Subgroups — C₁₉×#9143 #18015102

Order 4864.

1270 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2848	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#328	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1294	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₁₉	—	2	1	no	—
7	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	complemented
9	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
11	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
12	C₁₉×#385	—	2	2	no	—
13	C₁₉×#385	—	2	1	no	—
14	C₁₉×#380	C₄	1	2	yes	complemented
15	C₁₉×#380	C₂²	1	1	yes	characteristic
16	C₁₉×#379	—	2	1	no	—
17	C₂×C₁₉×#95	—	2	4	no	—
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₂×C₁₉×#95	C₂²	1	2	yes	—
20	C₁₉×#328	—	2	4	no	—
21	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
23	C₂³×C₄×C₁₉	—	2	4	no	—
24	C₂³×C₄×C₁₉	—	2	8	no	—
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂³×C₄×C₁₉	—	2	2	no	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	4	4	no	—
29	C₂³×C₄×C₁₉	—	4	4	no	—
30	C₂³×C₄×C₁₉	—	4	2	no	—
31	C₂³×C₄×C₁₉	—	4	2	no	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	—	2	2	no	—
37	C₁₉×C₂²⋊Q₈	—	2	2	no	—
38	C₁₉×C₂²⋊Q₈	—	2	2	no	—
39	C₁₉×C₂²⋊Q₈	—	4	4	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
44	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₁₉×C₂²⋊C₈	—	2	2	no	—
49	C₁₉×C₂²⋊C₈	—	2	2	no	—
50	C₁₉×C₂²⋊C₈	—	4	4	no	—
51	C₁₉×#95	—	2	4	no	—
52	C₁₉×#95	—	2	2	no	—
53	C₁₉×#95	—	2	2	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	D₄	1	4	yes	—
56	C₂⁴×C₁₉	—	2	4	no	—
57	C₂⁴×C₁₉	—	2	4	no	—
58	C₂⁴×C₁₉	—	2	1	no	—
59	C₂⁴×C₁₉	—	2	1	no	—
60	C₂⁴×C₁₉	—	2	1	no	—
61	C₂⁴×C₁₉	—	2	1	no	—
62	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₂⁴×C₁₉	SD₁₆	1	2	yes	—
64	C₂⁴×C₁₉	Q₁₆	1	2	yes	—
65	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂×Q₈×C₁₉	—	2	2	no	—
67	C₂×Q₈×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	2	16	no	—
69	C₂²×C₄×C₁₉	—	2	8	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	4	2	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	—	4	8	no	—
85	C₂²×C₄×C₁₉	—	4	8	no	—
86	C₂²×C₄×C₁₉	—	4	8	no	—
87	C₂²×C₄×C₁₉	—	4	16	no	—
88	C₂²×C₄×C₁₉	—	4	16	no	—
89	C₂²×C₄×C₁₉	—	4	4	no	—
90	C₂²×C₄×C₁₉	—	4	8	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₉	#41	1	2	yes	—
98	C₂×C₈×C₁₉	—	4	4	no	—
99	C₂×C₈×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	4	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₂²⋊C₄×C₁₉	—	4	4	no	—
105	C₂²⋊C₄×C₁₉	—	4	4	no	—
106	C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₂²⋊C₄×C₁₉	—	4	1	no	—
108	C₂²⋊C₄×C₁₉	—	4	1	no	—
109	C₂²⋊C₄×C₁₉	—	4	1	no	—
110	#9143	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	—	2	4	no	—
112	C₂³×C₁₉	—	2	4	no	—
113	C₂³×C₁₉	—	2	8	no	—
114	C₂³×C₁₉	—	2	4	no	—
115	C₂³×C₁₉	—	2	4	no	—
116	C₂³×C₁₉	—	2	8	no	—
117	C₂³×C₁₉	—	2	8	no	—
118	C₂³×C₁₉	—	2	8	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	#99	1	4	yes	—
130	C₂³×C₁₉	#103	1	4	yes	—
131	C₂³×C₁₉	#104	1	4	yes	—
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₁₉	#120	1	1	yes	characteristic
134	C₂³×C₁₉	#123	1	1	yes	characteristic
135	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
136	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
137	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂³×C₁₉	#137	1	1	yes	characteristic
139	Q₈×C₁₉	—	8	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	8	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	8	no	—
149	C₂×C₄×C₁₉	—	4	8	no	—
150	C₂×C₄×C₁₉	—	4	32	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	4	8	no	—
153	C₂×C₄×C₁₉	—	4	8	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	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	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₉	#121	1	2	yes	—
166	C₈×C₁₉	—	8	2	no	—
167	#2848	C₂×C₁₉	1	1	yes	characteristic
168	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
169	#1779	C₂×C₁₉	1	1	yes	characteristic
170	C₂×#328	C₂×C₁₉	1	2	yes	complemented
171	#1294	C₂×C₁₉	1	2	yes	complemented
172	C₂²×C₁₉	—	2	8	no	—
173	C₂²×C₁₉	—	2	8	no	—
174	C₂²×C₁₉	—	2	8	no	—
175	C₂²×C₁₉	—	2	8	no	—
176	C₂²×C₁₉	—	2	4	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	4	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	4	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	4	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	#328	1	8	yes	complemented
191	C₂²×C₁₉	#386	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#99	1	2	yes	—
193	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
194	C₂²×C₁₉	#417	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×#104	1	2	yes	—
196	C₂²×C₁₉	#450	1	1	yes	characteristic
197	C₂²×C₁₉	#451	1	1	yes	characteristic
198	C₂²×C₁₉	#483	1	1	yes	characteristic
199	C₂²×C₁₉	#484	1	1	yes	characteristic
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	4	8	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₂⁴×C₄	—	2	1	no	—
208	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	complemented
210	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₂²⋊C₈	—	2	2	no	—
212	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
213	#385	—	2	1	no	—
214	#385	—	2	2	no	—
215	#380	C₄×C₁₉	1	2	yes	complemented
216	#380	C₂²×C₁₉	1	1	yes	characteristic
217	#379	—	2	1	no	—
218	C₂×#95	—	2	1	no	—
219	C₂×#95	—	2	4	no	—
220	C₂×#95	C₂²×C₁₉	1	2	yes	—
221	#328	—	2	4	no	—
222	C₂×C₁₉	—	2	1	no	—
223	C₂×C₁₉	—	2	8	no	—
224	C₂×C₁₉	—	2	1	no	—
225	C₂×C₁₉	—	2	1	no	—
226	C₂×C₁₉	—	2	1	no	—
227	C₂×C₁₉	C₂×#328	1	2	yes	—
228	C₂×C₁₉	#1504	1	2	yes	—
229	C₂×C₁₉	#1872	1	1	yes	characteristic
230	C₂×C₁₉	#1896	1	1	yes	characteristic
231	C₂×C₁₉	#1898	1	1	yes	characteristic
232	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
233	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
234	C₂³×C₄	—	2	8	no	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	—	4	4	no	—
240	C₂³×C₄	—	4	4	no	—
241	C₂³×C₄	—	4	2	no	—
242	C₂³×C₄	—	4	2	no	—
243	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
244	C₂³×C₄	D₄×C₁₉	1	2	yes	—
245	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂²×C₈	—	2	2	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	—	4	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
254	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	—	4	4	no	—
262	#95	—	2	4	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	1	no	—
266	#95	D₄×C₁₉	1	4	yes	—
267	C₁₉	#9143	1	1	yes	characteristic, direct product factor, Sylow
268	C₂⁴	—	2	1	no	—
269	C₂⁴	—	2	1	no	—
270	C₂⁴	—	2	1	no	—
271	C₂⁴	—	2	1	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	2	4	no	—
274	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
275	C₂⁴	SD₁₆×C₁₉	1	2	yes	—
276	C₂⁴	Q₁₆×C₁₉	1	2	yes	—
277	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂²×C₄	—	2	16	no	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	8	no	—
297	C₂²×C₄	—	4	8	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	—	4	16	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	16	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	#41×C₁₉	1	2	yes	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	—	4	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	8	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	8	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	8	no	—
340	C₂³	C₁₉×#99	1	4	yes	—
341	C₂³	C₁₉×#103	1	4	yes	—
342	C₂³	C₁₉×#104	1	4	yes	—
343	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
344	C₂³	C₁₉×#120	1	1	yes	characteristic
345	C₂³	C₁₉×#123	1	1	yes	characteristic
346	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
347	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
348	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂³	C₁₉×#137	1	1	yes	characteristic
350	Q₈	—	8	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	32	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	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	C₄×D₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₁₉×#121	1	2	yes	—
377	C₈	—	8	2	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	2	8	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	2	8	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	C₁₉×#328	1	8	yes	complemented
397	C₂²	C₁₉×#386	1	1	yes	characteristic
398	C₂²	C₂×C₁₉×#99	1	2	yes	—
399	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
400	C₂²	C₁₉×#417	1	1	yes	characteristic
401	C₂²	C₂×C₁₉×#104	1	2	yes	—
402	C₂²	C₁₉×#450	1	1	yes	characteristic
403	C₂²	C₁₉×#451	1	1	yes	characteristic
404	C₂²	C₁₉×#483	1	1	yes	characteristic
405	C₂²	C₁₉×#484	1	1	yes	characteristic
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	8	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	2	8	no	—
418	C₂	C₂×C₁₉×#328	1	2	yes	—
419	C₂	C₁₉×#1504	1	2	yes	—
420	C₂	C₁₉×#1872	1	1	yes	characteristic
421	C₂	C₁₉×#1896	1	1	yes	characteristic
422	C₂	C₁₉×#1898	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#328	C₂	semidirect
5. C₁₉×#1294	C₂	semidirect
8. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
14. C₁₉×#380	C₄	semidirect
22. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
42. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
43. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
110. #9143	C₁₉	direct (N × H)
170. C₂×#328	C₂×C₁₉	semidirect
171. #1294	C₂×C₁₉	semidirect
190. C₂²×C₁₉	#328	semidirect
209. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
215. #380	C₄×C₁₉	semidirect
233. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
253. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
254. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
267. C₁₉	#9143	direct (N × H)
396. C₂²	C₁₉×#328	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#2848	2
C₂²×C₁₉×#95	2
C₁₉×#1779	2
C₂×C₁₉×#328	2
C₁₉×#1294	2
#9143	19

Subgroups — C19×#9143 #18015102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9143 #18015102