Subgroups — C₁₉×#8571 #18014530

Order 4864.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#327	C₂	1	2	yes	maximal
4	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1294	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₉	—	2	1	no	—
8	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
9	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₁₉×#390	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#388	—	2	1	no	—
16	C₁₉×#386	—	2	1	no	—
17	C₁₉×#380	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
19	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₂×C₁₉×#95	—	2	1	no	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#327	—	2	4	no	—
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	—	2	2	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₁₉×#121	—	2	1	no	—
33	C₁₉×#121	—	2	1	no	—
34	C₁₉×#121	D₄	1	2	yes	—
35	C₁₉×#121	Q₈	1	2	yes	—
36	C₄×D₄×C₁₉	—	4	2	no	—
37	C₄×D₄×C₁₉	—	4	2	no	—
38	C₄×D₄×C₁₉	—	4	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	4	2	no	—
53	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊C₈	—	4	2	no	—
58	C₁₉×C₂²⋊C₈	—	2	2	no	—
59	C₁₉×C₂²⋊C₈	—	2	2	no	—
60	C₁₉×#95	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	C₁₉×#95	—	2	2	no	—
64	C₁₉×#95	—	2	2	no	—
65	C₁₉×#95	—	4	2	no	—
66	C₂⁴×C₁₉	—	2	1	no	—
67	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	4	1	no	—
72	C₂×D₄×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	D₈	1	2	yes	—
104	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂×C₈×C₁₉	—	4	2	no	—
112	C₂×C₈×C₁₉	—	4	2	no	—
113	C₂×C₈×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	8	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
120	C₂²⋊C₄×C₁₉	—	2	2	no	—
121	C₂²⋊C₄×C₁₉	—	2	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	2	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	4	1	no	—
130	C₄²×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	—	4	2	no	—
132	#8571	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₁₉	#121	1	1	yes	characteristic
146	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
148	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂³×C₁₉	#137	1	1	yes	characteristic
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	—	8	2	no	—
193	C₂×C₄×C₁₉	—	8	4	no	—
194	C₂×C₄×C₁₉	#99	1	2	yes	—
195	C₂×C₄×C₁₉	#102	1	2	yes	—
196	C₂×C₄×C₁₉	#102	1	2	yes	—
197	C₂×C₄×C₁₉	#104	1	2	yes	—
198	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
202	C₈×C₁₉	—	8	2	no	—
203	C₄×#121	C₂×C₁₉	1	1	yes	characteristic
204	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
205	C₂×#327	C₂×C₁₉	1	2	yes	—
206	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#1294	C₂×C₁₉	1	2	yes	complemented
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	8	1	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	#380	1	1	yes	characteristic
228	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
229	C₂²×C₁₉	#410	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
231	C₂²×C₁₉	#417	1	1	yes	characteristic
232	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
233	C₂²×C₁₉	#421	1	1	yes	characteristic
234	C₂²×C₁₉	#459	1	1	yes	characteristic
235	C₂²×C₁₉	#461	1	1	yes	characteristic
236	C₂²×C₁₉	#474	1	1	yes	characteristic
237	C₂²×C₁₉	#476	1	1	yes	characteristic
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	4	1	no	—
245	C₄×C₁₉	—	4	1	no	—
246	C₄×C₁₉	—	8	4	no	—
247	C₄×C₁₉	—	8	1	no	—
248	C₄×C₁₉	—	8	1	no	—
249	C₄×C₁₉	#327	1	4	yes	complemented
250	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₄×D₄	—	2	1	no	—
252	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
253	C₂²×C₄⋊C₄	—	2	1	no	—
254	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₈	—	2	1	no	—
256	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
257	#390	C₄×C₁₉	1	1	yes	characteristic, complemented
258	#389	C₄×C₁₉	1	1	yes	characteristic, complemented
259	#388	—	2	1	no	—
260	#386	—	2	1	no	—
261	#380	C₂²×C₁₉	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
263	C₄×C₂²⋊C₄	—	2	1	no	—
264	C₂×#95	—	2	1	no	—
265	C₂×#95	C₂²×C₁₉	1	2	yes	—
266	#336	—	2	1	no	—
267	#327	—	2	4	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	—	8	2	no	—
273	C₂×C₁₉	C₂×#327	1	1	yes	characteristic
274	C₂×C₁₉	#1509	1	1	yes	characteristic
275	C₂×C₁₉	#1513	1	1	yes	characteristic
276	C₂×C₁₉	#1517	1	1	yes	characteristic
277	C₂×C₁₉	#1799	1	1	yes	characteristic
278	C₂×C₁₉	#1802	1	1	yes	characteristic
279	C₂×C₁₉	#1806	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	—	2	2	no	—
288	#121	—	2	1	no	—
289	#121	—	2	1	no	—
290	#121	D₄×C₁₉	1	2	yes	—
291	#121	Q₈×C₁₉	1	2	yes	—
292	C₄×D₄	—	4	2	no	—
293	C₄×D₄	—	4	2	no	—
294	C₄×D₄	—	4	2	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	4	2	no	—
298	C₂×C₄⋊C₄	—	4	2	no	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	4	2	no	—
309	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
311	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
313	C₄⋊C₈	—	4	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	4	2	no	—
322	C₁₉	#8571	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	—	2	1	no	—
324	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	D₈×C₁₉	1	2	yes	—
361	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	8	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	2	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
401	C₂³	C₁₉×#121	1	1	yes	characteristic
402	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
403	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
404	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
405	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
406	C₂³	C₁₉×#137	1	1	yes	characteristic
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	C₁₉×#99	1	2	yes	—
451	C₂×C₄	C₁₉×#102	1	2	yes	—
452	C₂×C₄	C₁₉×#102	1	2	yes	—
453	C₂×C₄	C₁₉×#104	1	2	yes	—
454	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
456	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
457	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
458	C₈	—	8	2	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	C₁₉×#380	1	1	yes	characteristic
479	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
480	C₂²	C₁₉×#410	1	1	yes	characteristic
481	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
482	C₂²	C₁₉×#417	1	1	yes	characteristic
483	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
484	C₂²	C₁₉×#421	1	1	yes	characteristic
485	C₂²	C₁₉×#459	1	1	yes	characteristic
486	C₂²	C₁₉×#461	1	1	yes	characteristic
487	C₂²	C₁₉×#474	1	1	yes	characteristic
488	C₂²	C₁₉×#476	1	1	yes	characteristic
489	C₄	—	2	2	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	2	no	—
497	C₄	—	8	4	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	1	no	—
500	C₄	C₁₉×#327	1	4	yes	complemented
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×C₁₉×#327	1	1	yes	characteristic
507	C₂	C₁₉×#1509	1	1	yes	characteristic
508	C₂	C₁₉×#1513	1	1	yes	characteristic
509	C₂	C₁₉×#1517	1	1	yes	characteristic
510	C₂	C₁₉×#1799	1	1	yes	characteristic
511	C₂	C₁₉×#1802	1	1	yes	characteristic
512	C₂	C₁₉×#1806	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1797	C₂	semidirect
4. C₁₉×C₄⋊#95	C₂	semidirect
5. C₁₉×#1294	C₂	semidirect
8. C₂×C₄×D₄×C₁₉	C₄	semidirect
13. C₁₉×#390	C₄	semidirect
14. C₁₉×#389	C₄	semidirect
18. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
77. C₂×D₄×C₁₉	C₄⋊C₄	semidirect
119. C₄⋊C₄×C₁₉	C₄⋊C₄	semidirect
132. #8571	C₁₉	direct (N × H)
204. #1797	C₂×C₁₉	semidirect
206. C₄⋊#95	C₂×C₁₉	semidirect
207. #1294	C₂×C₁₉	semidirect
249. C₄×C₁₉	#327	semidirect
252. C₂×C₄×D₄	C₄×C₁₉	semidirect
257. #390	C₄×C₁₉	semidirect
258. #389	C₄×C₁₉	semidirect
262. C₄×C₄⋊C₄	C₄×C₁₉	semidirect
322. C₁₉	#8571	direct (N × H)
334. C₂×D₄	C₄⋊C₄×C₁₉	semidirect
376. C₄⋊C₄	C₄⋊C₄×C₁₉	semidirect
500. C₄	C₁₉×#327	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×#121	2
C₁₉×#1797	2
C₂×C₁₉×#327	2
C₁₉×C₄⋊#95	2
C₁₉×#1294	2
#8571	19

Subgroups — C19×#8571 #18014530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8571 #18014530