Subgroups — C₁₉×#9041 #18015000

Order 4864.

1050 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2325	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1438	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1294	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₁₉	—	2	1	no	—
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	—	2	1	no	—
12	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
13	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
14	C₁₉×#447	—	2	2	no	—
15	C₁₉×#447	C₄	1	4	yes	complemented
16	C₂×C₁₉×#102	—	2	1	no	—
17	C₂×C₁₉×#102	—	2	1	no	—
18	C₂×C₁₉×#102	—	2	1	no	—
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₁₉×#388	—	2	1	no	—
22	C₁₉×#387	—	2	1	no	—
23	C₁₉×#386	—	2	1	no	—
24	C₁₉×#386	—	2	1	no	—
25	C₁₉×#385	—	2	1	no	—
26	C₁₉×#380	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₁₉×#327	—	2	2	no	—
30	C₂⁵×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	4	2	no	—
38	C₂²×D₄×C₁₉	—	4	2	no	—
39	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	complemented
40	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₁₉	—	2	4	no	—
47	C₂×D₈×C₁₉	—	4	2	no	—
48	C₂×D₈×C₁₉	—	4	2	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₁₉×#121	—	2	1	no	—
52	C₁₉×#121	—	2	1	no	—
53	C₁₉×#121	C₂×C₄	1	2	yes	—
54	C₁₉×#121	D₄	1	2	yes	—
55	C₄×D₄×C₁₉	—	4	2	no	—
56	C₄×D₄×C₁₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
72	C₂×C₄²×C₁₉	—	2	1	no	—
73	C₁₉×#102	—	2	4	no	—
74	C₁₉×#102	—	4	2	no	—
75	C₁₉×#102	—	4	2	no	—
76	C₁₉×C₂²⋊C₈	—	2	1	no	—
77	C₁₉×C₂²⋊C₈	—	2	1	no	—
78	C₁₉×C₂²⋊C₈	—	2	1	no	—
79	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	complemented
80	C₁₉×#95	—	2	1	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₁₉×#95	—	2	1	no	—
83	C₁₉×#95	—	2	1	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	—	2	1	no	—
91	C₂⁴×C₁₉	—	4	1	no	—
92	C₂⁴×C₁₉	—	4	1	no	—
93	C₂⁴×C₁₉	—	4	1	no	—
94	C₂⁴×C₁₉	—	4	1	no	—
95	C₂⁴×C₁₉	—	4	1	no	—
96	C₂⁴×C₁₉	—	4	1	no	—
97	C₂⁴×C₁₉	—	4	1	no	—
98	C₂⁴×C₁₉	—	4	1	no	—
99	C₂⁴×C₁₉	—	4	1	no	—
100	C₂⁴×C₁₉	—	4	1	no	—
101	C₂⁴×C₁₉	—	4	1	no	—
102	C₂⁴×C₁₉	—	4	1	no	—
103	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂×D₄×C₁₉	—	4	1	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂×D₄×C₁₉	—	4	4	no	—
121	C₂×D₄×C₁₉	—	4	4	no	—
122	C₂×D₄×C₁₉	—	4	4	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	1	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	—	4	1	no	—
143	C₂²×C₄×C₁₉	—	4	1	no	—
144	C₂²×C₄×C₁₉	—	4	1	no	—
145	C₂²×C₄×C₁₉	—	4	1	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	—	4	1	no	—
151	C₂²×C₄×C₁₉	—	4	1	no	—
152	C₂²×C₄×C₁₉	—	8	1	no	—
153	C₂²×C₄×C₁₉	—	8	1	no	—
154	C₂²×C₄×C₁₉	D₈	1	2	yes	complemented
155	C₂²×C₄×C₁₉	C₂²×C₄	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×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
161	D₈×C₁₉	—	4	8	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	4	1	no	—
164	C₂×C₈×C₁₉	—	4	1	no	—
165	C₂×C₈×C₁₉	—	4	1	no	—
166	C₂×C₈×C₁₉	—	4	1	no	—
167	C₂×C₈×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	4	1	no	—
170	C₄⋊C₄×C₁₉	—	4	1	no	—
171	C₄⋊C₄×C₁₉	—	4	2	no	—
172	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	4	2	no	—
176	C₂²⋊C₄×C₁₉	—	4	8	no	—
177	C₂²⋊C₄×C₁₉	—	4	8	no	—
178	C₂²⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	—	4	1	no	—
180	C₂²⋊C₄×C₁₉	—	8	1	no	—
181	C₂²⋊C₄×C₁₉	—	8	1	no	—
182	C₄²×C₁₉	—	4	2	no	—
183	#9041	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	1	no	—
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	1	no	—
188	C₂³×C₁₉	—	2	4	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	—	4	1	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	—	4	2	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	8	1	no	—
215	C₂³×C₁₉	—	8	1	no	—
216	C₂³×C₁₉	—	8	1	no	—
217	C₂³×C₁₉	—	8	1	no	—
218	C₂³×C₁₉	—	8	1	no	—
219	C₂³×C₁₉	—	8	1	no	—
220	C₂³×C₁₉	—	8	1	no	—
221	C₂³×C₁₉	—	8	1	no	—
222	C₂³×C₁₉	—	8	1	no	—
223	C₂³×C₁₉	—	8	1	no	—
224	C₂³×C₁₉	—	8	1	no	—
225	C₂³×C₁₉	—	8	1	no	—
226	C₂³×C₁₉	—	8	1	no	—
227	C₂³×C₁₉	—	8	1	no	—
228	C₂³×C₁₉	—	8	1	no	—
229	C₂³×C₁₉	—	8	1	no	—
230	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
231	C₂³×C₁₉	#120	1	1	yes	characteristic
232	C₂³×C₁₉	#121	1	1	yes	characteristic
233	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
234	C₂³×C₁₉	#135	1	1	yes	characteristic
235	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
237	D₄×C₁₉	—	2	4	no	—
238	D₄×C₁₉	—	2	4	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	4	2	no	—
246	D₄×C₁₉	—	4	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	8	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	8	1	no	—
280	C₂×C₄×C₁₉	—	8	4	no	—
281	C₂×C₄×C₁₉	—	8	1	no	—
282	C₂×C₄×C₁₉	—	8	1	no	—
283	C₂×C₄×C₁₉	—	8	1	no	—
284	C₂×C₄×C₁₉	—	8	1	no	—
285	C₂×C₄×C₁₉	—	8	1	no	—
286	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
289	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
290	C₈×C₁₉	—	4	2	no	—
291	C₈×C₁₉	—	8	1	no	—
292	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
293	#2325	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1438	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1294	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1280	C₂×C₁₉	1	1	yes	characteristic, complemented
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	1	no	—
306	C₂²×C₁₉	—	2	1	no	—
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	4	4	no	—
312	C₂²×C₁₉	—	4	4	no	—
313	C₂²×C₁₉	—	4	2	no	—
314	C₂²×C₁₉	—	4	2	no	—
315	C₂²×C₁₉	—	4	4	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	—	8	2	no	—
318	C₂²×C₁₉	—	8	2	no	—
319	C₂²×C₁₉	—	8	2	no	—
320	C₂²×C₁₉	—	8	2	no	—
321	C₂²×C₁₉	—	8	2	no	—
322	C₂²×C₁₉	—	8	2	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	2	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	—	8	2	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	2	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	2	no	—
331	C₂²×C₁₉	—	8	2	no	—
332	C₂²×C₁₉	—	8	2	no	—
333	C₂²×C₁₉	#386	1	1	yes	characteristic
334	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
335	C₂²×C₁₉	#442	1	1	yes	characteristic
336	C₂²×C₁₉	#447	1	1	yes	characteristic
337	C₂²×C₁₉	#449	1	1	yes	characteristic
338	C₂²×C₁₉	#453	1	1	yes	characteristic
339	C₂²×C₁₉	#454	1	1	yes	characteristic
340	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
341	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₁₉	#459	1	1	yes	characteristic
343	C₂²×C₁₉	#463	1	1	yes	characteristic
344	C₄×C₁₉	—	2	1	no	—
345	C₄×C₁₉	—	2	1	no	—
346	C₄×C₁₉	—	2	1	no	—
347	C₄×C₁₉	—	2	1	no	—
348	C₄×C₁₉	—	4	2	no	—
349	C₄×C₁₉	—	4	2	no	—
350	C₄×C₁₉	—	8	2	no	—
351	C₄×C₁₉	—	8	1	no	—
352	C₄×C₁₉	—	8	1	no	—
353	C₄×C₁₉	—	8	1	no	—
354	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
355	C₂²×D₈	—	2	1	no	—
356	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₄×D₄	—	2	1	no	—
358	C₂²×C₂²⋊C₄	—	2	1	no	—
359	C₂²×C₂²⋊C₄	—	2	1	no	—
360	#447	—	2	2	no	—
361	#447	C₄×C₁₉	1	4	yes	complemented
362	C₂×#102	—	2	1	no	—
363	C₂×#102	—	2	1	no	—
364	C₂×#102	—	2	1	no	—
365	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
367	#388	—	2	1	no	—
368	#387	—	2	1	no	—
369	#386	—	2	1	no	—
370	#386	—	2	1	no	—
371	#385	—	2	1	no	—
372	#380	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
375	#327	—	2	2	no	—
376	C₂×C₁₉	—	2	1	no	—
377	C₂×C₁₉	—	2	1	no	—
378	C₂×C₁₉	—	2	1	no	—
379	C₂×C₁₉	—	2	1	no	—
380	C₂×C₁₉	—	8	2	no	—
381	C₂×C₁₉	—	8	4	no	—
382	C₂×C₁₉	#1595	1	1	yes	characteristic
383	C₂×C₁₉	#1597	1	1	yes	characteristic
384	C₂×C₁₉	#1598	1	1	yes	characteristic
385	C₂×C₁₉	#1600	1	1	yes	characteristic
386	C₂×C₁₉	#1879	1	1	yes	characteristic
387	C₂×C₁₉	#1883	1	1	yes	characteristic
388	C₂×C₁₉	#1889	1	1	yes	characteristic
389	C₂⁵	—	2	1	no	—
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	—	4	2	no	—
397	C₂²×D₄	—	4	2	no	—
398	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	complemented
399	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
403	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×D₈	—	2	4	no	—
406	C₂×D₈	—	4	2	no	—
407	C₂×D₈	—	4	2	no	—
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	—	2	1	no	—
410	#121	—	2	1	no	—
411	#121	—	2	1	no	—
412	#121	C₂×C₄×C₁₉	1	2	yes	—
413	#121	D₄×C₁₉	1	2	yes	—
414	C₄×D₄	—	4	2	no	—
415	C₄×D₄	—	4	2	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	4	2	no	—
426	C₂×C₂²⋊C₄	—	4	2	no	—
427	C₂×C₂²⋊C₄	—	4	2	no	—
428	C₂×C₂²⋊C₄	—	4	2	no	—
429	C₂×C₂²⋊C₄	—	4	2	no	—
430	C₂×C₂²⋊C₄	—	4	2	no	—
431	C₂×C₄²	—	2	1	no	—
432	#102	—	2	4	no	—
433	#102	—	4	2	no	—
434	#102	—	4	2	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	complemented
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	C₁₉	#9041	1	1	yes	characteristic, direct product factor, Sylow
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	2	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	—	4	1	no	—
452	C₂⁴	—	4	1	no	—
453	C₂⁴	—	4	1	no	—
454	C₂⁴	—	4	1	no	—
455	C₂⁴	—	4	1	no	—
456	C₂⁴	—	4	1	no	—
457	C₂⁴	—	4	1	no	—
458	C₂⁴	—	4	1	no	—
459	C₂⁴	—	4	1	no	—
460	C₂⁴	—	4	1	no	—
461	C₂⁴	—	4	1	no	—
462	C₂⁴	—	4	1	no	—
463	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	4	4	no	—
480	C₂×D₄	—	4	4	no	—
481	C₂×D₄	—	4	4	no	—
482	C₂×D₄	—	4	4	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	4	1	no	—
488	C₂×D₄	—	4	1	no	—
489	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	—	4	1	no	—
504	C₂²×C₄	—	4	1	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	—	4	1	no	—
512	C₂²×C₄	—	8	1	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	D₈×C₁₉	1	2	yes	complemented
515	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
520	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
521	D₈	—	4	8	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	4	1	no	—
524	C₂×C₈	—	4	1	no	—
525	C₂×C₈	—	4	1	no	—
526	C₂×C₈	—	4	1	no	—
527	C₂×C₈	—	4	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	2	no	—
532	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	8	no	—
537	C₂²⋊C₄	—	4	8	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	—	8	1	no	—
541	C₂²⋊C₄	—	8	1	no	—
542	C₄²	—	4	2	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	8	1	no	—
574	C₂³	—	8	1	no	—
575	C₂³	—	8	1	no	—
576	C₂³	—	8	1	no	—
577	C₂³	—	8	1	no	—
578	C₂³	—	8	1	no	—
579	C₂³	—	8	1	no	—
580	C₂³	—	8	1	no	—
581	C₂³	—	8	1	no	—
582	C₂³	—	8	1	no	—
583	C₂³	—	8	1	no	—
584	C₂³	—	8	1	no	—
585	C₂³	—	8	1	no	—
586	C₂³	—	8	1	no	—
587	C₂³	—	8	1	no	—
588	C₂³	—	8	1	no	—
589	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
590	C₂³	C₁₉×#120	1	1	yes	characteristic
591	C₂³	C₁₉×#121	1	1	yes	characteristic
592	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
593	C₂³	C₁₉×#135	1	1	yes	characteristic
594	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
595	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
596	D₄	—	2	4	no	—
597	D₄	—	2	4	no	—
598	D₄	—	4	2	no	—
599	D₄	—	4	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	8	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	8	1	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	—	8	1	no	—
641	C₂×C₄	—	8	1	no	—
642	C₂×C₄	—	8	1	no	—
643	C₂×C₄	—	8	1	no	—
644	C₂×C₄	—	8	1	no	—
645	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
646	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
647	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
648	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
649	C₈	—	4	2	no	—
650	C₈	—	8	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	8	2	no	—
670	C₂²	—	8	2	no	—
671	C₂²	—	8	2	no	—
672	C₂²	—	8	2	no	—
673	C₂²	—	8	2	no	—
674	C₂²	—	8	2	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	2	no	—
677	C₂²	—	8	2	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	2	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	2	no	—
682	C₂²	—	8	1	no	—
683	C₂²	—	8	2	no	—
684	C₂²	—	8	2	no	—
685	C₂²	C₁₉×#386	1	1	yes	characteristic
686	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
687	C₂²	C₁₉×#442	1	1	yes	characteristic
688	C₂²	C₁₉×#447	1	1	yes	characteristic
689	C₂²	C₁₉×#449	1	1	yes	characteristic
690	C₂²	C₁₉×#453	1	1	yes	characteristic
691	C₂²	C₁₉×#454	1	1	yes	characteristic
692	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
693	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
694	C₂²	C₁₉×#459	1	1	yes	characteristic
695	C₂²	C₁₉×#463	1	1	yes	characteristic
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	8	2	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₂	—	2	1	no	—
707	C₂	—	2	1	no	—
708	C₂	—	2	1	no	—
709	C₂	—	2	1	no	—
710	C₂	—	8	4	no	—
711	C₂	—	8	2	no	—
712	C₂	C₁₉×#1595	1	1	yes	characteristic
713	C₂	C₁₉×#1597	1	1	yes	characteristic
714	C₂	C₁₉×#1598	1	1	yes	characteristic
715	C₂	C₁₉×#1600	1	1	yes	characteristic
716	C₂	C₁₉×#1879	1	1	yes	characteristic
717	C₂	C₁₉×#1883	1	1	yes	characteristic
718	C₂	C₁₉×#1889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2325	C₂	semidirect
3. C₁₉×#1786	C₂	semidirect
4. C₂×C₁₉×#327	C₂	semidirect
5. C₁₉×#1438	C₂	semidirect
6. C₁₉×#1294	C₂	semidirect
7. C₁₉×#1280	C₂	semidirect
15. C₁₉×#447	C₄	semidirect
39. C₂²×D₄×C₁₉	C₂×C₄	semidirect
79. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
129. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
154. C₂²×C₄×C₁₉	D₈	semidirect
172. C₄⋊C₄×C₁₉	C₂²⋊C₄	semidirect
183. #9041	C₁₉	direct (N × H)
293. #2325	C₂×C₁₉	semidirect
294. #1786	C₂×C₁₉	semidirect
295. C₂×#327	C₂×C₁₉	semidirect
296. #1438	C₂×C₁₉	semidirect
297. #1294	C₂×C₁₉	semidirect
298. #1280	C₂×C₁₉	semidirect
361. #447	C₄×C₁₉	semidirect
398. C₂²×D₄	C₂×C₄×C₁₉	semidirect
438. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
446. C₁₉	#9041	direct (N × H)
489. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
514. C₂²×C₄	D₈×C₁₉	semidirect
532. C₄⋊C₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#447	2
C₁₉×#2325	2
C₁₉×#1786	2
C₂×C₁₉×#327	2
C₁₉×#1438	2
C₁₉×#1294	2
C₁₉×#1280	2
#9041	19

Subgroups — C19×#9041 #18015000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9041 #18015000