Subgroups — C₁₉×#22818 #18028777

Order 4864.

762 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2356	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1971	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1927	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1927	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1847	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1771	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#441	C₄	1	8	yes	complemented
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#391	C₂²	1	1	yes	characteristic
36	C₁₉×#391	C₂²	1	1	yes	characteristic
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#387	—	2	1	no	—
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#384	C₂²	1	1	yes	characteristic
44	C₁₉×#383	—	2	1	no	—
45	C₁₉×#382	—	2	1	no	—
46	C₁₉×#382	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₁₉×#376	—	2	1	no	—
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×Q₁₆×C₁₉	—	2	2	no	—
64	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
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	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#107	—	2	2	no	—
95	C₁₉×#107	—	4	1	no	—
96	C₁₉×#106	—	2	2	no	—
97	C₁₉×#106	—	4	1	no	—
98	C₁₉×#106	C₂×C₄	1	4	yes	—
99	C₁₉×C₄⋊C₈	—	2	2	no	—
100	C₁₉×#103	—	4	1	no	—
101	C₁₉×#103	—	4	1	no	—
102	C₁₉×#103	—	4	1	no	—
103	C₁₉×#103	—	4	1	no	—
104	C₁₉×#103	C₂×C₄	1	4	yes	—
105	C₁₉×#103	C₂×C₄	1	4	yes	—
106	C₁₉×#97	—	2	2	no	—
107	C₁₉×#97	C₂×C₄	1	4	yes	—
108	C₄×C₈×C₁₉	—	2	2	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	D₄	1	1	yes	characteristic
124	C₁₉×#95	D₄	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
136	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
152	Q₁₆×C₁₉	—	2	8	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₁₉	#41	1	2	yes	—
164	C₂×C₈×C₁₉	#41	1	2	yes	—
165	C₄⋊C₄×C₁₉	—	2	4	no	—
166	C₄⋊C₄×C₁₉	—	2	4	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	2	no	—
180	C₄⋊C₄×C₁₉	—	8	1	no	—
181	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
182	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
183	C₄²×C₁₉	—	2	4	no	—
184	C₄²×C₁₉	—	2	4	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	4	2	no	—
190	C₄²×C₁₉	—	4	2	no	—
191	C₄²×C₁₉	—	8	1	no	—
192	C₄²×C₁₉	—	8	1	no	—
193	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
194	C₄²×C₁₉	#41	1	2	yes	—
195	#22818	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₉	—	2	2	no	—
198	Q₈×C₁₉	—	2	2	no	—
199	Q₈×C₁₉	—	2	2	no	—
200	Q₈×C₁₉	—	2	2	no	—
201	Q₈×C₁₉	—	4	1	no	—
202	Q₈×C₁₉	—	4	1	no	—
203	Q₈×C₁₉	—	4	1	no	—
204	Q₈×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₁₉	#137	1	2	yes	—
247	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
253	C₈×C₁₉	—	2	2	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	C₈×C₁₉	#117	1	4	yes	—
257	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
258	#2356	C₂×C₁₉	1	1	yes	characteristic
259	#2355	C₂×C₁₉	1	1	yes	characteristic
260	#1971	C₂×C₁₉	1	1	yes	characteristic
261	#1969	C₂×C₁₉	1	1	yes	characteristic
262	#1928	C₂×C₁₉	1	1	yes	characteristic
263	#1928	C₂×C₁₉	1	1	yes	characteristic
264	#1927	C₂×C₁₉	1	1	yes	characteristic
265	#1927	C₂×C₁₉	1	1	yes	characteristic
266	#1847	C₂×C₁₉	1	1	yes	characteristic
267	#1805	C₂×C₁₉	1	1	yes	characteristic
268	#1803	C₂×C₁₉	1	1	yes	characteristic
269	#1776	C₂×C₁₉	1	1	yes	characteristic
270	C₄×#106	C₂×C₁₉	1	1	yes	characteristic
271	#1771	C₂×C₁₉	1	1	yes	characteristic
272	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₁₉	#547	1	1	yes	characteristic
274	C₂²×C₁₉	#550	1	1	yes	characteristic
275	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
276	C₂²×C₁₉	#575	1	1	yes	characteristic
277	C₂²×C₁₉	#577	1	1	yes	characteristic
278	C₂²×C₁₉	#578	1	1	yes	characteristic
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	—	8	1	no	—
291	C₄×C₁₉	—	8	1	no	—
292	C₄×C₁₉	—	8	1	no	—
293	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
294	C₄×C₁₉	#520	1	1	yes	characteristic
295	C₄×C₁₉	#555	1	1	yes	characteristic
296	C₄×C₁₉	#556	1	1	yes	characteristic
297	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
300	#441	C₄×C₁₉	1	8	yes	complemented
301	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
316	#391	C₂²×C₁₉	1	1	yes	characteristic
317	#391	C₂²×C₁₉	1	1	yes	characteristic
318	#391	C₂²×C₁₉	1	1	yes	characteristic
319	#391	C₂²×C₁₉	1	1	yes	characteristic
320	#387	—	2	1	no	—
321	#387	—	2	1	no	—
322	#387	—	2	1	no	—
323	#387	—	2	1	no	—
324	#384	C₂²×C₁₉	1	1	yes	characteristic
325	#383	—	2	1	no	—
326	#382	—	2	1	no	—
327	#382	C₂²×C₁₉	1	1	yes	characteristic
328	C₄×C₄⋊C₄	—	2	1	no	—
329	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
333	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
334	#376	—	2	1	no	—
335	#340	C₂²×C₁₉	1	1	yes	characteristic
336	#340	C₂²×C₁₉	1	1	yes	characteristic
337	#340	C₂²×C₁₉	1	1	yes	characteristic
338	#340	C₂²×C₁₉	1	1	yes	characteristic
339	#336	C₂²×C₁₉	1	1	yes	characteristic
340	#336	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₁₉	#2354	1	1	yes	characteristic
342	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
343	C₂×C₁₉	#2947	1	1	yes	characteristic
344	C₂×C₁₉	#3344	1	1	yes	characteristic
345	C₂×C₁₉	#3349	1	1	yes	characteristic
346	C₂×C₁₉	#3398	1	1	yes	characteristic
347	C₂×C₁₉	#3401	1	1	yes	characteristic
348	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×Q₁₆	—	2	2	no	—
351	C₂×Q₁₆	—	2	2	no	—
352	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
353	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
360	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
382	#107	—	2	2	no	—
383	#107	—	4	1	no	—
384	#106	—	2	2	no	—
385	#106	—	4	1	no	—
386	#106	C₂×C₄×C₁₉	1	4	yes	—
387	C₄⋊C₈	—	2	2	no	—
388	#103	—	4	1	no	—
389	#103	—	4	1	no	—
390	#103	—	4	1	no	—
391	#103	—	4	1	no	—
392	#103	C₂×C₄×C₁₉	1	4	yes	—
393	#103	C₂×C₄×C₁₉	1	4	yes	—
394	#97	—	2	2	no	—
395	#97	C₂×C₄×C₁₉	1	4	yes	—
396	C₄×C₈	—	2	2	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	D₄×C₁₉	1	1	yes	characteristic
412	#95	D₄×C₁₉	1	1	yes	characteristic
413	C₁₉	#22818	1	1	yes	characteristic, direct product factor, Sylow
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
425	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
441	Q₁₆	—	2	8	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
451	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
452	C₂×C₈	#41×C₁₉	1	2	yes	—
453	C₂×C₈	#41×C₁₉	1	2	yes	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	8	1	no	—
470	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
471	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	2	no	—
479	C₄²	—	4	2	no	—
480	C₄²	—	8	1	no	—
481	C₄²	—	8	1	no	—
482	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
483	C₄²	#41×C₁₉	1	2	yes	—
484	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	2	2	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
533	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
534	C₂×C₄	C₁₉×#137	1	2	yes	—
535	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
536	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
537	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
539	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	C₁₉×#117	1	4	yes	—
545	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
546	C₂²	C₁₉×#547	1	1	yes	characteristic
547	C₂²	C₁₉×#550	1	1	yes	characteristic
548	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
549	C₂²	C₁₉×#575	1	1	yes	characteristic
550	C₂²	C₁₉×#577	1	1	yes	characteristic
551	C₂²	C₁₉×#578	1	1	yes	characteristic
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
567	C₄	C₁₉×#520	1	1	yes	characteristic
568	C₄	C₁₉×#555	1	1	yes	characteristic
569	C₄	C₁₉×#556	1	1	yes	characteristic
570	C₂	C₁₉×#2354	1	1	yes	characteristic
571	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
572	C₂	C₁₉×#2947	1	1	yes	characteristic
573	C₂	C₁₉×#3344	1	1	yes	characteristic
574	C₂	C₁₉×#3349	1	1	yes	characteristic
575	C₂	C₁₉×#3398	1	1	yes	characteristic
576	C₂	C₁₉×#3401	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
19. C₁₉×#441	C₄	semidirect
195. #22818	C₁₉	direct (N × H)
300. #441	C₄×C₁₉	semidirect
413. C₁₉	#22818	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#441	2
C₁₉×#2356	2
C₁₉×#2355	2
C₁₉×#1971	2
C₁₉×#1969	2
C₁₉×#1928	2
C₁₉×#1927	2
C₁₉×#1847	2
C₁₉×#1805	2
C₁₉×#1803	2
C₁₉×#1776	2
C₄×C₁₉×#106	2
C₁₉×#1771	2
#22818	19

Subgroups — C19×#22818 #18028777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22818 #18028777