Subgroups — C₁₉×#23142 #18029101

Order 4864.

926 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#468	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2363	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2360	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1762	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, complemented
15	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×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×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×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×#468	C₄	1	8	yes	complemented
25	C₂×C₁₉×#107	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×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	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×#390	—	2	1	no	—
37	C₁₉×#390	C₂²	1	1	yes	characteristic
38	C₁₉×#389	—	2	1	no	—
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#386	—	2	1	no	—
44	C₁₉×#385	—	2	1	no	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
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×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	4	1	no	—
67	C₂×SD₁₆×C₁₉	—	4	1	no	—
68	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
69	C₂×M₁₆×C₁₉	—	4	1	no	—
70	C₂×M₁₆×C₁₉	—	4	1	no	—
71	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	C₂×C₄	1	4	yes	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	4	1	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	4	1	no	—
84	C₁₉×#117	—	2	2	no	—
85	C₁₉×#117	—	4	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#107	C₂×C₄	1	4	yes	complemented
114	C₁₉×#103	—	2	2	no	—
115	C₁₉×#103	—	4	1	no	—
116	C₁₉×#103	C₂×C₄	1	4	yes	complemented
117	C₁₉×#102	—	2	2	no	—
118	C₁₉×#102	—	4	1	no	—
119	C₁₉×#102	C₂×C₄	1	4	yes	complemented
120	C₁₉×C₂²⋊C₈	—	2	2	no	—
121	C₁₉×#97	—	4	1	no	—
122	C₄×C₈×C₁₉	—	4	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	—	2	1	no	—
132	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₁₉	—	2	4	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	8	1	no	—
146	C₂×D₄×C₁₉	—	8	1	no	—
147	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	—	8	1	no	—
164	C₂²×C₄×C₁₉	—	8	1	no	—
165	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	#41	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	SD₁₆×C₁₉	—	4	4	no	—
174	M₁₆×C₁₉	—	4	4	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	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
186	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₁₉	—	2	4	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	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	4	2	no	—
197	C₄⋊C₄×C₁₉	—	4	2	no	—
198	C₄⋊C₄×C₁₉	—	8	1	no	—
199	C₄⋊C₄×C₁₉	—	8	1	no	—
200	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
201	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
202	C₄⋊C₄×C₁₉	#41	1	2	yes	—
203	C₄⋊C₄×C₁₉	#41	1	2	yes	—
204	C₂²⋊C₄×C₁₉	—	2	4	no	—
205	C₂²⋊C₄×C₁₉	—	2	4	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	2	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	8	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	4	2	no	—
217	C₄²×C₁₉	—	4	2	no	—
218	C₄²×C₁₉	—	8	1	no	—
219	C₄²×C₁₉	—	8	1	no	—
220	#23142	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	2	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	C₄×D₄	1	2	yes	—
235	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₁₉	—	2	2	no	—
237	Q₈×C₁₉	—	2	2	no	—
238	Q₈×C₁₉	—	4	1	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	2	2	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	8	4	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	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	1	no	—
266	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	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	—	8	4	no	—
284	C₂×C₄×C₁₉	—	8	4	no	—
285	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
286	C₂×C₄×C₁₉	#137	1	2	yes	—
287	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
293	C₈×C₁₉	—	2	2	no	—
294	C₈×C₁₉	—	2	2	no	—
295	C₈×C₁₉	—	4	1	no	—
296	C₈×C₁₉	—	4	1	no	—
297	C₂×#468	C₂×C₁₉	1	1	yes	characteristic
298	#2363	C₂×C₁₉	1	1	yes	characteristic
299	#2360	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1934	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1921	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1877	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#1874	C₂×C₁₉	1	1	yes	characteristic
307	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1762	C₂×C₁₉	1	1	yes	characteristic, complemented
309	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1753	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
312	C₂²×C₁₉	—	2	2	no	—
313	C₂²×C₁₉	—	2	2	no	—
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
327	C₂²×C₁₉	#546	1	1	yes	characteristic
328	C₂²×C₁₉	#546	1	1	yes	characteristic
329	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
330	C₂²×C₁₉	#575	1	1	yes	characteristic
331	C₂²×C₁₉	#576	1	1	yes	characteristic
332	C₂²×C₁₉	#577	1	1	yes	characteristic
333	C₄×C₁₉	—	2	2	no	—
334	C₄×C₁₉	—	2	2	no	—
335	C₄×C₁₉	—	4	1	no	—
336	C₄×C₁₉	—	4	2	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	4	2	no	—
339	C₄×C₁₉	—	4	1	no	—
340	C₄×C₁₉	—	4	2	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	2	no	—
343	C₄×C₁₉	—	8	1	no	—
344	C₄×C₁₉	—	8	1	no	—
345	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
346	C₄×C₁₉	#518	1	1	yes	characteristic
347	C₄×C₁₉	#553	1	1	yes	characteristic
348	C₄×C₁₉	#553	1	1	yes	characteristic
349	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
350	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
357	#468	C₄×C₁₉	1	8	yes	complemented
358	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
368	#391	C₂²×C₁₉	1	1	yes	characteristic
369	#390	—	2	1	no	—
370	#390	C₂²×C₁₉	1	1	yes	characteristic
371	#389	—	2	1	no	—
372	#389	C₂²×C₁₉	1	1	yes	characteristic
373	#389	C₂²×C₁₉	1	1	yes	characteristic
374	#388	—	2	1	no	—
375	#387	—	2	1	no	—
376	#386	—	2	1	no	—
377	#385	—	2	1	no	—
378	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
380	C₄×C₂²⋊C₄	—	2	1	no	—
381	C₄×C₂²⋊C₄	—	2	1	no	—
382	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
383	#340	C₂²×C₁₉	1	1	yes	characteristic
384	#340	C₂²×C₁₉	1	1	yes	characteristic
385	#340	C₂²×C₁₉	1	1	yes	characteristic
386	#340	C₂²×C₁₉	1	1	yes	characteristic
387	#340	C₂²×C₁₉	1	1	yes	characteristic
388	#340	C₂²×C₁₉	1	1	yes	characteristic
389	#340	C₂²×C₁₉	1	1	yes	characteristic
390	#340	C₂²×C₁₉	1	1	yes	characteristic
391	#336	C₂²×C₁₉	1	1	yes	characteristic
392	#336	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×C₁₉	—	4	2	no	—
394	C₂×C₁₉	—	8	2	no	—
395	C₂×C₁₉	#2364	1	1	yes	characteristic
396	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
397	C₂×C₁₉	#2946	1	1	yes	characteristic
398	C₂×C₁₉	#3319	1	1	yes	characteristic
399	C₂×C₁₉	#3320	1	1	yes	characteristic
400	C₂×C₁₉	#3323	1	1	yes	characteristic
401	C₂×C₁₉	#3333	1	1	yes	characteristic
402	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	—	2	1	no	—
407	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×SD₁₆	—	4	1	no	—
409	C₂×SD₁₆	—	4	1	no	—
410	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
411	C₂×M₁₆	—	4	1	no	—
412	C₂×M₁₆	—	4	1	no	—
413	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
414	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
420	#121	—	2	2	no	—
421	#121	C₂×C₄×C₁₉	1	4	yes	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	—	4	1	no	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	4	1	no	—
426	#117	—	2	2	no	—
427	#117	—	4	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	2	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	4	1	no	—
435	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
455	#107	C₂×C₄×C₁₉	1	4	yes	complemented
456	#103	—	2	2	no	—
457	#103	—	4	1	no	—
458	#103	C₂×C₄×C₁₉	1	4	yes	complemented
459	#102	—	2	2	no	—
460	#102	—	4	1	no	—
461	#102	C₂×C₄×C₁₉	1	4	yes	complemented
462	C₂²⋊C₈	—	2	2	no	—
463	#97	—	4	1	no	—
464	C₄×C₈	—	4	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	D₄×C₁₉	1	1	yes	characteristic
472	#95	D₄×C₁₉	1	1	yes	characteristic
473	C₁₉	#23142	1	1	yes	characteristic, direct product factor, Sylow
474	C₂⁴	—	2	1	no	—
475	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	8	1	no	—
489	C₂×D₄	—	8	1	no	—
490	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	8	1	no	—
507	C₂²×C₄	—	8	1	no	—
508	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂²×C₄	#41×C₁₉	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
516	SD₁₆	—	4	4	no	—
517	M₁₆	—	4	4	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
529	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	8	1	no	—
542	C₄⋊C₄	—	8	1	no	—
543	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
544	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
545	C₄⋊C₄	#41×C₁₉	1	2	yes	—
546	C₄⋊C₄	#41×C₁₉	1	2	yes	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	8	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	4	2	no	—
560	C₄²	—	4	2	no	—
561	C₄²	—	8	1	no	—
562	C₄²	—	8	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	C₄×D₄×C₁₉	1	2	yes	—
577	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	8	4	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	8	4	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
628	C₂×C₄	C₁₉×#137	1	2	yes	—
629	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
631	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
632	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
633	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
634	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
635	C₈	—	2	2	no	—
636	C₈	—	2	2	no	—
637	C₈	—	4	1	no	—
638	C₈	—	4	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
654	C₂²	C₁₉×#546	1	1	yes	characteristic
655	C₂²	C₁₉×#546	1	1	yes	characteristic
656	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
657	C₂²	C₁₉×#575	1	1	yes	characteristic
658	C₂²	C₁₉×#576	1	1	yes	characteristic
659	C₂²	C₁₉×#577	1	1	yes	characteristic
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	2	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
673	C₄	C₁₉×#518	1	1	yes	characteristic
674	C₄	C₁₉×#553	1	1	yes	characteristic
675	C₄	C₁₉×#553	1	1	yes	characteristic
676	C₂	—	4	2	no	—
677	C₂	—	8	2	no	—
678	C₂	C₁₉×#2364	1	1	yes	characteristic
679	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
680	C₂	C₁₉×#2946	1	1	yes	characteristic
681	C₂	C₁₉×#3319	1	1	yes	characteristic
682	C₂	C₁₉×#3320	1	1	yes	characteristic
683	C₂	C₁₉×#3323	1	1	yes	characteristic
684	C₂	C₁₉×#3333	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	C₂×C₁₉×#121	C₂²
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
3. C₁₉×#2360	C₂	semidirect
4. C₁₉×#1935	C₂	semidirect
5. C₁₉×#1934	C₂	semidirect
6. C₁₉×#1921	C₂	semidirect
7. C₁₉×#1918	C₂	semidirect
8. C₁₉×#1880	C₂	semidirect
9. C₁₉×#1877	C₂	semidirect
11. C₁₉×#1873	C₂	semidirect
12. C₁₉×#1762	C₂	semidirect
13. C₄×C₁₉×#103	C₂	semidirect
14. C₁₉×#1753	C₂	semidirect
15. C₁₉×#1736	C₂	semidirect
24. C₁₉×#468	C₄	semidirect
68. C₂×SD₁₆×C₁₉	C₂×C₄	semidirect
71. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
77. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
113. C₁₉×#107	C₂×C₄	semidirect
116. C₁₉×#103	C₂×C₄	semidirect
119. C₁₉×#102	C₂×C₄	semidirect
220. #23142	C₁₉	direct (N × H)
299. #2360	C₂×C₁₉	semidirect
300. #1935	C₂×C₁₉	semidirect
301. #1934	C₂×C₁₉	semidirect
302. #1921	C₂×C₁₉	semidirect
303. #1918	C₂×C₁₉	semidirect
304. #1880	C₂×C₁₉	semidirect
305. #1877	C₂×C₁₉	semidirect
307. #1873	C₂×C₁₉	semidirect
308. #1762	C₂×C₁₉	semidirect
309. C₄×#103	C₂×C₁₉	semidirect
310. #1753	C₂×C₁₉	semidirect
311. #1736	C₂×C₁₉	semidirect
357. #468	C₄×C₁₉	semidirect
410. C₂×SD₁₆	C₂×C₄×C₁₉	semidirect
413. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
419. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
455. #107	C₂×C₄×C₁₉	semidirect
458. #103	C₂×C₄×C₁₉	semidirect
461. #102	C₂×C₄×C₁₉	semidirect
473. C₁₉	#23142	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×#468	2
C₁₉×#2363	2
C₁₉×#2360	2
C₁₉×#1935	2
C₁₉×#1934	2
C₁₉×#1921	2
C₁₉×#1918	2
C₁₉×#1880	2
C₁₉×#1877	2
C₁₉×#1874	2
C₁₉×#1873	2
C₁₉×#1762	2
C₄×C₁₉×#103	2
C₁₉×#1753	2
C₁₉×#1736	2
#23142	19

Subgroups — C19×#23142 #18029101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23142 #18029101