Subgroups — C₂×C₁₉×#1890 #18026917

Order 4864.

2102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#123	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#381	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1890	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#342	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#123	—	2	4	no	—
10	C₂×C₁₉×#123	—	2	2	no	—
11	C₂×C₁₉×#123	C₄	1	8	yes	complemented
12	C₂×C₁₉×#123	C₂²	1	4	yes	—
13	C₁₉×#518	—	2	2	no	—
14	C₁₉×#518	—	2	4	no	—
15	C₁₉×#518	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₁₉	—	2	4	no	—
17	C₂×C₁₉×#117	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#99	—	2	4	no	—
25	C₂×C₁₉×#99	C₂²	1	4	yes	—
26	C₁₉×#381	—	2	4	no	—
27	C₁₉×#381	C₂²	1	8	yes	complemented
28	C₂×C₁₉×#95	—	2	4	no	—
29	C₁₉×#342	C₂²	1	8	yes	complemented
30	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
31	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	2	no	—
34	C₂²×D₄×C₁₉	—	2	4	no	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
36	C₂²×D₄×C₁₉	D₄	1	4	yes	—
37	C₂²×D₄×C₁₉	D₄	1	2	yes	—
38	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	4	no	—
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	complemented
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	D₄	1	4	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₁₉×#123	—	2	16	no	—
53	C₁₉×#123	—	2	8	no	—
54	C₁₉×#123	C₂×C₄	1	16	yes	complemented
55	C₄×D₄×C₁₉	—	2	16	no	—
56	C₄×D₄×C₁₉	—	2	16	no	—
57	C₁₉×#117	—	2	4	no	—
58	C₁₉×#117	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
77	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₁₉	—	2	2	no	—
82	C₁₉×#99	—	2	8	no	—
83	C₁₉×#95	—	2	16	no	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂⁴×C₁₉	—	2	1	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	4	4	no	—
88	C₂⁴×C₁₉	—	4	4	no	—
89	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
90	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
93	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
94	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
96	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
97	C₂⁴×C₁₉	#41	1	4	yes	—
98	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂×D₄×C₁₉	—	2	8	no	—
100	C₂×D₄×C₁₉	—	2	8	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	8	no	—
103	C₂×D₄×C₁₉	—	2	8	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
108	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
109	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	8	no	—
117	C₂²×C₄×C₁₉	—	2	8	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	8	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	—	4	4	no	—
132	C₂²×C₄×C₁₉	—	4	4	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	4	2	no	—
135	C₂²×C₄×C₁₉	—	4	8	no	—
136	C₂²×C₄×C₁₉	—	4	8	no	—
137	C₂²×C₄×C₁₉	—	4	4	no	—
138	C₂²×C₄×C₁₉	—	8	4	no	—
139	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	complemented
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
143	C₄⋊C₄×C₁₉	—	2	8	no	—
144	C₄⋊C₄×C₁₉	—	2	16	no	—
145	C₂²⋊C₄×C₁₉	—	2	8	no	—
146	C₂²⋊C₄×C₁₉	—	2	16	no	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	complemented
157	C₄²×C₁₉	—	2	8	no	—
158	C₂×#1890	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	8	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	4	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	4	4	no	—
166	C₂³×C₁₉	—	4	4	no	—
167	C₂³×C₁₉	—	4	4	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	8	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	8	no	—
172	C₂³×C₁₉	—	4	4	no	—
173	C₂³×C₁₉	—	4	4	no	—
174	C₂³×C₁₉	—	8	4	no	—
175	C₂³×C₁₉	—	8	2	no	—
176	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂³×C₁₉	C₄×D₄	1	4	yes	—
180	C₂³×C₁₉	C₄×D₄	1	4	yes	—
181	C₂³×C₁₉	#120	1	1	yes	characteristic
182	C₂³×C₁₉	#120	1	2	yes	—
183	C₂³×C₁₉	#120	1	1	yes	characteristic
184	C₂³×C₁₉	#121	1	4	yes	—
185	C₂³×C₁₉	#121	1	4	yes	—
186	C₂³×C₁₉	#123	1	2	yes	—
187	C₂³×C₁₉	#123	1	2	yes	—
188	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
191	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂³×C₁₉	C₂×#41	1	2	yes	—
193	D₄×C₁₉	—	2	8	no	—
194	D₄×C₁₉	—	2	8	no	—
195	D₄×C₁₉	—	2	16	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	8	no	—
203	C₂×C₄×C₁₉	—	2	8	no	—
204	C₂×C₄×C₁₉	—	4	8	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	4	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	8	no	—
211	C₂×C₄×C₁₉	—	4	4	no	—
212	C₂×C₄×C₁₉	—	4	8	no	—
213	C₂×C₄×C₁₉	—	4	8	no	—
214	C₂×C₄×C₁₉	—	4	8	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	8	4	no	—
217	C₂×C₄×C₁₉	—	8	8	no	—
218	C₂×C₄×C₁₉	—	8	8	no	—
219	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
220	C₂²×#123	C₂×C₁₉	1	1	yes	characteristic
221	C₂×#518	C₂×C₁₉	1	1	yes	characteristic
222	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic
223	C₂×#381	C₂×C₁₉	1	2	yes	complemented
224	#1890	C₂×C₁₉	1	8	yes	direct product factor
225	C₂×#342	C₂×C₁₉	1	2	yes	complemented
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	2	8	no	—
228	C₂²×C₁₉	—	2	4	no	—
229	C₂²×C₁₉	—	2	8	no	—
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	4	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	4	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	1	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	4	no	—
243	C₂²×C₁₉	—	4	8	no	—
244	C₂²×C₁₉	—	4	4	no	—
245	C₂²×C₁₉	—	8	2	no	—
246	C₂²×C₁₉	—	8	4	no	—
247	C₂²×C₁₉	#386	1	2	yes	—
248	C₂²×C₁₉	#386	1	4	yes	—
249	C₂²×C₁₉	#386	1	2	yes	—
250	C₂²×C₁₉	#458	1	4	yes	—
251	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
253	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
254	C₂²×C₁₉	C₂×#121	1	2	yes	—
255	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
256	C₄×C₁₉	—	2	4	no	—
257	C₄×C₁₉	—	4	4	no	—
258	C₄×C₁₉	—	4	8	no	—
259	C₄×C₁₉	—	4	4	no	—
260	C₄×C₁₉	—	8	4	no	—
261	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#123	—	2	4	no	—
264	C₂×#123	—	2	2	no	—
265	C₂×#123	C₄×C₁₉	1	8	yes	complemented
266	C₂×#123	C₂²×C₁₉	1	4	yes	—
267	#518	—	2	2	no	—
268	#518	—	2	4	no	—
269	#518	C₂²×C₁₉	1	4	yes	—
270	C₂×C₄×D₄	—	2	4	no	—
271	C₂×#117	—	2	1	no	—
272	C₂²×C₄⋊C₄	—	2	1	no	—
273	C₂²×C₂²⋊C₄	—	2	1	no	—
274	C₂²×C₂²⋊C₄	—	2	1	no	—
275	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×#99	—	2	4	no	—
279	C₂×#99	C₂²×C₁₉	1	4	yes	—
280	#381	—	2	4	no	—
281	#381	C₂²×C₁₉	1	8	yes	complemented
282	C₂×#95	—	2	4	no	—
283	#342	C₂²×C₁₉	1	8	yes	complemented
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	2	no	—
286	C₂×C₁₉	—	2	1	no	—
287	C₂×C₁₉	—	2	2	no	—
288	C₂×C₁₉	—	2	2	no	—
289	C₂×C₁₉	—	2	4	no	—
290	C₂×C₁₉	—	4	4	no	—
291	C₂×C₁₉	#1890	1	4	yes	direct product factor
292	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#458	1	2	yes	—
294	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
295	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	4	no	—
299	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
300	C₂²×D₄	D₄×C₁₉	1	4	yes	—
301	C₂²×D₄	D₄×C₁₉	1	2	yes	—
302	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	—	2	4	no	—
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	—	2	2	no	—
312	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	complemented
313	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
314	C₂³×C₄	D₄×C₁₉	1	4	yes	—
315	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
316	#123	—	2	16	no	—
317	#123	—	2	8	no	—
318	#123	C₂×C₄×C₁₉	1	16	yes	complemented
319	C₄×D₄	—	2	16	no	—
320	C₄×D₄	—	2	16	no	—
321	#117	—	2	4	no	—
322	#117	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	C₂×C₂²⋊C₄	—	2	8	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	C₂×C₂²⋊C₄	—	2	4	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
341	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
345	C₂×C₄²	—	2	2	no	—
346	#99	—	2	8	no	—
347	#95	—	2	16	no	—
348	C₁₉	C₂×#1890	1	1	yes	characteristic, direct product factor, Sylow
349	C₂⁴	—	2	1	no	—
350	C₂⁴	—	2	1	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	4	4	no	—
353	C₂⁴	—	4	4	no	—
354	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
355	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
356	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
358	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
359	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
361	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
362	C₂⁴	#41×C₁₉	1	4	yes	—
363	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
373	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
374	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	8	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	8	4	no	—
404	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
405	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	complemented
406	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	16	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	16	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	complemented
422	C₄²	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	8	no	—
436	C₂³	—	4	4	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	8	4	no	—
439	C₂³	—	8	2	no	—
440	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
441	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
442	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
443	C₂³	C₄×D₄×C₁₉	1	4	yes	—
444	C₂³	C₄×D₄×C₁₉	1	4	yes	—
445	C₂³	C₁₉×#120	1	1	yes	characteristic
446	C₂³	C₁₉×#120	1	2	yes	—
447	C₂³	C₁₉×#120	1	1	yes	characteristic
448	C₂³	C₁₉×#121	1	4	yes	—
449	C₂³	C₁₉×#121	1	4	yes	—
450	C₂³	C₁₉×#123	1	2	yes	—
451	C₂³	C₁₉×#123	1	2	yes	—
452	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
453	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
454	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
455	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
456	C₂³	C₂×#41×C₁₉	1	2	yes	—
457	D₄	—	2	16	no	—
458	D₄	—	2	8	no	—
459	D₄	—	2	8	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	8	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	8	4	no	—
481	C₂×C₄	—	8	8	no	—
482	C₂×C₄	—	8	8	no	—
483	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	8	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	8	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	4	no	—
504	C₂²	—	8	2	no	—
505	C₂²	C₁₉×#386	1	2	yes	—
506	C₂²	C₁₉×#386	1	4	yes	—
507	C₂²	C₁₉×#386	1	2	yes	—
508	C₂²	C₁₉×#458	1	4	yes	—
509	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
510	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
511	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
512	C₂²	C₂×C₁₉×#121	1	2	yes	—
513	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
514	C₄	—	2	4	no	—
515	C₄	—	4	4	no	—
516	C₄	—	4	8	no	—
517	C₄	—	4	4	no	—
518	C₄	—	8	4	no	—
519	C₂	—	2	1	no	—
520	C₂	—	2	2	no	—
521	C₂	—	2	2	no	—
522	C₂	—	2	1	no	—
523	C₂	—	2	4	no	—
524	C₂	—	2	2	no	—
525	C₂	—	4	4	no	—
526	C₂	C₁₉×#1890	1	4	yes	direct product factor
527	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
528	C₂	C₂×C₁₉×#458	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#381	C₂	semidirect
5. C₁₉×#1890	C₂	direct (N × H)
6. C₂×C₁₉×#342	C₂	semidirect
11. C₂×C₁₉×#123	C₄	semidirect
27. C₁₉×#381	C₂²	semidirect
29. C₁₉×#342	C₂²	semidirect
48. C₂³×C₄×C₁₉	C₂×C₄	semidirect
54. C₁₉×#123	C₂×C₄	semidirect
76. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
140. C₂²×C₄×C₁₉	C₂²×C₄	semidirect
156. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
158. C₂×#1890	C₁₉	direct (N × H)
223. C₂×#381	C₂×C₁₉	semidirect
224. #1890	C₂×C₁₉	direct (N × H)
225. C₂×#342	C₂×C₁₉	semidirect
265. C₂×#123	C₄×C₁₉	semidirect
281. #381	C₂²×C₁₉	semidirect
283. #342	C₂²×C₁₉	semidirect
291. C₂×C₁₉	#1890	direct (N × H)
312. C₂³×C₄	C₂×C₄×C₁₉	semidirect
318. #123	C₂×C₄×C₁₉	semidirect
340. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
348. C₁₉	C₂×#1890	direct (N × H)
405. C₂²×C₄	C₂²×C₄×C₁₉	semidirect
421. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
526. C₂	C₁₉×#1890	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#123	2
C₂×C₁₉×#518	2
C₂²×C₁₉×#99	2
C₂×C₁₉×#381	2
C₁₉×#1890	2
C₂×C₁₉×#342	2
C₂×#1890	19

Subgroups — C2×C19×#1890 #18026917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1890 #18026917