Subgroups — C₁₉×#22743 #18028702

Order 4864.

758 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1949	C₂	1	2	yes	maximal
5	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1947	C₂	1	2	yes	maximal
7	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1836	C₂	1	2	yes	maximal
9	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1776	C₂	1	2	yes	maximal
11	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#446	C₄	1	8	yes	complemented
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#107	C₂²	1	2	yes	—
17	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#106	C₂²	1	2	yes	—
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#391	—	2	1	no	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#389	—	2	2	no	—
26	C₁₉×#387	—	2	2	no	—
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#384	C₂²	1	2	yes	—
29	C₁₉×#384	C₂²	1	1	yes	characteristic
30	C₁₉×#382	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	1	yes	characteristic
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₄×Q₈×C₁₉	—	4	4	no	—
47	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
48	C₄×Q₈×C₁₉	Q₈	1	4	yes	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#107	—	2	2	no	—
70	C₁₉×#107	—	2	2	no	—
71	C₁₉×#107	—	2	4	no	—
72	C₁₉×#106	—	2	4	no	—
73	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
74	C₁₉×C₄⋊C₈	C₂×C₄	1	8	yes	—
75	C₁₉×#97	C₂×C₄	1	8	yes	—
76	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₂×C₈×C₁₉	—	2	1	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	1	no	—
102	C₂×C₈×C₁₉	—	2	1	no	—
103	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	4	4	no	—
117	C₄⋊C₄×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	8	2	no	—
120	C₄⋊C₄×C₁₉	—	8	1	no	—
121	C₄⋊C₄×C₁₉	—	8	1	no	—
122	C₄⋊C₄×C₁₉	C₄⋊C₄	1	8	yes	—
123	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
124	C₄⋊C₄×C₁₉	#41	1	2	yes	—
125	C₄⋊C₄×C₁₉	#41	1	2	yes	—
126	C₄²×C₁₉	—	4	4	no	—
127	C₄²×C₁₉	—	4	2	no	—
128	C₄²×C₁₉	—	4	2	no	—
129	C₄²×C₁₉	—	8	2	no	—
130	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
131	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
132	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
133	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
134	#22743	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₁₉	—	2	8	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₁₉	#137	1	2	yes	—
167	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₁₉	—	2	4	no	—
174	C₈×C₁₉	—	2	2	no	—
175	C₈×C₁₉	—	2	2	no	—
176	C₂×#446	C₂×C₁₉	1	1	yes	characteristic
177	#2355	C₂×C₁₉	1	1	yes	characteristic
178	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
179	#1949	C₂×C₁₉	1	2	yes	—
180	#1948	C₂×C₁₉	1	1	yes	characteristic
181	#1947	C₂×C₁₉	1	2	yes	—
182	#1947	C₂×C₁₉	1	1	yes	characteristic
183	#1836	C₂×C₁₉	1	2	yes	—
184	#1834	C₂×C₁₉	1	1	yes	characteristic
185	#1776	C₂×C₁₉	1	2	yes	—
186	C₄×#107	C₂×C₁₉	1	1	yes	characteristic
187	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₁₉	#548	1	1	yes	characteristic
189	C₂²×C₁₉	#548	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
192	C₂²×C₁₉	#576	1	1	yes	characteristic
193	C₂²×C₁₉	#578	1	1	yes	characteristic
194	C₄×C₁₉	—	2	4	no	—
195	C₄×C₁₉	—	2	4	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	4	2	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	8	2	no	—
200	C₄×C₁₉	—	8	1	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	#428	1	4	yes	—
204	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
205	C₄×C₁₉	#519	1	1	yes	characteristic
206	C₄×C₁₉	#557	1	1	yes	characteristic
207	C₄×C₁₉	#557	1	1	yes	characteristic
208	C₂×C₄×Q₈	—	2	1	no	—
209	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
210	#446	C₄×C₁₉	1	8	yes	complemented
211	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×#107	C₂²×C₁₉	1	2	yes	—
213	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#106	C₂²×C₁₉	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
217	C₂×#97	C₂²×C₁₉	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
219	#391	—	2	1	no	—
220	#389	—	2	1	no	—
221	#389	—	2	2	no	—
222	#387	—	2	2	no	—
223	#384	C₂²×C₁₉	1	1	yes	characteristic
224	#384	C₂²×C₁₉	1	1	yes	characteristic
225	#384	C₂²×C₁₉	1	2	yes	—
226	#382	C₂²×C₁₉	1	2	yes	—
227	C₄×C₄⋊C₄	—	2	1	no	—
228	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
232	#340	C₂²×C₁₉	1	2	yes	—
233	#340	C₂²×C₁₉	1	2	yes	—
234	#340	C₂²×C₁₉	1	1	yes	characteristic
235	#340	C₂²×C₁₉	1	2	yes	—
236	#340	C₂²×C₁₉	1	2	yes	—
237	#340	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₁₉	#2351	1	1	yes	characteristic
239	C₂×C₁₉	C₂×#428	1	1	yes	characteristic
240	C₂×C₁₉	#2913	1	1	yes	characteristic
241	C₂×C₁₉	#3366	1	1	yes	characteristic
242	C₂×C₁₉	#3367	1	1	yes	characteristic
243	C₂×C₁₉	#3374	1	1	yes	characteristic
244	C₂×C₁₉	#3375	1	1	yes	characteristic
245	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
249	C₄×Q₈	—	4	4	no	—
250	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
251	C₄×Q₈	Q₈×C₁₉	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
271	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
272	#107	—	2	2	no	—
273	#107	—	2	2	no	—
274	#107	—	2	4	no	—
275	#106	—	2	4	no	—
276	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
277	C₄⋊C₈	C₂×C₄×C₁₉	1	8	yes	—
278	#97	C₂×C₄×C₁₉	1	8	yes	—
279	C₄×C₈	C₂×C₄×C₁₉	1	4	yes	—
280	#95	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	2	no	—
286	C₁₉	#22743	1	1	yes	characteristic, direct product factor, Sylow
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	C₄⋊C₄×C₁₉	1	4	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
308	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
309	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	8	2	no	—
324	C₄⋊C₄	—	8	1	no	—
325	C₄⋊C₄	—	8	1	no	—
326	C₄⋊C₄	C₄⋊C₄×C₁₉	1	8	yes	—
327	C₄⋊C₄	C₄⋊C₄×C₁₉	1	4	yes	—
328	C₄⋊C₄	#41×C₁₉	1	2	yes	—
329	C₄⋊C₄	#41×C₁₉	1	2	yes	—
330	C₄²	—	4	4	no	—
331	C₄²	—	4	2	no	—
332	C₄²	—	4	2	no	—
333	C₄²	—	8	2	no	—
334	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
335	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
336	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
337	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
338	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
339	Q₈	—	2	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
365	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
366	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
367	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
368	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
369	C₂×C₄	C₁₉×#137	1	2	yes	—
370	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
371	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
380	C₂²	C₁₉×#548	1	1	yes	characteristic
381	C₂²	C₁₉×#548	1	1	yes	characteristic
382	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
384	C₂²	C₁₉×#576	1	1	yes	characteristic
385	C₂²	C₁₉×#578	1	1	yes	characteristic
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	4	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	2	no	—
395	C₄	C₁₉×#428	1	4	yes	—
396	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
397	C₄	C₁₉×#519	1	1	yes	characteristic
398	C₄	C₁₉×#557	1	1	yes	characteristic
399	C₄	C₁₉×#557	1	1	yes	characteristic
400	C₂	C₁₉×#2351	1	1	yes	characteristic
401	C₂	C₂×C₁₉×#428	1	1	yes	characteristic
402	C₂	C₁₉×#2913	1	1	yes	characteristic
403	C₂	C₁₉×#3366	1	1	yes	characteristic
404	C₂	C₁₉×#3367	1	1	yes	characteristic
405	C₂	C₁₉×#3374	1	1	yes	characteristic
406	C₂	C₁₉×#3375	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₁₉×#446	C₄	semidirect
134. #22743	C₁₉	direct (N × H)
210. #446	C₄×C₁₉	semidirect
286. C₁₉	#22743	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×#446	2
C₁₉×#2355	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#1949	2
C₁₉×#1948	2
C₁₉×#1947	2
C₁₉×#1836	2
C₁₉×#1834	2
C₁₉×#1776	2
C₄×C₁₉×#107	2
#22743	19

Subgroups — C19×#22743 #18028702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22743 #18028702