²	1	4	yes	—
29	C₁₉×#344	C₂²	1	4	yes	—
30	C₁₉×H(3,ℤ/4)	C₂²	1	4	yes	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
43	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
44	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
67	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
70	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₂²×C₈×C₁₉	—	2	1	no	—
73	C₂²×C₈×C₁₉	—	2	1	no	—
74	C₂²×C₈×C₁₉	D₄	1	2	yes	—
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	C₂³	1	2	yes	—
82	C₁₉×#117	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₁₉×#108	—	2	8	no	—
90	C₁₉×#103	—	2	8	no	—
91	C₁₉×#103	—	2	8	no	—
92	C₁₉×#101	—	2	8	no	—
93	C₂⁴×C₁₉	#41	1	1	yes	characteristic
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₁₉	—	2	2	no	—
146	M₁₆×C₁₉	—	2	2	no	—
147	M₁₆×C₁₉	—	2	2	no	—
148	M₁₆×C₁₉	—	2	2	no	—
149	M₁₆×C₁₉	—	2	2	no	—
150	M₁₆×C₁₉	—	2	2	no	—
151	M₁₆×C₁₉	—	2	2	no	—
152	M₁₆×C₁₉	—	2	2	no	—
153	M₁₆×C₁₉	—	2	2	no	—
154	M₁₆×C₁₉	—	2	2	no	—
155	M₁₆×C₁₉	—	4	1	no	—
156	M₁₆×C₁₉	—	4	1	no	—
157	M₁₆×C₁₉	—	4	1	no	—
158	M₁₆×C₁₉	—	4	1	no	—
159	M₁₆×C₁₉	—	4	1	no	—
160	M₁₆×C₁₉	—	4	1	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	4	1	no	—
167	C₂×C₈×C₁₉	—	4	1	no	—
168	C₂×C₈×C₁₉	—	4	1	no	—
169	C₂×C₈×C₁₉	—	4	1	no	—
170	C₂×C₈×C₁₉	—	4	1	no	—
171	C₂×C₈×C₁₉	—	4	1	no	—
172	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	4	1	no	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	4	1	no	—
180	C₂²⋊C₄×C₁₉	—	4	1	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	4	1	no	—
184	C₄²×C₁₉	—	4	1	no	—
185	C₂×#2082	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	#123	1	1	yes	characteristic
188	C₂³×C₁₉	#123	1	1	yes	characteristic
189	C₂³×C₁₉	#124	1	1	yes	characteristic
190	C₂³×C₁₉	#124	1	1	yes	characteristic
191	C₂³×C₁₉	#126	1	1	yes	characteristic
192	C₂³×C₁₉	#126	1	1	yes	characteristic
193	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
194	Q₈×C₁₉	—	2	4	no	—
195	Q₈×C₁₉	—	2	4	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	Q₈×C₁₉	—	4	2	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
241	C₈×C₁₉	—	2	4	no	—
242	C₈×C₁₉	—	4	2	no	—
243	C₈×C₁₉	—	4	2	no	—
244	C₈×C₁₉	—	4	2	no	—
245	C₂×#430	C₂×C₁₉	1	1	yes	characteristic
246	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
247	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
248	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic
249	#2082	C₂×C₁₉	1	8	yes	direct product factor
250	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
251	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
252	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	2	2	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	—	4	1	no	—
259	C₂²×C₁₉	—	4	1	no	—
260	C₂²×C₁₉	#397	1	1	yes	characteristic
261	C₂²×C₁₉	#397	1	1	yes	characteristic
262	C₂²×C₁₉	#397	1	1	yes	characteristic
263	C₂²×C₁₉	#397	1	1	yes	characteristic
264	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
265	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
266	C₂²×C₁₉	C₂×#126	1	1	yes	characteristic
267	C₄×C₁₉	—	4	4	no	—
268	C₄×C₁₉	—	8	2	no	—
269	C₄×C₁₉	—	8	2	no	—
270	C₄×C₁₉	#397	1	1	yes	characteristic
271	C₄×C₁₉	#397	1	1	yes	characteristic
272	C₄×C₁₉	#397	1	1	yes	characteristic
273	C₄×C₁₉	#397	1	1	yes	characteristic
274	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
275	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
276	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
277	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
278	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
282	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
285	#430	—	2	2	no	—
286	#430	C₂²×C₁₉	1	4	yes	—
287	C₂×#108	—	2	2	no	—
288	#419	—	2	2	no	—
289	#419	—	2	2	no	—
290	#419	C₂²×C₁₉	1	4	yes	—
291	#419	C₂²×C₁₉	1	4	yes	—
292	C₂×#103	—	2	2	no	—
293	C₂×#103	—	2	2	no	—
294	C₂×#101	—	2	2	no	—
295	C₂×#101	—	2	2	no	—
296	C₂×#101	C₂²×C₁₉	1	4	yes	—
297	#344	C₂²×C₁₉	1	4	yes	—
298	#344	C₂²×C₁₉	1	4	yes	—
299	H(3,ℤ/4)	C₂²×C₁₉	1	4	yes	—
300	C₂×C₁₉	—	2	1	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	2	1	no	—
304	C₂×C₁₉	—	2	1	no	—
305	C₂×C₁₉	—	2	1	no	—
306	C₂×C₁₉	#2082	1	2	yes	direct product factor
307	C₂×C₁₉	C₂×#397	1	1	yes	characteristic
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	—	2	1	no	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
320	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
321	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
344	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
345	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
346	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
347	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	1	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	D₄×C₁₉	1	2	yes	—
352	#117	—	2	1	no	—
353	#117	—	2	1	no	—
354	#117	—	2	1	no	—
355	#117	—	2	1	no	—
356	#117	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	C₂³×C₁₉	1	2	yes	—
359	#117	C₂³×C₁₉	1	2	yes	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	#108	—	2	8	no	—
367	#103	—	2	8	no	—
368	#103	—	2	8	no	—
369	#101	—	2	8	no	—
370	C₁₉	C₂×#2082	1	1	yes	characteristic, direct product factor, Sylow
371	C₂⁴	#41×C₁₉	1	1	yes	characteristic
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	—	4	1	no	—
389	C₂×Q₈	—	4	1	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	1	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	1	no	—
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	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	4	1	no	—
434	M₁₆	—	4	1	no	—
435	M₁₆	—	4	1	no	—
436	M₁₆	—	4	1	no	—
437	M₁₆	—	4	1	no	—
438	M₁₆	—	4	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	4	1	no	—
445	C₂×C₈	—	4	1	no	—
446	C₂×C₈	—	4	1	no	—
447	C₂×C₈	—	4	1	no	—
448	C₂×C₈	—	4	1	no	—
449	C₂×C₈	—	4	1	no	—
450	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	4	1	no	—
458	C₂²⋊C₄	—	4	1	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	4	1	no	—
462	C₄²	—	4	1	no	—
463	C₂³	—	4	2	no	—
464	C₂³	C₁₉×#123	1	1	yes	characteristic
465	C₂³	C₁₉×#123	1	1	yes	characteristic
466	C₂³	C₁₉×#124	1	1	yes	characteristic
467	C₂³	C₁₉×#124	1	1	yes	characteristic
468	C₂³	C₁₉×#126	1	1	yes	characteristic
469	C₂³	C₁₉×#126	1	1	yes	characteristic
470	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
471	Q₈	—	2	4	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	2	no	—
478	Q₈	—	4	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
491	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
492	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
493	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
494	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
495	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
496	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
498	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
499	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
500	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
501	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
502	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
503	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
507	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
508	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
509	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
510	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
511	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
518	C₈	—	2	4	no	—
519	C₈	—	4	2	no	—
520	C₈	—	4	2	no	—
521	C₈	—	4	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	C₁₉×#397	1	1	yes	characteristic
530	C₂²	C₁₉×#397	1	1	yes	characteristic
531	C₂²	C₁₉×#397	1	1	yes	characteristic
532	C₂²	C₁₉×#397	1	1	yes	characteristic
533	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
534	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
535	C₂²	C₂×C₁₉×#126	1	1	yes	characteristic
536	C₄	—	4	4	no	—
537	C₄	—	8	2	no	—
538	C₄	—	8	2	no	—
539	C₄	C₁₉×#397	1	1	yes	characteristic
540	C₄	C₁₉×#397	1	1	yes	characteristic
541	C₄	C₁₉×#397	1	1	yes	characteristic
542	C₄	C₁₉×#397	1	1	yes	characteristic
543	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
544	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
545	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
546	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
547	C₂	—	2	1	no	—
548	C₂	—	2	1	no	—
549	C₂	—	2	1	no	—
550	C₂	—	2	1	no	—
551	C₂	—	2	1	no	—
552	C₂	—	2	1	no	—
553	C₂	C₁₉×#2082	1	2	yes	direct product factor
554	C₂	C₂×C₁₉×#397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#397
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2082	C₂	direct (N × H)
185. C₂×#2082	C₁₉	direct (N × H)
249. #2082	C₂×C₁₉	direct (N × H)
306. C₂×C₁₉	#2082	direct (N × H)
370. C₁₉	C₂×#2082	direct (N × H)
553. C₂	C₁₉×#2082	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×#430	2
C₂×C₁₉×#419	2
C₂²×C₁₉×#101	2
C₁₉×#2082	2
C₂×C₁₉×#344	2
C₂×C₁₉×H(3,ℤ/4)	2
C₂×#2082	19

Subgroups — C2×C19×#2082 #18029610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2082 #18029610