Subgroups — C₁₉×#23132 #18029091

Order 4864.

1066 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2361	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1936	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1921	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1879	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1762	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#121	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₉	—	2	2	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#466	C₄	1	8	yes	complemented
17	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#102	C₂²	1	2	yes	—
19	C₂×C₁₉×#102	C₂²	1	2	yes	—
20	C₂×C₁₉×#102	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#97	C₂²	1	2	yes	—
23	C₁₉×#390	C₂²	1	2	yes	—
24	C₁₉×#389	C₂²	1	2	yes	—
25	C₁₉×#388	—	2	2	no	—
26	C₁₉×#386	—	2	2	no	—
27	C₁₉×#385	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	1	yes	characteristic
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	—	2	2	no	—
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×D₈×C₁₉	—	4	2	no	—
42	C₂×D₈×C₁₉	C₂×C₄	1	4	yes	complemented
43	C₂²×C₈×C₁₉	—	4	2	no	—
44	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₁₉×#121	—	2	4	no	—
49	C₁₉×#121	C₂×C₄	1	8	yes	complemented
50	C₄×D₄×C₁₉	—	2	4	no	—
51	C₄×D₄×C₁₉	—	4	2	no	—
52	C₄×D₄×C₁₉	—	4	8	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
67	C₁₉×#107	C₂×C₄	1	4	yes	complemented
68	C₁₉×#102	—	2	4	no	—
69	C₁₉×#102	—	4	2	no	—
70	C₁₉×#102	C₂×C₄	1	8	yes	complemented
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×#97	—	4	2	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	D₄	1	1	yes	characteristic
76	C₁₉×#95	D₄	1	1	yes	characteristic
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₁₉	—	2	8	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	4	4	no	—
86	C₂×D₄×C₁₉	—	4	4	no	—
87	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	4	4	no	—
94	C₂²×C₄×C₁₉	—	4	4	no	—
95	C₂²×C₄×C₁₉	—	4	4	no	—
96	C₂²×C₄×C₁₉	—	4	4	no	—
97	C₂²×C₄×C₁₉	—	8	2	no	—
98	C₂²×C₄×C₁₉	—	8	2	no	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
105	D₈×C₁₉	—	4	4	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	4	4	no	—
112	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	4	4	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₄⋊C₄×C₁₉	#41	1	4	yes	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	8	no	—
124	C₂²⋊C₄×C₁₉	—	4	4	no	—
125	C₂²⋊C₄×C₁₉	—	4	4	no	—
126	C₂²⋊C₄×C₁₉	—	8	2	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	4	4	no	—
130	#23132	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	C₄×D₄	1	2	yes	—
142	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
143	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	D₄×C₁₉	—	2	4	no	—
145	D₄×C₁₉	—	2	4	no	—
146	D₄×C₁₉	—	4	16	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	8	8	no	—
169	C₂×C₄×C₁₉	—	8	8	no	—
170	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
175	C₈×C₁₉	—	2	2	no	—
176	C₈×C₁₉	—	2	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₂×#466	C₂×C₁₉	1	1	yes	characteristic
179	#2361	C₂×C₁₉	1	2	yes	complemented
180	#1936	C₂×C₁₉	1	2	yes	complemented
181	#1921	C₂×C₁₉	1	2	yes	complemented
182	#1879	C₂×C₁₉	1	2	yes	complemented
183	#1874	C₂×C₁₉	1	2	yes	complemented
184	#1762	C₂×C₁₉	1	2	yes	complemented
185	#1752	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	#442	1	4	yes	—
199	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂²×C₁₉	#546	1	2	yes	—
201	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
202	C₂²×C₁₉	#576	1	1	yes	characteristic
203	C₂²×C₁₉	#578	1	1	yes	characteristic
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
211	C₄×C₁₉	#518	1	1	yes	characteristic
212	C₄×C₁₉	#553	1	2	yes	—
213	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×#121	C₂²×C₁₉	1	2	yes	—
216	C₂×C₄×D₄	—	2	2	no	—
217	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
219	#466	C₄×C₁₉	1	8	yes	complemented
220	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#102	C₂²×C₁₉	1	2	yes	—
222	C₂×#102	C₂²×C₁₉	1	2	yes	—
223	C₂×#102	C₂²×C₁₉	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#97	C₂²×C₁₉	1	2	yes	—
226	#390	C₂²×C₁₉	1	2	yes	—
227	#389	C₂²×C₁₉	1	2	yes	—
228	#388	—	2	2	no	—
229	#386	—	2	2	no	—
230	#385	—	2	2	no	—
231	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
232	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
233	#340	C₂²×C₁₉	1	2	yes	—
234	#340	C₂²×C₁₉	1	2	yes	—
235	#340	C₂²×C₁₉	1	2	yes	—
236	#340	C₂²×C₁₉	1	1	yes	characteristic
237	#340	C₂²×C₁₉	1	1	yes	characteristic
238	#336	C₂²×C₁₉	1	2	yes	—
239	C₂×C₁₉	—	2	4	no	—
240	C₂×C₁₉	—	8	4	no	—
241	C₂×C₁₉	#2364	1	1	yes	characteristic
242	C₂×C₁₉	C₂×#442	1	1	yes	characteristic
243	C₂×C₁₉	#2951	1	1	yes	characteristic
244	C₂×C₁₉	#3308	1	2	yes	—
245	C₂×C₁₉	#3318	1	2	yes	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×D₈	—	4	2	no	—
252	C₂×D₈	C₂×C₄×C₁₉	1	4	yes	complemented
253	C₂²×C₈	—	4	2	no	—
254	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	complemented
255	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
258	#121	—	2	4	no	—
259	#121	C₂×C₄×C₁₉	1	8	yes	complemented
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	4	2	no	—
262	C₄×D₄	—	4	8	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	4	2	no	—
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
277	#107	C₂×C₄×C₁₉	1	4	yes	complemented
278	#102	—	2	4	no	—
279	#102	—	4	2	no	—
280	#102	C₂×C₄×C₁₉	1	8	yes	complemented
281	C₂²⋊C₈	—	2	2	no	—
282	#97	—	4	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	D₄×C₁₉	1	1	yes	characteristic
286	#95	D₄×C₁₉	1	1	yes	characteristic
287	C₁₉	#23132	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	—	2	2	no	—
289	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
316	D₈	—	4	4	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	4	no	—
323	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
324	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
332	C₄⋊C₄	#41×C₁₉	1	4	yes	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	8	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	4	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₄×D₄×C₁₉	1	2	yes	—
352	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
353	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	16	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	8	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
383	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
384	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	C₁₉×#442	1	4	yes	—
400	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
401	C₂²	C₁₉×#546	1	2	yes	—
402	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
403	C₂²	C₁₉×#576	1	1	yes	characteristic
404	C₂²	C₁₉×#578	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	2	no	—
411	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
412	C₄	C₁₉×#518	1	1	yes	characteristic
413	C₄	C₁₉×#553	1	2	yes	—
414	C₂	—	2	4	no	—
415	C₂	—	8	4	no	—
416	C₂	C₁₉×#2364	1	1	yes	characteristic
417	C₂	C₂×C₁₉×#442	1	1	yes	characteristic
418	C₂	C₁₉×#2951	1	1	yes	characteristic
419	C₂	C₁₉×#3308	1	2	yes	—
420	C₂	C₁₉×#3318	1	2	yes	—

	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×#466	C₂
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
2. C₁₉×#2361	C₂	semidirect
3. C₁₉×#1936	C₂	semidirect
4. C₁₉×#1921	C₂	semidirect
5. C₁₉×#1879	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1762	C₂	semidirect
8. C₁₉×#1752	C₂	semidirect
9. C₂×C₁₉×#340	C₂	semidirect
16. C₁₉×#466	C₄	semidirect
42. C₂×D₈×C₁₉	C₂×C₄	semidirect
44. C₂²×C₈×C₁₉	C₂×C₄	semidirect
49. C₁₉×#121	C₂×C₄	semidirect
67. C₁₉×#107	C₂×C₄	semidirect
70. C₁₉×#102	C₂×C₄	semidirect
130. #23132	C₁₉	direct (N × H)
179. #2361	C₂×C₁₉	semidirect
180. #1936	C₂×C₁₉	semidirect
181. #1921	C₂×C₁₉	semidirect
182. #1879	C₂×C₁₉	semidirect
183. #1874	C₂×C₁₉	semidirect
184. #1762	C₂×C₁₉	semidirect
185. #1752	C₂×C₁₉	semidirect
186. C₂×#340	C₂×C₁₉	semidirect
219. #466	C₄×C₁₉	semidirect
252. C₂×D₈	C₂×C₄×C₁₉	semidirect
254. C₂²×C₈	C₂×C₄×C₁₉	semidirect
259. #121	C₂×C₄×C₁₉	semidirect
277. #107	C₂×C₄×C₁₉	semidirect
280. #102	C₂×C₄×C₁₉	semidirect
287. C₁₉	#23132	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×#466	2
C₁₉×#2361	2
C₁₉×#1936	2
C₁₉×#1921	2
C₁₉×#1879	2
C₁₉×#1874	2
C₁₉×#1762	2
C₁₉×#1752	2
C₂×C₁₉×#340	2
#23132	19

Subgroups — C19×#23132 #18029091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23132 #18029091