Subgroups — C₁₉×#26238 #18032197

Order 4864.

918 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2540	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2352	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1958	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊Q₈	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×C₁₉×#121	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×#484	—	2	4	no	—
25	C₁₉×#482	—	2	4	no	—
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#399	—	2	1	no	—
45	C₁₉×#392	—	2	1	no	—
46	C₁₉×#390	—	2	1	no	—
47	C₁₉×#390	—	2	1	no	—
48	C₁₉×#388	—	2	1	no	—
49	C₁₉×#387	—	2	1	no	—
50	C₁₉×#386	—	2	1	no	—
51	C₁₉×#382	C₂²	1	1	yes	characteristic
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₁₉×#380	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	—	2	1	no	—
64	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×#124	—	2	2	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	4	1	no	—
78	C₁₉×C₂²⋊Q₈	—	4	1	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#121	—	2	2	no	—
81	C₁₉×#121	—	4	1	no	—
82	C₁₉×#121	—	4	1	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₁₉×#117	—	2	2	no	—
86	C₁₉×#117	—	4	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	—	4	1	no	—
92	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	—	2	1	no	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	2	no	—
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×#107	D₄	1	4	yes	complemented
117	C₁₉×#106	—	2	2	no	—
118	C₁₉×C₄⋊C₈	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	4	1	no	—
122	C₁₉×#103	—	4	1	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	4	1	no	—
126	C₁₉×#102	—	4	1	no	—
127	C₁₉×C₂²⋊C₈	—	2	2	no	—
128	C₁₉×C₂²⋊C₈	—	2	2	no	—
129	C₁₉×C₂²⋊C₈	—	4	1	no	—
130	C₁₉×C₂²⋊C₈	—	4	1	no	—
131	C₄×C₈×C₁₉	—	2	2	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	—	2	1	no	—
137	C₁₉×#95	—	2	1	no	—
138	C₂⁴×C₁₉	—	2	1	no	—
139	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	4	1	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	—	4	2	no	—
158	C₂×D₄×C₁₉	—	4	2	no	—
159	C₂×D₄×C₁₉	—	4	2	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	—	8	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
182	C₂²×C₄×C₁₉	—	4	2	no	—
183	C₂²×C₄×C₁₉	—	8	1	no	—
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
200	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	4	2	no	—
212	C₄⋊C₄×C₁₉	—	4	2	no	—
213	C₄⋊C₄×C₁₉	—	4	2	no	—
214	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₁₉	#41	1	2	yes	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	4	2	no	—
220	C₂²⋊C₄×C₁₉	—	4	2	no	—
221	C₂²⋊C₄×C₁₉	—	4	2	no	—
222	C₂²⋊C₄×C₁₉	—	4	2	no	—
223	C₂²⋊C₄×C₁₉	—	4	2	no	—
224	C₂²⋊C₄×C₁₉	—	4	2	no	—
225	C₂²⋊C₄×C₁₉	—	4	2	no	—
226	C₂²⋊C₄×C₁₉	—	4	2	no	—
227	C₂²⋊C₄×C₁₉	—	8	1	no	—
228	C₄²×C₁₉	—	4	2	no	—
229	C₄²×C₁₉	—	8	1	no	—
230	C₄²×C₁₉	—	8	1	no	—
231	C₄²×C₁₉	#41	1	2	yes	—
232	C₄²×C₁₉	#41	1	2	yes	—
233	#26238	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	1	no	—
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	—	2	1	no	—
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	—	2	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	4	1	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	#135	1	2	yes	—
255	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₁₉	—	4	1	no	—
257	Q₈×C₁₉	—	4	1	no	—
258	Q₈×C₁₉	—	4	1	no	—
259	Q₈×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	4	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	8	4	no	—
266	D₄×C₁₉	—	8	4	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	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	—	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	—	8	4	no	—
307	C₂×C₄×C₁₉	#123	1	2	yes	—
308	C₂×C₄×C₁₉	#123	1	2	yes	—
309	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
313	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
315	C₈×C₁₉	—	2	2	no	—
316	C₈×C₁₉	—	4	1	no	—
317	C₈×C₁₉	—	4	1	no	—
318	C₈×C₁₉	—	4	1	no	—
319	C₂×#484	C₂×C₁₉	1	1	yes	characteristic, complemented
320	C₂×#482	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#2540	C₂×C₁₉	1	1	yes	characteristic
322	#2352	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#2035	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#1983	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#1958	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1954	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1949	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
333	C₄×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
334	C₂²×C₁₉	—	2	2	no	—
335	C₂²×C₁₉	—	2	2	no	—
336	C₂²×C₁₉	—	2	2	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	1	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	8	1	no	—
349	C₂²×C₁₉	—	8	1	no	—
350	C₂²×C₁₉	—	8	1	no	—
351	C₂²×C₁₉	—	8	1	no	—
352	C₂²×C₁₉	—	8	1	no	—
353	C₂²×C₁₉	—	8	1	no	—
354	C₂²×C₁₉	—	8	1	no	—
355	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
356	C₂²×C₁₉	D₄²	1	1	yes	characteristic
357	C₂²×C₁₉	#546	1	1	yes	characteristic
358	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
359	C₂²×C₁₉	#575	1	1	yes	characteristic
360	C₂²×C₁₉	#576	1	1	yes	characteristic
361	C₂²×C₁₉	#578	1	1	yes	characteristic
362	C₄×C₁₉	—	2	2	no	—
363	C₄×C₁₉	—	2	2	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	4	1	no	—
366	C₄×C₁₉	—	4	2	no	—
367	C₄×C₁₉	—	4	2	no	—
368	C₄×C₁₉	—	4	2	no	—
369	C₄×C₁₉	—	8	1	no	—
370	C₄×C₁₉	—	8	1	no	—
371	C₄×C₁₉	—	8	1	no	—
372	C₄×C₁₉	—	8	1	no	—
373	C₄×C₁₉	#532	1	1	yes	characteristic
374	C₄×C₁₉	#540	1	1	yes	characteristic
375	C₄×C₁₉	#550	1	1	yes	characteristic
376	C₄×C₁₉	#559	1	1	yes	characteristic
377	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
385	#484	—	2	4	no	—
386	#482	—	2	4	no	—
387	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
400	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
404	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
405	#399	—	2	1	no	—
406	#392	—	2	1	no	—
407	#390	—	2	1	no	—
408	#390	—	2	1	no	—
409	#388	—	2	1	no	—
410	#387	—	2	1	no	—
411	#386	—	2	1	no	—
412	#382	C₂²×C₁₉	1	1	yes	characteristic
413	#380	C₂²×C₁₉	1	1	yes	characteristic
414	#380	C₂²×C₁₉	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
416	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
417	C₄×C₂²⋊C₄	—	2	1	no	—
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	#340	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×C₁₉	—	4	2	no	—
423	C₂×C₁₉	—	8	1	no	—
424	C₂×C₁₉	—	16	1	no	—
425	C₂×C₁₉	#2445	1	1	yes	characteristic
426	C₂×C₁₉	#3091	1	1	yes	characteristic
427	C₂×C₁₉	#3098	1	1	yes	characteristic
428	C₂×C₁₉	#3273	1	1	yes	characteristic
429	C₂×C₁₉	#3285	1	1	yes	characteristic
430	C₂×C₁₉	#3297	1	1	yes	characteristic
431	C₂×C₁₉	#3327	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	#124	—	2	2	no	—
445	#124	—	2	2	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	4	1	no	—
449	C₂²⋊Q₈	—	4	1	no	—
450	#121	—	2	2	no	—
451	#121	—	2	2	no	—
452	#121	—	4	1	no	—
453	#121	—	4	1	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	#117	—	2	2	no	—
457	#117	—	4	1	no	—
458	C₂×C₄⋊C₄	—	2	2	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	4	1	no	—
463	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	—	2	1	no	—
483	C₂×C₄²	—	2	1	no	—
484	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
485	#107	—	2	2	no	—
486	#107	—	2	2	no	—
487	#107	D₄×C₁₉	1	4	yes	complemented
488	#106	—	2	2	no	—
489	C₄⋊C₈	—	2	2	no	—
490	#103	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	4	1	no	—
493	#103	—	4	1	no	—
494	#102	—	2	2	no	—
495	#102	—	2	2	no	—
496	#102	—	4	1	no	—
497	#102	—	4	1	no	—
498	C₂²⋊C₈	—	2	2	no	—
499	C₂²⋊C₈	—	2	2	no	—
500	C₂²⋊C₈	—	4	1	no	—
501	C₂²⋊C₈	—	4	1	no	—
502	C₄×C₈	—	2	2	no	—
503	#95	—	2	1	no	—
504	#95	—	2	1	no	—
505	#95	—	2	1	no	—
506	#95	—	2	1	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	C₁₉	#26238	1	1	yes	characteristic, direct product factor, Sylow
510	C₂⁴	—	2	1	no	—
511	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	4	1	no	—
528	C₂×D₄	—	4	2	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	—	8	1	no	—
533	C₂×D₄	—	8	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	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	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	8	1	no	—
556	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
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	C₂×D₄×C₁₉	1	2	yes	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	4	2	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
587	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
588	C₄⋊C₄	#41×C₁₉	1	2	yes	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	4	2	no	—
592	C₂²⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	8	1	no	—
600	C₄²	—	4	2	no	—
601	C₄²	—	8	1	no	—
602	C₄²	—	8	1	no	—
603	C₄²	#41×C₁₉	1	2	yes	—
604	C₄²	#41×C₁₉	1	2	yes	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	C₁₉×#135	1	2	yes	—
626	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	D₄	—	4	4	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	8	4	no	—
637	D₄	—	8	4	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	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	C₁₉×#123	1	2	yes	—
679	C₂×C₄	C₁₉×#123	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
681	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
682	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
683	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
684	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
686	C₈	—	2	2	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
712	C₂²	D₄²×C₁₉	1	1	yes	characteristic
713	C₂²	C₁₉×#546	1	1	yes	characteristic
714	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
715	C₂²	C₁₉×#575	1	1	yes	characteristic
716	C₂²	C₁₉×#576	1	1	yes	characteristic
717	C₂²	C₁₉×#578	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	8	1	no	—
726	C₄	—	8	1	no	—
727	C₄	—	8	1	no	—
728	C₄	—	8	1	no	—
729	C₄	C₁₉×#532	1	1	yes	characteristic
730	C₄	C₁₉×#540	1	1	yes	characteristic
731	C₄	C₁₉×#550	1	1	yes	characteristic
732	C₄	C₁₉×#559	1	1	yes	characteristic
733	C₂	—	4	2	no	—
734	C₂	—	8	1	no	—
735	C₂	—	16	1	no	—
736	C₂	C₁₉×#2445	1	1	yes	characteristic
737	C₂	C₁₉×#3091	1	1	yes	characteristic
738	C₂	C₁₉×#3098	1	1	yes	characteristic
739	C₂	C₁₉×#3273	1	1	yes	characteristic
740	C₂	C₁₉×#3285	1	1	yes	characteristic
741	C₂	C₁₉×#3297	1	1	yes	characteristic
742	C₂	C₁₉×#3327	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2540	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#484	C₂	semidirect
2. C₂×C₁₉×#482	C₂	semidirect
4. C₁₉×#2352	C₂	semidirect
5. C₁₉×#2036	C₂	semidirect
6. C₁₉×#2035	C₂	semidirect
7. C₁₉×#2033	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#1983	C₂	semidirect
10. C₁₉×#1958	C₂	semidirect
11. C₁₉×#1954	C₂	semidirect
12. C₁₉×#1949	C₂	semidirect
13. C₁₉×#1874	C₂	semidirect
14. C₁₉×#1873	C₂	semidirect
15. C₄×C₁₉×#107	C₂	semidirect
116. C₁₉×#107	D₄	semidirect
233. #26238	C₁₉	direct (N × H)
319. C₂×#484	C₂×C₁₉	semidirect
320. C₂×#482	C₂×C₁₉	semidirect
322. #2352	C₂×C₁₉	semidirect
323. #2036	C₂×C₁₉	semidirect
324. #2035	C₂×C₁₉	semidirect
325. #2033	C₂×C₁₉	semidirect
326. #2033	C₂×C₁₉	semidirect
327. #1983	C₂×C₁₉	semidirect
328. #1958	C₂×C₁₉	semidirect
329. #1954	C₂×C₁₉	semidirect
330. #1949	C₂×C₁₉	semidirect
331. #1874	C₂×C₁₉	semidirect
332. #1873	C₂×C₁₉	semidirect
333. C₄×#107	C₂×C₁₉	semidirect
487. #107	D₄×C₁₉	semidirect
509. C₁₉	#26238	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×#484	2
C₂×C₁₉×#482	2
C₁₉×#2540	2
C₁₉×#2352	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2033	2
C₁₉×#1983	2
C₁₉×#1958	2
C₁₉×#1954	2
C₁₉×#1949	2
C₁₉×#1874	2
C₁₉×#1873	2
C₄×C₁₉×#107	2
#26238	19

Subgroups — C19×#26238 #18032197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26238 #18032197