Subgroups — C₁₉×#23139 #18029098

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#470	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2362	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2360	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1753	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#470	C₄	1	8	yes	complemented
25	C₂×C₁₉×#106	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×C₂²⋊C₈	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×#389	—	2	1	no	—
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#387	—	2	1	no	—
44	C₁₉×#385	—	2	1	no	—
45	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
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	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	—	4	1	no	—
65	C₂×Q₁₆×C₁₉	—	4	1	no	—
66	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
67	C₂×M₁₆×C₁₉	—	4	1	no	—
68	C₂×M₁₆×C₁₉	—	4	1	no	—
69	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
77	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	4	1	no	—
81	C₄×Q₈×C₁₉	—	4	1	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₁₉×#117	—	4	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
111	C₁₉×#106	C₂×C₄	1	4	yes	complemented
112	C₁₉×#103	—	2	2	no	—
113	C₁₉×#103	—	2	2	no	—
114	C₁₉×#103	—	4	1	no	—
115	C₁₉×#103	—	4	1	no	—
116	C₁₉×#103	C₂×C₄	1	4	yes	complemented
117	C₁₉×#103	C₂×C₄	1	4	yes	complemented
118	C₁₉×C₂²⋊C₈	—	2	2	no	—
119	C₁₉×#97	—	4	1	no	—
120	C₄×C₈×C₁₉	—	4	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	D₄	1	1	yes	characteristic
130	C₁₉×#95	D₄	1	1	yes	characteristic
131	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	4	2	no	—
157	C₂²×C₄×C₁₉	—	4	2	no	—
158	C₂²×C₄×C₁₉	—	8	1	no	—
159	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
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	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	#41	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₁₉	—	4	4	no	—
168	M₁₆×C₁₉	—	4	4	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
180	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
181	C₄⋊C₄×C₁₉	—	2	4	no	—
182	C₄⋊C₄×C₁₉	—	2	4	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	4	2	no	—
192	C₄⋊C₄×C₁₉	—	4	2	no	—
193	C₄⋊C₄×C₁₉	—	4	2	no	—
194	C₄⋊C₄×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	8	1	no	—
196	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	#41	1	2	yes	—
199	C₄⋊C₄×C₁₉	#41	1	2	yes	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	2	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	4	2	no	—
210	C₄²×C₁₉	—	4	2	no	—
211	C₄²×C₁₉	—	4	2	no	—
212	C₄²×C₁₉	—	4	2	no	—
213	C₄²×C₁₉	—	8	1	no	—
214	#23139	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	C₄×D₄	1	2	yes	—
222	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₁₉	—	2	2	no	—
224	Q₈×C₁₉	—	2	2	no	—
225	Q₈×C₁₉	—	2	2	no	—
226	Q₈×C₁₉	—	2	2	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	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	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	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	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	8	4	no	—
273	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
274	C₂×C₄×C₁₉	#137	1	2	yes	—
275	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
281	C₈×C₁₉	—	2	2	no	—
282	C₈×C₁₉	—	2	2	no	—
283	C₈×C₁₉	—	4	1	no	—
284	C₈×C₁₉	—	4	1	no	—
285	C₂×#470	C₂×C₁₉	1	1	yes	characteristic
286	#2362	C₂×C₁₉	1	1	yes	characteristic
287	#2360	C₂×C₁₉	1	1	yes	characteristic
288	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1919	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1919	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1878	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1878	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1873	C₂×C₁₉	1	1	yes	characteristic
295	#1872	C₂×C₁₉	1	1	yes	characteristic
296	#1763	C₂×C₁₉	1	1	yes	characteristic, complemented
297	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1753	C₂×C₁₉	1	1	yes	characteristic
299	#1736	C₂×C₁₉	1	1	yes	characteristic
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	2	2	no	—
302	C₂²×C₁₉	—	2	2	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	C₂×C₄×D₄	1	1	yes	characteristic
308	C₂²×C₁₉	#546	1	1	yes	characteristic
309	C₂²×C₁₉	#546	1	1	yes	characteristic
310	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
311	C₂²×C₁₉	#575	1	1	yes	characteristic
312	C₂²×C₁₉	#577	1	1	yes	characteristic
313	C₂²×C₁₉	#578	1	1	yes	characteristic
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	2	no	—
320	C₄×C₁₉	—	4	2	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	4	1	no	—
324	C₄×C₁₉	—	4	2	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	—	8	1	no	—
327	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
328	C₄×C₁₉	#518	1	1	yes	characteristic
329	C₄×C₁₉	#553	1	1	yes	characteristic
330	C₄×C₁₉	#553	1	1	yes	characteristic
331	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
332	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
339	#470	C₄×C₁₉	1	8	yes	complemented
340	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
350	#391	C₂²×C₁₉	1	1	yes	characteristic
351	#391	C₂²×C₁₉	1	1	yes	characteristic
352	#389	—	2	1	no	—
353	#389	C₂²×C₁₉	1	1	yes	characteristic
354	#389	C₂²×C₁₉	1	1	yes	characteristic
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#385	—	2	1	no	—
360	C₄×C₄⋊C₄	—	2	1	no	—
361	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
362	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
363	C₄×C₂²⋊C₄	—	2	1	no	—
364	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
365	#340	C₂²×C₁₉	1	1	yes	characteristic
366	#340	C₂²×C₁₉	1	1	yes	characteristic
367	#340	C₂²×C₁₉	1	1	yes	characteristic
368	#340	C₂²×C₁₉	1	1	yes	characteristic
369	#340	C₂²×C₁₉	1	1	yes	characteristic
370	#340	C₂²×C₁₉	1	1	yes	characteristic
371	#340	C₂²×C₁₉	1	1	yes	characteristic
372	#340	C₂²×C₁₉	1	1	yes	characteristic
373	#336	C₂²×C₁₉	1	1	yes	characteristic
374	#336	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×C₁₉	—	4	2	no	—
376	C₂×C₁₉	#2364	1	1	yes	characteristic
377	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
378	C₂×C₁₉	#2947	1	1	yes	characteristic
379	C₂×C₁₉	#3315	1	1	yes	characteristic
380	C₂×C₁₉	#3316	1	1	yes	characteristic
381	C₂×C₁₉	#3323	1	1	yes	characteristic
382	C₂×C₁₉	#3328	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×Q₁₆	—	4	1	no	—
388	C₂×Q₁₆	—	4	1	no	—
389	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
390	C₂×M₁₆	—	4	1	no	—
391	C₂×M₁₆	—	4	1	no	—
392	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
393	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
400	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	4	1	no	—
404	C₄×Q₈	—	4	1	no	—
405	#117	—	2	2	no	—
406	#117	—	4	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	4	1	no	—
416	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
434	#106	C₂×C₄×C₁₉	1	4	yes	complemented
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	4	1	no	—
438	#103	—	4	1	no	—
439	#103	C₂×C₄×C₁₉	1	4	yes	complemented
440	#103	C₂×C₄×C₁₉	1	4	yes	complemented
441	C₂²⋊C₈	—	2	2	no	—
442	#97	—	4	1	no	—
443	C₄×C₈	—	4	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	D₄×C₁₉	1	1	yes	characteristic
453	#95	D₄×C₁₉	1	1	yes	characteristic
454	C₁₉	#23139	1	1	yes	characteristic, direct product factor, Sylow
455	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
467	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	8	1	no	—
483	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	#41×C₁₉	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
491	Q₁₆	—	4	4	no	—
492	M₁₆	—	4	4	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
504	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	8	1	no	—
520	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
521	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
522	C₄⋊C₄	#41×C₁₉	1	2	yes	—
523	C₄⋊C₄	#41×C₁₉	1	2	yes	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	4	2	no	—
534	C₄²	—	4	2	no	—
535	C₄²	—	4	2	no	—
536	C₄²	—	4	2	no	—
537	C₄²	—	8	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	C₄×D₄×C₁₉	1	2	yes	—
545	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
546	Q₈	—	2	2	no	—
547	Q₈	—	2	2	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	4	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	8	4	no	—
596	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
597	C₂×C₄	C₁₉×#137	1	2	yes	—
598	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
600	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
601	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
602	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
603	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
604	C₈	—	2	2	no	—
605	C₈	—	2	2	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
616	C₂²	C₁₉×#546	1	1	yes	characteristic
617	C₂²	C₁₉×#546	1	1	yes	characteristic
618	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
619	C₂²	C₁₉×#575	1	1	yes	characteristic
620	C₂²	C₁₉×#577	1	1	yes	characteristic
621	C₂²	C₁₉×#578	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	1	no	—
635	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
636	C₄	C₁₉×#518	1	1	yes	characteristic
637	C₄	C₁₉×#553	1	1	yes	characteristic
638	C₄	C₁₉×#553	1	1	yes	characteristic
639	C₂	—	4	2	no	—
640	C₂	C₁₉×#2364	1	1	yes	characteristic
641	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
642	C₂	C₁₉×#2947	1	1	yes	characteristic
643	C₂	C₁₉×#3315	1	1	yes	characteristic
644	C₂	C₁₉×#3316	1	1	yes	characteristic
645	C₂	C₁₉×#3323	1	1	yes	characteristic
646	C₂	C₁₉×#3328	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1935	C₂	semidirect
5. C₁₉×#1933	C₂	semidirect
6. C₁₉×#1919	C₂	semidirect
7. C₁₉×#1919	C₂	semidirect
8. C₁₉×#1878	C₂	semidirect
9. C₁₉×#1878	C₂	semidirect
12. C₁₉×#1763	C₂	semidirect
13. C₄×C₁₉×#103	C₂	semidirect
24. C₁₉×#470	C₄	semidirect
66. C₂×Q₁₆×C₁₉	C₂×C₄	semidirect
111. C₁₉×#106	C₂×C₄	semidirect
116. C₁₉×#103	C₂×C₄	semidirect
117. C₁₉×#103	C₂×C₄	semidirect
214. #23139	C₁₉	direct (N × H)
288. #1935	C₂×C₁₉	semidirect
289. #1933	C₂×C₁₉	semidirect
290. #1919	C₂×C₁₉	semidirect
291. #1919	C₂×C₁₉	semidirect
292. #1878	C₂×C₁₉	semidirect
293. #1878	C₂×C₁₉	semidirect
296. #1763	C₂×C₁₉	semidirect
297. C₄×#103	C₂×C₁₉	semidirect
339. #470	C₄×C₁₉	semidirect
389. C₂×Q₁₆	C₂×C₄×C₁₉	semidirect
434. #106	C₂×C₄×C₁₉	semidirect
439. #103	C₂×C₄×C₁₉	semidirect
440. #103	C₂×C₄×C₁₉	semidirect
454. C₁₉	#23139	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×#470	2
C₁₉×#2362	2
C₁₉×#2360	2
C₁₉×#1935	2
C₁₉×#1933	2
C₁₉×#1919	2
C₁₉×#1878	2
C₁₉×#1873	2
C₁₉×#1872	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
C₁₉×#1753	2
C₁₉×#1736	2
#23139	19

Subgroups — C19×#23139 #18029098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23139 #18029098