Subgroups — C₁₉×#21843 #18027802

Order 4864.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#433	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#544	—	2	4	no	—
17	C₁₉×#544	C₄	1	8	yes	complemented
18	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#125	—	2	1	no	—
22	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#433	—	2	4	no	—
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#388	—	2	1	no	—
37	C₁₉×#388	—	2	1	no	—
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#384	C₂²	1	1	yes	characteristic
41	C₁₉×#382	C₂²	1	1	yes	characteristic
42	C₁₉×#380	C₂²	1	1	yes	characteristic
43	C₁₉×#380	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₁₉×#340	C₂²	1	1	yes	characteristic
47	C₁₉×#340	C₂²	1	1	yes	characteristic
48	C₁₉×#340	C₂²	1	1	yes	characteristic
49	C₁₉×#340	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×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#340	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	—	2	1	no	—
63	C₂²×Q₈×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	—	2	8	no	—
71	C₁₉×C₄⋊Q₈	—	2	2	no	—
72	C₁₉×C₄⋊Q₈	—	2	2	no	—
73	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
74	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
75	C₁₉×#125	—	2	8	no	—
76	C₁₉×#125	—	2	2	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	C₂×C₄	1	4	yes	—
79	C₁₉×#125	C₂×C₄	1	4	yes	—
80	C₁₉×C₂²⋊Q₈	—	2	8	no	—
81	C₁₉×C₂²⋊Q₈	—	2	8	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₁₉×#117	C₂×C₄	1	4	yes	—
84	C₁₉×#117	C₂×C₄	1	4	yes	—
85	C₁₉×#117	D₄	1	4	yes	—
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	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	—	2	1	no	—
114	C₂×C₄²×C₁₉	—	2	1	no	—
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	—	2	2	no	—
118	C₁₉×C₄⋊C₈	—	2	2	no	—
119	C₁₉×C₂²⋊C₈	—	2	2	no	—
120	C₁₉×C₂²⋊C₈	—	2	2	no	—
121	C₁₉×#97	—	2	2	no	—
122	C₄×C₈×C₁₉	—	2	2	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	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₉	—	2	4	no	—
131	C₂×Q₈×C₁₉	—	2	4	no	—
132	C₂×Q₈×C₁₉	—	8	1	no	—
133	C₂×Q₈×C₁₉	—	8	1	no	—
134	C₂×Q₈×C₁₉	—	8	1	no	—
135	C₂×Q₈×C₁₉	—	8	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	4	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	—	8	1	no	—
150	C₂²×C₄×C₁₉	—	8	1	no	—
151	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	4	no	—
172	C₄⋊C₄×C₁₉	—	2	4	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	4	no	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	2	4	no	—
177	C₄⋊C₄×C₁₉	—	2	4	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	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	—	8	1	no	—
191	C₄⋊C₄×C₁₉	—	8	1	no	—
192	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
193	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
194	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
195	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
196	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
198	C₂²⋊C₄×C₁₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₉	—	8	1	no	—
200	C₂²⋊C₄×C₁₉	—	8	1	no	—
201	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
202	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
203	C₄²×C₁₉	—	2	4	no	—
204	C₄²×C₁₉	—	8	1	no	—
205	C₄²×C₁₉	—	8	1	no	—
206	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
207	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
208	C₄²×C₁₉	C₂×D₄	1	2	yes	—
209	C₄²×C₁₉	C₂×D₄	1	2	yes	—
210	#21843	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₁₉	—	8	4	no	—
220	Q₈×C₁₉	—	8	4	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	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	—	8	4	no	—
260	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
270	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
271	C₈×C₁₉	—	4	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
276	C₂×#433	C₂×C₁₉	1	1	yes	characteristic
277	#2314	C₂×C₁₉	1	1	yes	characteristic
278	#1993	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1992	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1991	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1990	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1989	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1989	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1988	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1987	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1825	C₂×C₁₉	1	1	yes	characteristic
287	#1825	C₂×C₁₉	1	1	yes	characteristic
288	#1824	C₂×C₁₉	1	1	yes	characteristic
289	#1823	C₂×C₁₉	1	1	yes	characteristic
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₁₉	#536	1	1	yes	characteristic
299	C₂²×C₁₉	#536	1	1	yes	characteristic
300	C₂²×C₁₉	#576	1	1	yes	characteristic
301	C₂²×C₁₉	#577	1	1	yes	characteristic
302	C₂²×C₁₉	#577	1	1	yes	characteristic
303	C₂²×C₁₉	#578	1	1	yes	characteristic
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	2	no	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	2	no	—
309	C₄×C₁₉	—	4	2	no	—
310	C₄×C₁₉	—	4	2	no	—
311	C₄×C₁₉	—	4	2	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₄×C₁₉	—	8	1	no	—
314	C₄×C₁₉	—	8	1	no	—
315	C₄×C₁₉	—	8	1	no	—
316	C₄×C₁₉	—	8	1	no	—
317	C₄×C₁₉	#519	1	1	yes	characteristic
318	C₄×C₁₉	#519	1	1	yes	characteristic
319	C₄×C₁₉	#536	1	1	yes	characteristic
320	C₄×C₁₉	#536	1	1	yes	characteristic
321	#544	—	2	4	no	—
322	#544	C₄×C₁₉	1	8	yes	complemented
323	C₂×C₄⋊Q₈	—	2	1	no	—
324	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#125	—	2	1	no	—
327	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×C₂²⋊Q₈	—	2	1	no	—
330	C₂×C₂²⋊Q₈	—	2	1	no	—
331	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
334	#433	—	2	4	no	—
335	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#387	—	2	1	no	—
344	#387	—	2	1	no	—
345	#384	C₂²×C₁₉	1	1	yes	characteristic
346	#382	C₂²×C₁₉	1	1	yes	characteristic
347	#380	C₂²×C₁₉	1	1	yes	characteristic
348	#380	C₂²×C₁₉	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
351	#340	C₂²×C₁₉	1	1	yes	characteristic
352	#340	C₂²×C₁₉	1	1	yes	characteristic
353	#340	C₂²×C₁₉	1	1	yes	characteristic
354	#340	C₂²×C₁₉	1	1	yes	characteristic
355	#340	C₂²×C₁₉	1	1	yes	characteristic
356	#340	C₂²×C₁₉	1	1	yes	characteristic
357	#340	C₂²×C₁₉	1	1	yes	characteristic
358	#340	C₂²×C₁₉	1	1	yes	characteristic
359	#340	C₂²×C₁₉	1	1	yes	characteristic
360	#340	C₂²×C₁₉	1	1	yes	characteristic
361	#340	C₂²×C₁₉	1	1	yes	characteristic
362	#340	C₂²×C₁₉	1	1	yes	characteristic
363	#340	C₂²×C₁₉	1	1	yes	characteristic
364	#340	C₂²×C₁₉	1	1	yes	characteristic
365	#340	C₂²×C₁₉	1	1	yes	characteristic
366	#340	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₁₉	—	4	2	no	—
368	C₂×C₁₉	#2310	1	1	yes	characteristic
369	C₂×C₁₉	#2897	1	1	yes	characteristic
370	C₂×C₁₉	#2898	1	1	yes	characteristic
371	C₂×C₁₉	#3241	1	1	yes	characteristic
372	C₂×C₁₉	#3242	1	1	yes	characteristic
373	C₂×C₁₉	#3243	1	1	yes	characteristic
374	C₂×C₁₉	#3244	1	1	yes	characteristic
375	C₂²×Q₈	—	2	1	no	—
376	C₂²×Q₈	—	2	1	no	—
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₄⋊Q₈	—	2	8	no	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	—	2	2	no	—
386	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
387	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
388	#125	—	2	8	no	—
389	#125	—	2	2	no	—
390	#125	—	2	2	no	—
391	#125	C₂×C₄×C₁₉	1	4	yes	—
392	#125	C₂×C₄×C₁₉	1	4	yes	—
393	C₂²⋊Q₈	—	2	8	no	—
394	C₂²⋊Q₈	—	2	8	no	—
395	#117	—	2	2	no	—
396	#117	C₂×C₄×C₁₉	1	4	yes	—
397	#117	C₂×C₄×C₁₉	1	4	yes	—
398	#117	D₄×C₁₉	1	4	yes	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
410	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
430	C₄⋊C₈	—	2	2	no	—
431	C₄⋊C₈	—	2	2	no	—
432	C₂²⋊C₈	—	2	2	no	—
433	C₂²⋊C₈	—	2	2	no	—
434	#97	—	2	2	no	—
435	C₄×C₈	—	2	2	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	C₁₉	#21843	1	1	yes	characteristic, direct product factor, Sylow
443	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	8	1	no	—
447	C₂×Q₈	—	8	1	no	—
448	C₂×Q₈	—	8	1	no	—
449	C₂×Q₈	—	8	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	8	1	no	—
464	C₂²×C₄	—	8	1	no	—
465	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	8	1	no	—
505	C₄⋊C₄	—	8	1	no	—
506	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
507	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
508	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
509	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
510	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
511	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	8	1	no	—
514	C₂²⋊C₄	—	8	1	no	—
515	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
516	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
517	C₄²	—	2	4	no	—
518	C₄²	—	8	1	no	—
519	C₄²	—	8	1	no	—
520	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
521	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
522	C₄²	C₂×D₄×C₁₉	1	2	yes	—
523	C₄²	C₂×D₄×C₁₉	1	2	yes	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
531	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
532	Q₈	—	8	4	no	—
533	Q₈	—	8	4	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	4	no	—
573	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
574	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
575	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
576	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
577	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
578	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
580	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
581	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
582	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
583	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
596	C₂²	C₁₉×#536	1	1	yes	characteristic
597	C₂²	C₁₉×#536	1	1	yes	characteristic
598	C₂²	C₁₉×#576	1	1	yes	characteristic
599	C₂²	C₁₉×#577	1	1	yes	characteristic
600	C₂²	C₁₉×#577	1	1	yes	characteristic
601	C₂²	C₁₉×#578	1	1	yes	characteristic
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	C₁₉×#519	1	1	yes	characteristic
616	C₄	C₁₉×#519	1	1	yes	characteristic
617	C₄	C₁₉×#536	1	1	yes	characteristic
618	C₄	C₁₉×#536	1	1	yes	characteristic
619	C₂	—	4	2	no	—
620	C₂	C₁₉×#2310	1	1	yes	characteristic
621	C₂	C₁₉×#2897	1	1	yes	characteristic
622	C₂	C₁₉×#2898	1	1	yes	characteristic
623	C₂	C₁₉×#3241	1	1	yes	characteristic
624	C₂	C₁₉×#3242	1	1	yes	characteristic
625	C₂	C₁₉×#3243	1	1	yes	characteristic
626	C₂	C₁₉×#3244	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 ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1993	C₂	semidirect
5. C₁₉×#1992	C₂	semidirect
6. C₁₉×#1991	C₂	semidirect
7. C₁₉×#1990	C₂	semidirect
8. C₁₉×#1989	C₂	semidirect
9. C₁₉×#1989	C₂	semidirect
10. C₁₉×#1988	C₂	semidirect
11. C₁₉×#1987	C₂	semidirect
17. C₁₉×#544	C₄	semidirect
210. #21843	C₁₉	direct (N × H)
278. #1993	C₂×C₁₉	semidirect
279. #1992	C₂×C₁₉	semidirect
280. #1991	C₂×C₁₉	semidirect
281. #1990	C₂×C₁₉	semidirect
282. #1989	C₂×C₁₉	semidirect
283. #1989	C₂×C₁₉	semidirect
284. #1988	C₂×C₁₉	semidirect
285. #1987	C₂×C₁₉	semidirect
322. #544	C₄×C₁₉	semidirect
442. C₁₉	#21843	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×#544	2
C₂×C₁₉×#433	2
C₁₉×#2314	2
C₁₉×#1993	2
C₁₉×#1992	2
C₁₉×#1991	2
C₁₉×#1990	2
C₁₉×#1989	2
C₁₉×#1988	2
C₁₉×#1987	2
C₁₉×#1825	2
C₁₉×#1824	2
C₁₉×#1823	2
#21843	19

Subgroups — C19×#21843 #18027802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21843 #18027802