Subgroups — C₁₉×#8408 #18014367

Order 4864.

1040 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#538	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#323	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#538	—	2	2	no	—
9	C₁₉×#538	—	2	2	no	—
10	C₁₉×#538	—	2	2	no	—
11	C₁₉×#538	C₄	1	4	yes	complemented
12	C₂×C₁₉×#126	—	2	1	no	—
13	C₂×C₁₉×#124	—	2	1	no	—
14	C₂×C₁₉×#123	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	—	2	1	no	—
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#120	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	—	2	1	no	—
24	C₂×C₁₉×#102	—	2	1	no	—
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#95	—	2	1	no	—
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₁₉×#340	—	2	1	no	—
30	C₁₉×#340	—	2	1	no	—
31	C₁₉×#328	—	2	2	no	—
32	C₁₉×#327	—	2	2	no	—
33	C₁₉×#323	—	2	2	no	—
34	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₁₉×#126	—	2	4	no	—
48	C₁₉×#126	—	2	4	no	—
49	C₁₉×#124	—	2	4	no	—
50	C₁₉×#124	—	2	4	no	—
51	C₁₉×#123	—	2	4	no	—
52	C₁₉×#123	—	2	4	no	—
53	C₁₉×C₂²⋊Q₈	—	2	1	no	—
54	C₁₉×C₂²⋊Q₈	—	2	1	no	—
55	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	2	4	no	—
59	C₁₉×#121	—	2	1	no	—
60	C₁₉×#121	—	2	1	no	—
61	C₁₉×#121	C₂×C₄	1	2	yes	—
62	C₁₉×#121	D₄	1	2	yes	—
63	C₁₉×#120	—	2	4	no	—
64	C₁₉×#120	—	2	4	no	—
65	C₄×D₄×C₁₉	—	2	4	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₁₉×#103	—	4	2	no	—
90	C₁₉×#102	—	4	2	no	—
91	C₁₉×C₂²⋊C₈	—	2	1	no	—
92	C₁₉×C₂²⋊C₈	—	2	1	no	—
93	C₁₉×C₂²⋊C₈	—	2	1	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₁₉×#95	—	2	1	no	—
97	C₁₉×#95	—	4	2	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	1	no	—
100	C₂⁴×C₁₉	—	2	1	no	—
101	C₂⁴×C₁₉	—	2	1	no	—
102	C₂⁴×C₁₉	—	2	1	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	—	2	1	no	—
105	C₂⁴×C₁₉	—	4	1	no	—
106	C₂⁴×C₁₉	—	4	1	no	—
107	C₂⁴×C₁₉	—	4	1	no	—
108	C₂⁴×C₁₉	—	4	1	no	—
109	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
110	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	complemented
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	4	no	—
118	C₂×D₄×C₁₉	—	2	4	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂×D₄×C₁₉	—	4	1	no	—
122	C₂×D₄×C₁₉	—	4	1	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	—	8	1	no	—
127	C₂×D₄×C₁₉	—	8	1	no	—
128	C₂×D₄×C₁₉	—	8	1	no	—
129	C₂×D₄×C₁₉	—	8	1	no	—
130	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	1	no	—
141	C₂²×C₄×C₁₉	—	4	1	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	—	4	1	no	—
153	C₂²×C₄×C₁₉	—	4	1	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	—	8	1	no	—
156	C₂²×C₄×C₁₉	—	8	1	no	—
157	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂×C₈×C₁₉	—	4	1	no	—
169	C₂×C₈×C₁₉	—	4	1	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
180	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₉	—	2	4	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	4	8	no	—
193	C₄²×C₁₉	—	2	4	no	—
194	#8408	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	2	1	no	—
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	2	no	—
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	2	2	no	—
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	4	2	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	—	4	1	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	4	1	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	—	4	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₁₉	#120	1	1	yes	characteristic
231	C₂³×C₁₉	#120	1	1	yes	characteristic
232	C₂³×C₁₉	#135	1	1	yes	characteristic
233	C₂³×C₁₉	#135	1	1	yes	characteristic
234	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂³×C₁₉	#137	1	1	yes	characteristic
236	Q₈×C₁₉	—	4	2	no	—
237	Q₈×C₁₉	—	8	1	no	—
238	D₄×C₁₉	—	4	2	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	—	8	1	no	—
244	D₄×C₁₉	—	8	4	no	—
245	D₄×C₁₉	—	8	4	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	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	1	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	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	2	no	—
273	C₂×C₄×C₁₉	—	8	1	no	—
274	C₂×C₄×C₁₉	—	8	4	no	—
275	C₂×C₄×C₁₉	—	8	1	no	—
276	C₂×C₄×C₁₉	—	8	1	no	—
277	C₂×C₄×C₁₉	—	8	1	no	—
278	C₂×C₄×C₁₉	—	8	1	no	—
279	C₂×C₄×C₁₉	—	8	1	no	—
280	C₂×C₄×C₁₉	—	8	1	no	—
281	C₂×C₄×C₁₉	—	8	1	no	—
282	C₂×C₄×C₁₉	—	8	1	no	—
283	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
286	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
287	C₈×C₁₉	—	8	1	no	—
288	C₈×C₁₉	—	8	1	no	—
289	C₂×#538	C₂×C₁₉	1	1	yes	characteristic
290	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
292	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂×#323	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1439	C₂×C₁₉	1	1	yes	characteristic, complemented
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	1	no	—
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	—	4	4	no	—
309	C₂²×C₁₉	—	4	2	no	—
310	C₂²×C₁₉	—	4	2	no	—
311	C₂²×C₁₉	—	4	2	no	—
312	C₂²×C₁₉	—	4	2	no	—
313	C₂²×C₁₉	—	4	2	no	—
314	C₂²×C₁₉	—	4	2	no	—
315	C₂²×C₁₉	—	8	2	no	—
316	C₂²×C₁₉	—	8	2	no	—
317	C₂²×C₁₉	—	8	2	no	—
318	C₂²×C₁₉	—	8	1	no	—
319	C₂²×C₁₉	—	8	1	no	—
320	C₂²×C₁₉	—	8	1	no	—
321	C₂²×C₁₉	—	8	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	#379	1	1	yes	characteristic
327	C₂²×C₁₉	#416	1	1	yes	characteristic
328	C₂²×C₁₉	#417	1	1	yes	characteristic
329	C₂²×C₁₉	#449	1	1	yes	characteristic
330	C₂²×C₁₉	#449	1	1	yes	characteristic
331	C₂²×C₁₉	#452	1	1	yes	characteristic
332	C₂²×C₁₉	#452	1	1	yes	characteristic
333	C₂²×C₁₉	#453	1	1	yes	characteristic
334	C₂²×C₁₉	#455	1	1	yes	characteristic
335	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
336	C₂²×C₁₉	#458	1	1	yes	characteristic
337	C₄×C₁₉	—	2	1	no	—
338	C₄×C₁₉	—	2	1	no	—
339	C₄×C₁₉	—	2	1	no	—
340	C₄×C₁₉	—	2	1	no	—
341	C₄×C₁₉	—	4	2	no	—
342	C₄×C₁₉	—	4	2	no	—
343	C₄×C₁₉	—	4	2	no	—
344	C₄×C₁₉	—	4	2	no	—
345	C₄×C₁₉	—	8	2	no	—
346	C₄×C₁₉	—	8	2	no	—
347	#538	—	2	2	no	—
348	#538	—	2	2	no	—
349	#538	—	2	2	no	—
350	#538	C₄×C₁₉	1	4	yes	complemented
351	C₂×#126	—	2	1	no	—
352	C₂×#124	—	2	1	no	—
353	C₂×#123	—	2	1	no	—
354	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#121	—	2	1	no	—
356	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#120	—	2	1	no	—
358	C₂×C₄×D₄	—	2	1	no	—
359	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
360	C₂²×C₂²⋊C₄	—	2	1	no	—
361	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#103	—	2	1	no	—
363	C₂×#102	—	2	1	no	—
364	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#95	—	2	1	no	—
367	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
368	#340	—	2	1	no	—
369	#340	—	2	1	no	—
370	#328	—	2	2	no	—
371	#327	—	2	2	no	—
372	#323	—	2	2	no	—
373	C₂×C₁₉	—	2	1	no	—
374	C₂×C₁₉	—	2	1	no	—
375	C₂×C₁₉	—	2	1	no	—
376	C₂×C₁₉	—	2	1	no	—
377	C₂×C₁₉	—	8	2	no	—
378	C₂×C₁₉	—	8	2	no	—
379	C₂×C₁₉	#1600	1	1	yes	characteristic
380	C₂×C₁₉	#1606	1	1	yes	characteristic
381	C₂×C₁₉	#1612	1	1	yes	characteristic
382	C₂×C₁₉	#1618	1	1	yes	characteristic
383	C₂×C₁₉	#1788	1	1	yes	characteristic
384	C₂×C₁₉	#1790	1	1	yes	characteristic
385	C₂×C₁₉	#1792	1	1	yes	characteristic
386	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
387	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	—	2	1	no	—
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	2	1	no	—
399	#126	—	2	4	no	—
400	#126	—	2	4	no	—
401	#124	—	2	4	no	—
402	#124	—	2	4	no	—
403	#123	—	2	4	no	—
404	#123	—	2	4	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
408	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
409	#121	—	2	4	no	—
410	#121	—	2	4	no	—
411	#121	—	2	1	no	—
412	#121	—	2	1	no	—
413	#121	C₂×C₄×C₁₉	1	2	yes	—
414	#121	D₄×C₁₉	1	2	yes	—
415	#120	—	2	4	no	—
416	#120	—	2	4	no	—
417	C₄×D₄	—	2	4	no	—
418	C₄×D₄	—	2	4	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	4	2	no	—
424	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	4	2	no	—
436	C₂×C₂²⋊C₄	—	4	2	no	—
437	C₂×C₂²⋊C₄	—	4	2	no	—
438	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
439	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
440	C₂×C₄²	—	2	1	no	—
441	#103	—	4	2	no	—
442	#102	—	4	2	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	C₂²⋊C₈	—	2	1	no	—
446	C₂²⋊C₈	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	4	2	no	—
450	C₁₉	#8408	1	1	yes	characteristic, direct product factor, Sylow
451	C₂⁴	—	2	1	no	—
452	C₂⁴	—	2	1	no	—
453	C₂⁴	—	2	1	no	—
454	C₂⁴	—	2	1	no	—
455	C₂⁴	—	2	1	no	—
456	C₂⁴	—	2	1	no	—
457	C₂⁴	—	2	1	no	—
458	C₂⁴	—	4	1	no	—
459	C₂⁴	—	4	1	no	—
460	C₂⁴	—	4	1	no	—
461	C₂⁴	—	4	1	no	—
462	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
463	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	4	1	no	—
466	C₂×Q₈	—	4	1	no	—
467	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	complemented
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	4	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	—	8	1	no	—
480	C₂×D₄	—	8	1	no	—
481	C₂×D₄	—	8	1	no	—
482	C₂×D₄	—	8	1	no	—
483	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	4	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	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	—	8	1	no	—
509	C₂²×C₄	—	8	1	no	—
510	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
511	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₈	—	4	1	no	—
518	C₂×C₈	—	4	1	no	—
519	C₂×C₈	—	4	1	no	—
520	C₂×C₈	—	4	1	no	—
521	C₂×C₈	—	4	1	no	—
522	C₂×C₈	—	4	1	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
533	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	4	8	no	—
546	C₄²	—	2	4	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	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	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	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	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	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	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
582	C₂³	C₁₉×#120	1	1	yes	characteristic
583	C₂³	C₁₉×#120	1	1	yes	characteristic
584	C₂³	C₁₉×#135	1	1	yes	characteristic
585	C₂³	C₁₉×#135	1	1	yes	characteristic
586	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
587	C₂³	C₁₉×#137	1	1	yes	characteristic
588	Q₈	—	4	2	no	—
589	Q₈	—	8	1	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	8	1	no	—
596	D₄	—	8	4	no	—
597	D₄	—	8	4	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	8	1	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	8	1	no	—
629	C₂×C₄	—	8	1	no	—
630	C₂×C₄	—	8	1	no	—
631	C₂×C₄	—	8	1	no	—
632	C₂×C₄	—	8	1	no	—
633	C₂×C₄	—	8	1	no	—
634	C₂×C₄	—	8	1	no	—
635	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
637	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
638	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
639	C₈	—	8	1	no	—
640	C₈	—	8	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	8	2	no	—
661	C₂²	—	8	2	no	—
662	C₂²	—	8	2	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	C₁₉×#379	1	1	yes	characteristic
672	C₂²	C₁₉×#416	1	1	yes	characteristic
673	C₂²	C₁₉×#417	1	1	yes	characteristic
674	C₂²	C₁₉×#449	1	1	yes	characteristic
675	C₂²	C₁₉×#449	1	1	yes	characteristic
676	C₂²	C₁₉×#452	1	1	yes	characteristic
677	C₂²	C₁₉×#452	1	1	yes	characteristic
678	C₂²	C₁₉×#453	1	1	yes	characteristic
679	C₂²	C₁₉×#455	1	1	yes	characteristic
680	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
681	C₂²	C₁₉×#458	1	1	yes	characteristic
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	8	2	no	—
691	C₄	—	8	2	no	—
692	C₂	—	2	1	no	—
693	C₂	—	2	1	no	—
694	C₂	—	2	1	no	—
695	C₂	—	2	1	no	—
696	C₂	—	8	2	no	—
697	C₂	—	8	2	no	—
698	C₂	C₁₉×#1600	1	1	yes	characteristic
699	C₂	C₁₉×#1606	1	1	yes	characteristic
700	C₂	C₁₉×#1612	1	1	yes	characteristic
701	C₂	C₁₉×#1618	1	1	yes	characteristic
702	C₂	C₁₉×#1788	1	1	yes	characteristic
703	C₂	C₁₉×#1790	1	1	yes	characteristic
704	C₂	C₁₉×#1792	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×#538	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×#1874	C₂	semidirect
3. C₁₉×#1872	C₂	semidirect
4. C₂×C₁₉×#328	C₂	semidirect
5. C₂×C₁₉×#327	C₂	semidirect
6. C₂×C₁₉×#323	C₂	semidirect
7. C₁₉×#1439	C₂	semidirect
11. C₁₉×#538	C₄	semidirect
114. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
130. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
179. C₄⋊C₄×C₁₉	C₂²⋊C₄	semidirect
180. C₄⋊C₄×C₁₉	C₂²⋊C₄	semidirect
194. #8408	C₁₉	direct (N × H)
290. #1874	C₂×C₁₉	semidirect
291. #1872	C₂×C₁₉	semidirect
292. C₂×#328	C₂×C₁₉	semidirect
293. C₂×#327	C₂×C₁₉	semidirect
294. C₂×#323	C₂×C₁₉	semidirect
295. #1439	C₂×C₁₉	semidirect
350. #538	C₄×C₁₉	semidirect
450. C₁₉	#8408	direct (N × H)
467. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
483. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
532. C₄⋊C₄	C₂²⋊C₄×C₁₉	semidirect
533. 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×#538	2
C₁₉×#1874	2
C₁₉×#1872	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₂×C₁₉×#323	2
C₁₉×#1439	2
#8408	19

Subgroups — C19×#8408 #18014367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8408 #18014367