Subgroups — C₁₉×#32968 #18038927

Order 4864.

1274 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2629	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₁₉×#520	—	2	4	no	—
19	C₁₉×#520	—	2	4	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	—	2	1	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	—	2	1	no	—
27	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#479	—	2	4	no	—
31	C₁₉×#478	—	2	4	no	—
32	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₁₉×#398	—	2	1	no	—
49	C₁₉×#398	—	2	1	no	—
50	C₁₉×#396	—	2	1	no	—
51	C₁₉×#396	—	2	1	no	—
52	C₁₉×#389	C₂²	1	1	yes	characteristic
53	C₁₉×#389	C₂²	1	1	yes	characteristic
54	C₁₉×#384	C₂²	1	1	yes	characteristic
55	C₁₉×#380	C₂²	1	1	yes	characteristic
56	C₁₉×#380	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	C₂×#41×C₁₉	—	2	2	no	—
64	C₂×#41×C₁₉	—	2	2	no	—
65	C₂×#41×C₁₉	—	2	2	no	—
66	C₂×#41×C₁₉	—	2	2	no	—
67	C₂×#41×C₁₉	—	2	2	no	—
68	C₂×#41×C₁₉	Q₈	1	4	yes	—
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	—	2	1	no	—
73	C₂³×C₄×C₁₉	—	2	1	no	—
74	C₂³×C₄×C₁₉	—	2	1	no	—
75	C₂³×C₄×C₁₉	—	2	1	no	—
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×#125	—	2	2	no	—
82	C₁₉×#125	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×Q₈×C₁₉	D₄	1	4	yes	—
87	C₄×D₄×C₁₉	—	2	8	no	—
88	C₄×D₄×C₁₉	—	2	8	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	D₄	1	4	yes	—
93	C₁₉×#117	—	2	8	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	2	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	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₁₉	—	2	1	no	—
123	C₂×C₄²×C₁₉	—	2	1	no	—
124	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₁₉×#107	—	2	2	no	—
127	C₁₉×#107	—	2	2	no	—
128	C₁₉×#106	—	2	2	no	—
129	C₁₉×#106	—	2	2	no	—
130	C₁₉×C₄⋊C₈	—	2	2	no	—
131	C₁₉×C₄⋊C₈	—	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×#102	—	2	2	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×C₂²⋊C₈	—	2	2	no	—
141	C₁₉×C₂²⋊C₈	—	2	2	no	—
142	C₁₉×#95	—	2	1	no	—
143	C₁₉×#95	—	2	1	no	—
144	C₁₉×#95	—	2	1	no	—
145	C₁₉×#95	—	2	1	no	—
146	C₂⁴×C₁₉	—	2	1	no	—
147	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
148	#41×C₁₉	—	2	8	no	—
149	#41×C₁₉	—	2	8	no	—
150	#41×C₁₉	—	2	8	no	—
151	#41×C₁₉	—	2	8	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	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
157	C₂×Q₈×C₁₉	#41	1	2	yes	—
158	C₂×D₄×C₁₉	—	2	4	no	—
159	C₂×D₄×C₁₉	—	2	4	no	—
160	C₂×D₄×C₁₉	—	2	4	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
166	C₂×D₄×C₁₉	#41	1	2	yes	—
167	C₂²×C₄×C₁₉	—	2	4	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	4	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	4	no	—
178	C₂²×C₄×C₁₉	—	2	4	no	—
179	C₂²×C₄×C₁₉	—	2	4	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	8	1	no	—
185	C₂²×C₄×C₁₉	—	8	1	no	—
186	C₂²×C₄×C₁₉	—	8	1	no	—
187	C₂²×C₄×C₁₉	—	8	1	no	—
188	C₂²×C₄×C₁₉	—	8	1	no	—
189	C₂²×C₄×C₁₉	—	8	1	no	—
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
196	C₂²×C₄×C₁₉	#41	1	2	yes	—
197	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	2	1	no	—
207	C₂×C₈×C₁₉	—	2	1	no	—
208	C₂×C₈×C₁₉	—	2	1	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	4	no	—
211	C₄⋊C₄×C₁₉	—	2	4	no	—
212	C₄⋊C₄×C₁₉	—	2	2	no	—
213	C₄⋊C₄×C₁₉	—	2	4	no	—
214	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	4	2	no	—
226	C₄⋊C₄×C₁₉	—	4	2	no	—
227	C₄⋊C₄×C₁₉	—	8	1	no	—
228	C₄⋊C₄×C₁₉	—	8	1	no	—
229	C₄⋊C₄×C₁₉	—	8	1	no	—
230	C₄⋊C₄×C₁₉	—	8	1	no	—
231	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
232	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
233	C₂²⋊C₄×C₁₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₉	—	2	4	no	—
235	C₂²⋊C₄×C₁₉	—	2	2	no	—
236	C₂²⋊C₄×C₁₉	—	2	2	no	—
237	C₂²⋊C₄×C₁₉	—	8	1	no	—
238	C₂²⋊C₄×C₁₉	—	8	1	no	—
239	C₄²×C₁₉	—	2	4	no	—
240	C₄²×C₁₉	—	2	4	no	—
241	C₄²×C₁₉	—	2	1	no	—
242	C₄²×C₁₉	—	2	1	no	—
243	C₄²×C₁₉	C₂×D₄	1	2	yes	—
244	C₄²×C₁₉	C₂×D₄	1	2	yes	—
245	#32968	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂³×C₁₉	—	2	1	no	—
247	C₂³×C₁₉	—	2	2	no	—
248	C₂³×C₁₉	—	2	2	no	—
249	C₂³×C₁₉	—	2	1	no	—
250	C₂³×C₁₉	—	2	2	no	—
251	C₂³×C₁₉	—	2	1	no	—
252	C₂³×C₁₉	—	2	1	no	—
253	C₂³×C₁₉	—	2	1	no	—
254	C₂³×C₁₉	—	2	1	no	—
255	C₂³×C₁₉	—	4	1	no	—
256	C₂³×C₁₉	—	4	1	no	—
257	C₂³×C₁₉	—	4	1	no	—
258	C₂³×C₁₉	—	4	1	no	—
259	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
260	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	Q₈×C₁₉	—	2	2	no	—
262	Q₈×C₁₉	—	2	2	no	—
263	Q₈×C₁₉	—	2	2	no	—
264	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	—
265	D₄×C₁₉	—	2	16	no	—
266	D₄×C₁₉	—	2	2	no	—
267	D₄×C₁₉	—	2	2	no	—
268	D₄×C₁₉	—	2	2	no	—
269	D₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
270	C₂×C₄×C₁₉	—	2	16	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	1	no	—
285	C₂×C₄×C₁₉	—	2	1	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	1	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	8	4	no	—
309	C₂×C₄×C₁₉	—	8	4	no	—
310	C₂×C₄×C₁₉	—	8	4	no	—
311	C₂×C₄×C₁₉	#120	1	2	yes	—
312	C₂×C₄×C₁₉	#120	1	2	yes	—
313	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
314	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
317	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
320	C₈×C₁₉	—	4	1	no	—
321	C₈×C₁₉	—	4	1	no	—
322	C₈×C₁₉	—	4	1	no	—
323	C₈×C₁₉	—	4	1	no	—
324	C₂×#520	C₂×C₁₉	1	1	yes	characteristic
325	C₂×#479	C₂×C₁₉	1	1	yes	characteristic, complemented
326	C₂×#478	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#2629	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#1865	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1862	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1802	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1798	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#1788	C₂×C₁₉	1	1	yes	characteristic
338	#1788	C₂×C₁₉	1	1	yes	characteristic
339	C₂²×C₁₉	—	2	2	no	—
340	C₂²×C₁₉	—	2	2	no	—
341	C₂²×C₁₉	—	2	2	no	—
342	C₂²×C₁₉	—	2	4	no	—
343	C₂²×C₁₉	—	4	2	no	—
344	C₂²×C₁₉	—	4	2	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	2	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	2	no	—
349	C₂²×C₁₉	—	4	1	no	—
350	C₂²×C₁₉	—	4	2	no	—
351	C₂²×C₁₉	—	4	1	no	—
352	C₂²×C₁₉	—	4	2	no	—
353	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
354	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
355	C₂²×C₁₉	#525	1	1	yes	characteristic
356	C₂²×C₁₉	#576	1	1	yes	characteristic
357	C₂²×C₁₉	#577	1	1	yes	characteristic
358	C₂²×C₁₉	#577	1	1	yes	characteristic
359	C₂²×C₁₉	#578	1	1	yes	characteristic
360	C₄×C₁₉	—	2	2	no	—
361	C₄×C₁₉	—	2	4	no	—
362	C₄×C₁₉	—	2	2	no	—
363	C₄×C₁₉	—	2	2	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	4	2	no	—
366	C₄×C₁₉	—	4	2	no	—
367	C₄×C₁₉	—	4	1	no	—
368	C₄×C₁₉	—	8	1	no	—
369	C₄×C₁₉	—	8	1	no	—
370	C₄×C₁₉	—	8	1	no	—
371	C₄×C₁₉	—	8	1	no	—
372	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
373	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
374	C₄×C₁₉	#525	1	1	yes	characteristic
375	C₄×C₁₉	#525	1	1	yes	characteristic
376	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
378	#520	—	2	4	no	—
379	#520	—	2	4	no	—
380	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×C₄×D₄	—	2	1	no	—
383	C₂×C₄×D₄	—	2	1	no	—
384	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#117	—	2	1	no	—
387	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	—	2	1	no	—
389	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
390	#479	—	2	4	no	—
391	#478	—	2	4	no	—
392	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
400	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
404	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
408	#398	—	2	1	no	—
409	#398	—	2	1	no	—
410	#396	—	2	1	no	—
411	#396	—	2	1	no	—
412	#389	C₂²×C₁₉	1	1	yes	characteristic
413	#389	C₂²×C₁₉	1	1	yes	characteristic
414	#384	C₂²×C₁₉	1	1	yes	characteristic
415	#380	C₂²×C₁₉	1	1	yes	characteristic
416	#380	C₂²×C₁₉	1	1	yes	characteristic
417	#340	C₂²×C₁₉	1	1	yes	characteristic
418	#340	C₂²×C₁₉	1	1	yes	characteristic
419	#340	C₂²×C₁₉	1	1	yes	characteristic
420	#340	C₂²×C₁₉	1	1	yes	characteristic
421	#336	C₂²×C₁₉	1	1	yes	characteristic
422	#336	C₂²×C₁₉	1	1	yes	characteristic
423	C₂×C₁₉	—	4	2	no	—
424	C₂×C₁₉	—	4	4	no	—
425	C₂×C₁₉	#2848	1	1	yes	characteristic
426	C₂×C₁₉	#3012	1	1	yes	characteristic
427	C₂×C₁₉	#3013	1	1	yes	characteristic
428	C₂×C₁₉	#3083	1	1	yes	characteristic
429	C₂×C₁₉	#3084	1	1	yes	characteristic
430	C₂×C₁₉	#3119	1	1	yes	characteristic
431	C₂×C₁₉	#3120	1	1	yes	characteristic
432	C₂×#41	—	2	2	no	—
433	C₂×#41	—	2	2	no	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	2	2	no	—
436	C₂×#41	—	2	2	no	—
437	C₂×#41	Q₈×C₁₉	1	4	yes	—
438	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
450	#125	—	2	2	no	—
451	#125	—	2	2	no	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	—	2	2	no	—
455	C₄×Q₈	D₄×C₁₉	1	4	yes	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	—	2	8	no	—
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	D₄×C₁₉	1	4	yes	—
462	#117	—	2	8	no	—
463	#117	—	2	2	no	—
464	#117	—	2	2	no	—
465	C₂×C₄⋊C₄	—	2	8	no	—
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	2	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	—	2	1	no	—
493	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
495	#107	—	2	2	no	—
496	#107	—	2	2	no	—
497	#106	—	2	2	no	—
498	#106	—	2	2	no	—
499	C₄⋊C₈	—	2	2	no	—
500	C₄⋊C₈	—	2	2	no	—
501	#103	—	2	2	no	—
502	#103	—	2	2	no	—
503	#103	—	2	2	no	—
504	#103	—	2	2	no	—
505	#102	—	2	2	no	—
506	#102	—	2	2	no	—
507	#102	—	2	2	no	—
508	#102	—	2	2	no	—
509	C₂²⋊C₈	—	2	2	no	—
510	C₂²⋊C₈	—	2	2	no	—
511	#95	—	2	1	no	—
512	#95	—	2	1	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	C₁₉	#32968	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	—	2	1	no	—
517	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
518	#41	—	2	8	no	—
519	#41	—	2	8	no	—
520	#41	—	2	8	no	—
521	#41	—	2	8	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
526	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
527	C₂×Q₈	#41×C₁₉	1	2	yes	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
535	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
536	C₂×D₄	#41×C₁₉	1	2	yes	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	8	1	no	—
555	C₂²×C₄	—	8	1	no	—
556	C₂²×C₄	—	8	1	no	—
557	C₂²×C₄	—	8	1	no	—
558	C₂²×C₄	—	8	1	no	—
559	C₂²×C₄	—	8	1	no	—
560	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
566	C₂²×C₄	#41×C₁₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	4	2	no	—
596	C₄⋊C₄	—	4	2	no	—
597	C₄⋊C₄	—	8	1	no	—
598	C₄⋊C₄	—	8	1	no	—
599	C₄⋊C₄	—	8	1	no	—
600	C₄⋊C₄	—	8	1	no	—
601	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
602	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	8	1	no	—
608	C₂²⋊C₄	—	8	1	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	C₂×D₄×C₁₉	1	2	yes	—
614	C₄²	C₂×D₄×C₁₉	1	2	yes	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
629	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
630	Q₈	—	2	2	no	—
631	Q₈	—	2	2	no	—
632	Q₈	—	2	2	no	—
633	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
634	D₄	—	2	16	no	—
635	D₄	—	2	2	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	2	no	—
638	D₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
639	C₂×C₄	—	2	16	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	4	no	—
680	C₂×C₄	C₁₉×#120	1	2	yes	—
681	C₂×C₄	C₁₉×#120	1	2	yes	—
682	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
685	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
686	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
687	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
688	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	2	no	—
707	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
708	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
709	C₂²	C₁₉×#525	1	1	yes	characteristic
710	C₂²	C₁₉×#576	1	1	yes	characteristic
711	C₂²	C₁₉×#577	1	1	yes	characteristic
712	C₂²	C₁₉×#577	1	1	yes	characteristic
713	C₂²	C₁₉×#578	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	4	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	1	no	—
722	C₄	—	8	1	no	—
723	C₄	—	8	1	no	—
724	C₄	—	8	1	no	—
725	C₄	—	8	1	no	—
726	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
727	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
728	C₄	C₁₉×#525	1	1	yes	characteristic
729	C₄	C₁₉×#525	1	1	yes	characteristic
730	C₂	—	4	2	no	—
731	C₂	—	4	4	no	—
732	C₂	C₁₉×#2848	1	1	yes	characteristic
733	C₂	C₁₉×#3012	1	1	yes	characteristic
734	C₂	C₁₉×#3013	1	1	yes	characteristic
735	C₂	C₁₉×#3083	1	1	yes	characteristic
736	C₂	C₁₉×#3084	1	1	yes	characteristic
737	C₂	C₁₉×#3119	1	1	yes	characteristic
738	C₂	C₁₉×#3120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
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×#479	C₂	semidirect
3. C₂×C₁₉×#478	C₂	semidirect
4. C₁₉×#2629	C₂	semidirect
5. C₁₉×#1865	C₂	semidirect
6. C₁₉×#1864	C₂	semidirect
7. C₁₉×#1863	C₂	semidirect
8. C₁₉×#1862	C₂	semidirect
9. C₁₉×#1853	C₂	semidirect
10. C₁₉×#1852	C₂	semidirect
11. C₁₉×#1803	C₂	semidirect
12. C₁₉×#1802	C₂	semidirect
13. C₁₉×#1798	C₂	semidirect
245. #32968	C₁₉	direct (N × H)
325. C₂×#479	C₂×C₁₉	semidirect
326. C₂×#478	C₂×C₁₉	semidirect
327. #2629	C₂×C₁₉	semidirect
328. #1865	C₂×C₁₉	semidirect
329. #1864	C₂×C₁₉	semidirect
330. #1863	C₂×C₁₉	semidirect
331. #1862	C₂×C₁₉	semidirect
332. #1853	C₂×C₁₉	semidirect
333. #1852	C₂×C₁₉	semidirect
334. #1803	C₂×C₁₉	semidirect
335. #1802	C₂×C₁₉	semidirect
336. #1798	C₂×C₁₉	semidirect
515. C₁₉	#32968	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×#520	2
C₂×C₁₉×#479	2
C₂×C₁₉×#478	2
C₁₉×#2629	2
C₁₉×#1865	2
C₁₉×#1864	2
C₁₉×#1863	2
C₁₉×#1862	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1803	2
C₁₉×#1802	2
C₁₉×#1798	2
C₁₉×#1788	2
#32968	19

Subgroups — C19×#32968 #18038927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32968 #18038927