Subgroups — C₁₉×#32981 #18038940

Order 4864.

1508 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#482	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1875	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1825	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#120	—	2	1	no	—
17	C₂×C₁₉×#117	—	2	1	no	—
18	C₂×C₁₉×#117	—	2	1	no	—
19	C₂×C₁₉×#117	—	2	8	no	—
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂×C₁₉×#117	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄²×C₁₉	—	2	1	no	—
26	C₁₉×#482	—	2	8	no	—
27	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
28	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
29	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
30	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₁₉×#386	—	2	1	no	—
36	C₁₉×#386	—	2	1	no	—
37	C₁₉×#386	—	2	1	no	—
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₁₉×#380	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#340	C₂²	1	2	yes	complemented
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	4	no	—
51	C₂³×C₄×C₁₉	—	2	4	no	—
52	C₂³×C₄×C₁₉	—	2	2	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	4	no	—
68	C₁₉×#120	—	4	4	no	—
69	C₁₉×#117	—	2	8	no	—
70	C₁₉×#117	—	2	8	no	—
71	C₁₉×#117	—	2	4	no	—
72	C₁₉×#117	—	2	4	no	—
73	C₁₉×#117	—	2	4	no	—
74	C₁₉×#117	D₄	1	8	yes	complemented
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	8	no	—
94	C₂×C₄²×C₁₉	—	2	2	no	—
95	C₂×C₄²×C₁₉	—	2	2	no	—
96	C₁₉×#107	—	2	4	no	—
97	C₁₉×#106	—	2	4	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×C₂²⋊C₈	—	2	4	no	—
101	C₁₉×C₂²⋊C₈	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	2	2	no	—
103	C₁₉×C₂²⋊C₈	—	2	4	no	—
104	C₁₉×#95	—	2	1	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₂⁴×C₁₉	—	2	2	no	—
108	C₂⁴×C₁₉	—	2	2	no	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	—	2	2	no	—
111	C₂⁴×C₁₉	—	2	2	no	—
112	C₂⁴×C₁₉	—	2	1	no	—
113	C₂⁴×C₁₉	—	4	1	no	—
114	C₂⁴×C₁₉	—	4	1	no	—
115	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	2	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	2	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂²×C₄×C₁₉	—	2	16	no	—
132	C₂²×C₄×C₁₉	—	2	16	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	4	2	no	—
158	C₂²×C₄×C₁₉	—	4	2	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	#41	1	4	yes	—
166	C₂²×C₄×C₁₉	#41	1	2	yes	—
167	C₂²×C₄×C₁₉	#41	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	2	4	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
185	C₂²⋊C₄×C₁₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₉	—	2	8	no	—
187	C₂²⋊C₄×C₁₉	—	4	2	no	—
188	C₂²⋊C₄×C₁₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₉	—	4	2	no	—
190	C₂²⋊C₄×C₁₉	—	4	2	no	—
191	C₂²⋊C₄×C₁₉	—	4	2	no	—
192	C₂²⋊C₄×C₁₉	—	4	2	no	—
193	C₄²×C₁₉	—	2	8	no	—
194	C₄²×C₁₉	—	2	8	no	—
195	#32981	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	2	1	no	—
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	8	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	4	4	no	—
214	C₂³×C₁₉	—	4	4	no	—
215	C₂³×C₁₉	—	4	4	no	—
216	C₂³×C₁₉	—	4	4	no	—
217	C₂³×C₁₉	—	4	4	no	—
218	C₂³×C₁₉	—	4	4	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	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	#120	1	2	yes	—
227	C₂³×C₁₉	#123	1	2	yes	—
228	C₂³×C₁₉	#123	1	2	yes	—
229	C₂³×C₁₉	#135	1	2	yes	—
230	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
231	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	D₄×C₁₉	—	4	2	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	8	4	no	—
235	D₄×C₁₉	—	8	4	no	—
236	D₄×C₁₉	—	8	4	no	—
237	C₂×C₄×C₁₉	—	2	8	no	—
238	C₂×C₄×C₁₉	—	2	8	no	—
239	C₂×C₄×C₁₉	—	2	8	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	2	4	no	—
251	C₂×C₄×C₁₉	—	2	4	no	—
252	C₂×C₄×C₁₉	—	2	4	no	—
253	C₂×C₄×C₁₉	—	2	4	no	—
254	C₂×C₄×C₁₉	—	4	8	no	—
255	C₂×C₄×C₁₉	—	4	8	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	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	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	#120	1	2	yes	—
270	C₂×C₄×C₁₉	#123	1	2	yes	—
271	C₂×C₄×C₁₉	#123	1	2	yes	—
272	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
276	C₈×C₁₉	—	4	2	no	—
277	C₈×C₁₉	—	4	2	no	—
278	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
279	C₂×#482	C₂×C₁₉	1	2	yes	complemented
280	#2847	C₂×C₁₉	1	1	yes	characteristic
281	#1875	C₂×C₁₉	1	2	yes	complemented
282	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1854	C₂×C₁₉	1	2	yes	complemented
285	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1825	C₂×C₁₉	1	2	yes	complemented
288	#1779	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	4	16	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	8	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	#482	1	4	yes	complemented
318	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
319	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
320	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
321	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
322	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₂²×C₁₉	#575	1	1	yes	characteristic
324	C₂²×C₁₉	#575	1	1	yes	characteristic
325	C₄×C₁₉	—	2	2	no	—
326	C₄×C₁₉	—	2	2	no	—
327	C₄×C₁₉	—	2	2	no	—
328	C₄×C₁₉	—	4	4	no	—
329	C₄×C₁₉	—	4	4	no	—
330	C₄×C₁₉	—	8	1	no	—
331	C₄×C₁₉	—	8	1	no	—
332	C₄×C₁₉	—	8	1	no	—
333	C₄×C₁₉	#525	1	2	yes	—
334	C₄×C₁₉	#525	1	2	yes	—
335	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#120	—	2	1	no	—
340	C₂×#117	—	2	1	no	—
341	C₂×#117	—	2	1	no	—
342	C₂×#117	—	2	8	no	—
343	C₂×#117	C₂²×C₁₉	1	2	yes	—
344	C₂×#117	C₂²×C₁₉	1	2	yes	—
345	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
346	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	—	2	1	no	—
348	C₂²×C₄²	—	2	1	no	—
349	#482	—	2	8	no	—
350	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
351	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
352	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
353	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
354	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
355	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
358	#386	—	2	1	no	—
359	#386	—	2	1	no	—
360	#386	—	2	1	no	—
361	#380	C₂²×C₁₉	1	1	yes	characteristic
362	#380	C₂²×C₁₉	1	1	yes	characteristic
363	#380	C₂²×C₁₉	1	1	yes	characteristic
364	#340	C₂²×C₁₉	1	2	yes	complemented
365	#340	C₂²×C₁₉	1	2	yes	complemented
366	#340	C₂²×C₁₉	1	2	yes	complemented
367	#340	C₂²×C₁₉	1	2	yes	complemented
368	C₂×C₁₉	—	2	4	no	—
369	C₂×C₁₉	—	4	2	no	—
370	C₂×C₁₉	—	4	2	no	—
371	C₂×C₁₉	—	16	1	no	—
372	C₂×C₁₉	#2849	1	1	yes	characteristic
373	C₂×C₁₉	#3002	1	1	yes	characteristic
374	C₂×C₁₉	#3006	1	1	yes	characteristic
375	C₂×C₁₉	C₂×#482	1	1	yes	characteristic
376	C₂×C₁₉	#3091	1	1	yes	characteristic
377	C₂×C₁₉	#3093	1	1	yes	characteristic
378	C₂×C₁₉	#3094	1	1	yes	characteristic
379	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	1	no	—
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	—	2	4	no	—
386	C₂³×C₄	—	2	2	no	—
387	C₂³×C₄	—	2	2	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
391	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
392	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
397	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
398	#121	—	2	4	no	—
399	#121	—	2	2	no	—
400	#121	—	2	2	no	—
401	#121	—	2	4	no	—
402	#120	—	4	4	no	—
403	#117	—	2	8	no	—
404	#117	—	2	8	no	—
405	#117	—	2	4	no	—
406	#117	—	2	4	no	—
407	#117	—	2	4	no	—
408	#117	D₄×C₁₉	1	8	yes	complemented
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	4	no	—
412	C₂×C₄⋊C₄	—	2	4	no	—
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
418	C₂×C₂²⋊C₄	—	2	8	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	—	2	2	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	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₄²	—	2	8	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	2	2	no	—
430	#107	—	2	4	no	—
431	#106	—	2	4	no	—
432	#102	—	2	4	no	—
433	#102	—	2	4	no	—
434	C₂²⋊C₈	—	2	4	no	—
435	C₂²⋊C₈	—	2	2	no	—
436	C₂²⋊C₈	—	2	2	no	—
437	C₂²⋊C₈	—	2	4	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	C₁₉	#32981	1	1	yes	characteristic, direct product factor, Sylow
442	C₂⁴	—	2	2	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	2	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	1	no	—
448	C₂⁴	—	4	1	no	—
449	C₂⁴	—	4	1	no	—
450	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂²×C₄	—	2	16	no	—
467	C₂²×C₄	—	2	16	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	4	2	no	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
498	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂²×C₄	#41×C₁₉	1	4	yes	—
501	C₂²×C₄	#41×C₁₉	1	2	yes	—
502	C₂²×C₄	#41×C₁₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
519	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
520	C₂²⋊C₄	—	2	8	no	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₂²⋊C₄	—	4	2	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₄²	—	2	8	no	—
529	C₄²	—	2	8	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	8	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	4	no	—
551	C₂³	—	4	4	no	—
552	C₂³	—	4	4	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	C₁₉×#120	1	2	yes	—
561	C₂³	C₁₉×#123	1	2	yes	—
562	C₂³	C₁₉×#123	1	2	yes	—
563	C₂³	C₁₉×#135	1	2	yes	—
564	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
565	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
566	D₄	—	4	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	8	4	no	—
569	D₄	—	8	4	no	—
570	D₄	—	8	4	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	4	8	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	C₁₉×#120	1	2	yes	—
604	C₂×C₄	C₁₉×#123	1	2	yes	—
605	C₂×C₄	C₁₉×#123	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
607	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
608	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
610	C₈	—	4	2	no	—
611	C₈	—	4	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	16	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	—	8	1	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	C₁₉×#482	1	4	yes	complemented
641	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
642	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
643	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
644	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
645	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
646	C₂²	C₁₉×#575	1	1	yes	characteristic
647	C₂²	C₁₉×#575	1	1	yes	characteristic
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	4	4	no	—
652	C₄	—	4	4	no	—
653	C₄	—	8	1	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	C₁₉×#525	1	2	yes	—
657	C₄	C₁₉×#525	1	2	yes	—
658	C₂	—	2	4	no	—
659	C₂	—	4	2	no	—
660	C₂	—	4	2	no	—
661	C₂	—	16	1	no	—
662	C₂	C₁₉×#2849	1	1	yes	characteristic
663	C₂	C₁₉×#3002	1	1	yes	characteristic
664	C₂	C₁₉×#3006	1	1	yes	characteristic
665	C₂	C₂×C₁₉×#482	1	1	yes	characteristic
666	C₂	C₁₉×#3091	1	1	yes	characteristic
667	C₂	C₁₉×#3093	1	1	yes	characteristic
668	C₂	C₁₉×#3094	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#117	C₂	semidirect
2. C₂×C₁₉×#482	C₂	semidirect
4. C₁₉×#1875	C₂	semidirect
5. C₁₉×#1874	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1854	C₂	semidirect
8. C₁₉×#1853	C₂	semidirect
9. C₁₉×#1852	C₂	semidirect
10. C₁₉×#1825	C₂	semidirect
11. C₁₉×#1779	C₂	semidirect
27. C₂×C₁₉×#107	C₂²	semidirect
28. C₂×C₁₉×#106	C₂²	semidirect
29. C₂×C₁₉×#102	C₂²	semidirect
30. C₂×C₁₉×#102	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#340	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
74. C₁₉×#117	D₄	semidirect
195. #32981	C₁₉	direct (N × H)
278. C₂²×#117	C₂×C₁₉	semidirect
279. C₂×#482	C₂×C₁₉	semidirect
281. #1875	C₂×C₁₉	semidirect
282. #1874	C₂×C₁₉	semidirect
283. #1874	C₂×C₁₉	semidirect
284. #1854	C₂×C₁₉	semidirect
285. #1853	C₂×C₁₉	semidirect
286. #1852	C₂×C₁₉	semidirect
287. #1825	C₂×C₁₉	semidirect
288. #1779	C₂×C₁₉	semidirect
317. C₂²×C₁₉	#482	semidirect
350. C₂×#107	C₂²×C₁₉	semidirect
351. C₂×#106	C₂²×C₁₉	semidirect
352. C₂×#102	C₂²×C₁₉	semidirect
353. C₂×#102	C₂²×C₁₉	semidirect
364. #340	C₂²×C₁₉	semidirect
365. #340	C₂²×C₁₉	semidirect
366. #340	C₂²×C₁₉	semidirect
367. #340	C₂²×C₁₉	semidirect
408. #117	D₄×C₁₉	semidirect
441. C₁₉	#32981	direct (N × H)
640. C₂²	C₁₉×#482	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#117	2
C₂×C₁₉×#482	2
C₁₉×#2847	2
C₁₉×#1875	2
C₁₉×#1874	2
C₁₉×#1854	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1825	2
C₁₉×#1779	2
#32981	19

Subgroups — C19×#32981 #18038940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32981 #18038940