Subgroups — C₁₉×#23586 #18029545

Order 4864.

1058 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2323	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2035	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2001	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2001	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#541	—	2	4	no	—
19	C₁₉×#541	—	2	4	no	—
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#126	—	2	1	no	—
22	C₂×C₁₉×#126	—	2	1	no	—
23	C₂×C₁₉×#125	—	2	1	no	—
24	C₂×C₁₉×#125	—	2	1	no	—
25	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
33	C₁₉×#441	—	2	4	no	—
34	C₄×Q₁₆×C₁₉	—	2	4	no	—
35	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#391	C₂²	1	1	yes	characteristic
50	C₁₉×#389	—	2	1	no	—
51	C₁₉×#389	C₂²	1	1	yes	characteristic
52	C₁₉×#388	—	2	1	no	—
53	C₁₉×#388	—	2	1	no	—
54	C₁₉×#387	—	2	1	no	—
55	C₁₉×#380	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#336	C₂²	1	1	yes	characteristic
62	C₁₉×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×Q₁₆×C₁₉	—	2	2	no	—
68	C₂×Q₁₆×C₁₉	—	2	2	no	—
69	C₂×Q₁₆×C₁₉	—	2	2	no	—
70	C₂×Q₁₆×C₁₉	—	2	2	no	—
71	C₂×Q₁₆×C₁₉	—	2	2	no	—
72	C₂×Q₁₆×C₁₉	—	2	2	no	—
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	—	2	2	no	—
78	C₁₉×C₄⋊Q₈	—	2	2	no	—
79	C₁₉×#126	—	2	8	no	—
80	C₁₉×#126	—	2	8	no	—
81	C₁₉×#125	—	2	8	no	—
82	C₁₉×#125	—	2	8	no	—
83	C₁₉×#125	—	2	2	no	—
84	C₁₉×#125	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	2	2	no	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×Q₈×C₁₉	—	2	2	no	—
94	C₄×Q₈×C₁₉	—	2	2	no	—
95	C₄×Q₈×C₁₉	D₄	1	4	yes	—
96	C₄×Q₈×C₁₉	D₄	1	4	yes	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₁₉	—	2	1	no	—
124	C₂×C₄²×C₁₉	—	2	1	no	—
125	C₂×C₄²×C₁₉	—	2	1	no	—
126	C₂×C₄²×C₁₉	—	2	1	no	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
129	C₁₉×#107	—	2	2	no	—
130	C₁₉×#106	—	2	2	no	—
131	C₁₉×#103	—	2	2	no	—
132	C₁₉×#103	—	2	2	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×C₂²⋊C₈	—	2	2	no	—
140	C₁₉×C₂²⋊C₈	—	2	2	no	—
141	C₁₉×#97	—	2	2	no	—
142	C₄×C₈×C₁₉	—	2	2	no	—
143	C₁₉×#95	—	2	1	no	—
144	C₁₉×#95	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	—	2	1	no	—
147	C₁₉×#95	—	2	1	no	—
148	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	—	2	1	no	—
160	C₂×Q₈×C₁₉	—	2	1	no	—
161	C₂×Q₈×C₁₉	—	2	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
166	C₂×Q₈×C₁₉	#41	1	2	yes	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
187	Q₁₆×C₁₉	—	2	8	no	—
188	Q₁₆×C₁₉	—	2	8	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	#41	1	2	yes	—
200	C₂×C₈×C₁₉	#41	1	2	yes	—
201	C₄⋊C₄×C₁₉	—	2	4	no	—
202	C₄⋊C₄×C₁₉	—	2	4	no	—
203	C₄⋊C₄×C₁₉	—	2	4	no	—
204	C₄⋊C₄×C₁₉	—	2	4	no	—
205	C₄⋊C₄×C₁₉	—	2	4	no	—
206	C₄⋊C₄×C₁₉	—	2	4	no	—
207	C₄⋊C₄×C₁₉	—	2	4	no	—
208	C₄⋊C₄×C₁₉	—	2	4	no	—
209	C₄⋊C₄×C₁₉	—	2	4	no	—
210	C₄⋊C₄×C₁₉	—	2	2	no	—
211	C₄⋊C₄×C₁₉	—	2	2	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	4	2	no	—
220	C₄⋊C₄×C₁₉	—	8	1	no	—
221	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
222	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
223	C₄⋊C₄×C₁₉	#41	1	2	yes	—
224	C₂²⋊C₄×C₁₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₉	—	2	4	no	—
226	C₂²⋊C₄×C₁₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	8	1	no	—
230	C₄²×C₁₉	—	2	4	no	—
231	C₄²×C₁₉	—	2	4	no	—
232	C₄²×C₁₉	—	2	1	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	—	4	2	no	—
235	C₄²×C₁₉	—	8	1	no	—
236	C₄²×C₁₉	C₂×D₄	1	2	yes	—
237	C₄²×C₁₉	C₂×D₄	1	2	yes	—
238	#23586	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	1	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₁₉	—	2	2	no	—
248	Q₈×C₁₉	—	2	2	no	—
249	Q₈×C₁₉	—	2	2	no	—
250	Q₈×C₁₉	—	2	2	no	—
251	Q₈×C₁₉	—	2	2	no	—
252	Q₈×C₁₉	—	2	2	no	—
253	Q₈×C₁₉	—	4	1	no	—
254	Q₈×C₁₉	—	4	1	no	—
255	Q₈×C₁₉	—	4	1	no	—
256	Q₈×C₁₉	—	4	1	no	—
257	Q₈×C₁₉	—	4	1	no	—
258	Q₈×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	#120	1	2	yes	—
301	C₂×C₄×C₁₉	#120	1	2	yes	—
302	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
308	C₈×C₁₉	—	2	2	no	—
309	C₈×C₁₉	—	2	2	no	—
310	C₈×C₁₉	—	4	1	no	—
311	C₈×C₁₉	—	4	1	no	—
312	C₂×#541	C₂×C₁₉	1	1	yes	characteristic
313	C₂×#441	C₂×C₁₉	1	1	yes	characteristic, complemented
314	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#2323	C₂×C₁₉	1	1	yes	characteristic
316	#2059	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#2043	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#2036	C₂×C₁₉	1	1	yes	characteristic
319	#2035	C₂×C₁₉	1	1	yes	characteristic
320	#2026	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#2016	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#2001	C₂×C₁₉	1	1	yes	characteristic
323	#2001	C₂×C₁₉	1	1	yes	characteristic
324	#1763	C₂×C₁₉	1	1	yes	characteristic, complemented
325	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#1750	C₂×C₁₉	1	1	yes	characteristic
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	1	no	—
333	C₂²×C₁₉	—	4	1	no	—
334	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
335	C₂²×C₁₉	#525	1	1	yes	characteristic
336	C₂²×C₁₉	#532	1	1	yes	characteristic
337	C₂²×C₁₉	#577	1	1	yes	characteristic
338	C₂²×C₁₉	#578	1	1	yes	characteristic
339	C₂²×C₁₉	#578	1	1	yes	characteristic
340	C₂²×C₁₉	#578	1	1	yes	characteristic
341	C₄×C₁₉	—	2	2	no	—
342	C₄×C₁₉	—	2	2	no	—
343	C₄×C₁₉	—	4	2	no	—
344	C₄×C₁₉	—	4	1	no	—
345	C₄×C₁₉	—	4	2	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	—	4	2	no	—
348	C₄×C₁₉	—	4	1	no	—
349	C₄×C₁₉	—	4	2	no	—
350	C₄×C₁₉	—	4	1	no	—
351	C₄×C₁₉	—	4	2	no	—
352	C₄×C₁₉	—	8	1	no	—
353	C₄×C₁₉	—	8	1	no	—
354	C₄×C₁₉	#525	1	1	yes	characteristic
355	C₄×C₁₉	#525	1	1	yes	characteristic
356	C₄×C₁₉	#532	1	1	yes	characteristic
357	C₄×C₁₉	#532	1	1	yes	characteristic
358	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
359	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
360	#541	—	2	4	no	—
361	#541	—	2	4	no	—
362	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#126	—	2	1	no	—
364	C₂×#126	—	2	1	no	—
365	C₂×#125	—	2	1	no	—
366	C₂×#125	—	2	1	no	—
367	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
375	#441	—	2	4	no	—
376	C₄×Q₁₆	—	2	4	no	—
377	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
391	#391	C₂²×C₁₉	1	1	yes	characteristic
392	#389	—	2	1	no	—
393	#389	C₂²×C₁₉	1	1	yes	characteristic
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#387	—	2	1	no	—
397	#380	C₂²×C₁₉	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
399	#340	C₂²×C₁₉	1	1	yes	characteristic
400	#340	C₂²×C₁₉	1	1	yes	characteristic
401	#340	C₂²×C₁₉	1	1	yes	characteristic
402	#340	C₂²×C₁₉	1	1	yes	characteristic
403	#336	C₂²×C₁₉	1	1	yes	characteristic
404	#336	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×C₁₉	—	8	1	no	—
406	C₂×C₁₉	#2388	1	1	yes	characteristic
407	C₂×C₁₉	#3011	1	1	yes	characteristic
408	C₂×C₁₉	#3013	1	1	yes	characteristic
409	C₂×C₁₉	#3120	1	1	yes	characteristic
410	C₂×C₁₉	#3127	1	1	yes	characteristic
411	C₂×C₁₉	#3177	1	1	yes	characteristic
412	C₂×C₁₉	#3178	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×Q₁₆	—	2	2	no	—
418	C₂×Q₁₆	—	2	2	no	—
419	C₂×Q₁₆	—	2	2	no	—
420	C₂×Q₁₆	—	2	2	no	—
421	C₂×Q₁₆	—	2	2	no	—
422	C₂×Q₁₆	—	2	2	no	—
423	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₄⋊Q₈	—	2	2	no	—
428	C₄⋊Q₈	—	2	2	no	—
429	#126	—	2	8	no	—
430	#126	—	2	8	no	—
431	#125	—	2	8	no	—
432	#125	—	2	8	no	—
433	#125	—	2	2	no	—
434	#125	—	2	2	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	—	2	2	no	—
438	C₂²⋊Q₈	—	2	2	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×Q₈	—	2	2	no	—
443	C₄×Q₈	—	2	2	no	—
444	C₄×Q₈	—	2	2	no	—
445	C₄×Q₈	D₄×C₁₉	1	4	yes	—
446	C₄×Q₈	D₄×C₁₉	1	4	yes	—
447	#117	—	2	2	no	—
448	#117	—	2	2	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	2	1	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄²	—	2	1	no	—
474	C₂×C₄²	—	2	1	no	—
475	C₂×C₄²	—	2	1	no	—
476	C₂×C₄²	—	2	1	no	—
477	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
479	#107	—	2	2	no	—
480	#106	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	2	2	no	—
483	#103	—	2	2	no	—
484	#103	—	2	2	no	—
485	#103	—	2	2	no	—
486	#103	—	2	2	no	—
487	#103	—	2	2	no	—
488	#103	—	2	2	no	—
489	C₂²⋊C₈	—	2	2	no	—
490	C₂²⋊C₈	—	2	2	no	—
491	#97	—	2	2	no	—
492	C₄×C₈	—	2	2	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	C₁₉	#23586	1	1	yes	characteristic, direct product factor, Sylow
499	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
516	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
517	C₂×Q₈	#41×C₁₉	1	2	yes	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
538	Q₁₆	—	2	8	no	—
539	Q₁₆	—	2	8	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	#41×C₁₉	1	2	yes	—
551	C₂×C₈	#41×C₁₉	1	2	yes	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	—	8	1	no	—
572	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
573	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
574	C₄⋊C₄	#41×C₁₉	1	2	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	8	1	no	—
581	C₄²	—	2	4	no	—
582	C₄²	—	2	4	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	4	2	no	—
586	C₄²	—	8	1	no	—
587	C₄²	C₂×D₄×C₁₉	1	2	yes	—
588	C₄²	C₂×D₄×C₁₉	1	2	yes	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	2	2	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	Q₈	—	4	1	no	—
609	C₂×C₄	—	2	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	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	4	1	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	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	C₁₉×#120	1	2	yes	—
651	C₂×C₄	C₁₉×#120	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
653	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
654	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
655	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
656	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
657	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
658	C₈	—	2	2	no	—
659	C₈	—	2	2	no	—
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
670	C₂²	C₁₉×#525	1	1	yes	characteristic
671	C₂²	C₁₉×#532	1	1	yes	characteristic
672	C₂²	C₁₉×#577	1	1	yes	characteristic
673	C₂²	C₁₉×#578	1	1	yes	characteristic
674	C₂²	C₁₉×#578	1	1	yes	characteristic
675	C₂²	C₁₉×#578	1	1	yes	characteristic
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	C₁₉×#525	1	1	yes	characteristic
690	C₄	C₁₉×#525	1	1	yes	characteristic
691	C₄	C₁₉×#532	1	1	yes	characteristic
692	C₄	C₁₉×#532	1	1	yes	characteristic
693	C₂	—	8	1	no	—
694	C₂	C₁₉×#2388	1	1	yes	characteristic
695	C₂	C₁₉×#3011	1	1	yes	characteristic
696	C₂	C₁₉×#3013	1	1	yes	characteristic
697	C₂	C₁₉×#3120	1	1	yes	characteristic
698	C₂	C₁₉×#3127	1	1	yes	characteristic
699	C₂	C₁₉×#3177	1	1	yes	characteristic
700	C₂	C₁₉×#3178	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#441	C₂	semidirect
3. C₂×C₄×Q₁₆×C₁₉	C₂	semidirect
5. C₁₉×#2059	C₂	semidirect
6. C₁₉×#2043	C₂	semidirect
9. C₁₉×#2026	C₂	semidirect
10. C₁₉×#2016	C₂	semidirect
13. C₁₉×#1763	C₂	semidirect
14. C₄×C₁₉×#103	C₂	semidirect
238. #23586	C₁₉	direct (N × H)
313. C₂×#441	C₂×C₁₉	semidirect
314. C₂×C₄×Q₁₆	C₂×C₁₉	semidirect
316. #2059	C₂×C₁₉	semidirect
317. #2043	C₂×C₁₉	semidirect
320. #2026	C₂×C₁₉	semidirect
321. #2016	C₂×C₁₉	semidirect
324. #1763	C₂×C₁₉	semidirect
325. C₄×#103	C₂×C₁₉	semidirect
498. C₁₉	#23586	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×#541	2
C₂×C₁₉×#441	2
C₂×C₄×Q₁₆×C₁₉	2
C₁₉×#2323	2
C₁₉×#2059	2
C₁₉×#2043	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2026	2
C₁₉×#2016	2
C₁₉×#2001	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
C₁₉×#1750	2
#23586	19

Subgroups — C19×#23586 #18029545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23586 #18029545