Subgroups — C₁₉×#12690 #18018649

Order 4864.

1228 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#534	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#352	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1781	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#534	—	2	4	no	—
9	C₁₉×#534	—	2	4	no	—
10	C₂×C₁₉×#123	—	2	1	no	—
11	C₂×C₁₉×#123	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	—	2	1	no	—
15	C₂×C₁₉×#120	—	2	1	no	—
16	C₂×C₁₉×#120	C₄	1	1	yes	characteristic, complemented
17	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
19	C₂×C₁₉×#100	—	2	1	no	—
20	C₂×C₁₉×#100	C₂²	1	2	yes	—
21	C₂×C₁₉×#99	—	2	1	no	—
22	C₂×C₁₉×#99	C₂²	1	2	yes	—
23	C₁₉×#407	—	2	1	no	—
24	C₁₉×#379	—	2	1	no	—
25	C₁₉×#352	—	2	4	no	—
26	C₁₉×AΣL(1,𝔽₁₆)	—	2	4	no	—
27	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	4	2	no	—
39	C₂²×D₄×C₁₉	—	4	2	no	—
40	C₂²×D₄×C₁₉	—	4	2	no	—
41	C₂²×D₄×C₁₉	—	4	2	no	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₁₉×#123	—	2	8	no	—
51	C₁₉×#123	—	2	2	no	—
52	C₁₉×#123	—	2	2	no	—
53	C₁₉×#123	—	2	2	no	—
54	C₁₉×#123	D₄	1	4	yes	—
55	C₁₉×#121	—	2	8	no	—
56	C₁₉×#121	—	2	8	no	—
57	C₁₉×#120	—	2	8	no	—
58	C₁₉×#120	—	2	2	no	—
59	C₁₉×#120	—	2	2	no	—
60	C₁₉×#120	—	2	2	no	—
61	C₁₉×#120	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₁₉×#100	—	2	2	no	—
76	C₁₉×#100	—	2	2	no	—
77	C₁₉×#100	—	4	2	no	—
78	C₁₉×#99	—	2	2	no	—
79	C₁₉×#99	—	2	2	no	—
80	C₁₉×#99	—	4	2	no	—
81	C₁₉×C₂²⋊C₈	—	4	2	no	—
82	C₂⁴×C₁₉	—	2	2	no	—
83	C₂⁴×C₁₉	—	2	2	no	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂⁴×C₁₉	—	2	1	no	—
86	C₂⁴×C₁₉	—	2	1	no	—
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	—	2	1	no	—
89	C₂⁴×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	—	4	1	no	—
91	C₂⁴×C₁₉	—	4	1	no	—
92	C₂⁴×C₁₉	—	4	1	no	—
93	C₂⁴×C₁₉	—	8	2	no	—
94	C₂⁴×C₁₉	—	8	2	no	—
95	C₂⁴×C₁₉	—	8	2	no	—
96	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	complemented
100	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	4	1	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂×D₄×C₁₉	—	4	8	no	—
119	C₂×D₄×C₁₉	—	4	8	no	—
120	C₂×D₄×C₁₉	—	4	8	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	8	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	8	2	no	—
127	C₂×D₄×C₁₉	—	8	2	no	—
128	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	8	2	no	—
142	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	M₁₆×C₁₉	—	4	2	no	—
146	M₁₆×C₁₉	—	4	2	no	—
147	C₂×C₈×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	2	1	no	—
154	C₂²⋊C₄×C₁₉	—	2	1	no	—
155	C₂²⋊C₄×C₁₉	—	2	4	no	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	4	2	no	—
158	C₂²⋊C₄×C₁₉	—	4	2	no	—
159	C₂²⋊C₄×C₁₉	—	8	4	no	—
160	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
161	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	complemented
162	#12690	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	4	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	4	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	4	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	8	2	no	—
191	C₂³×C₁₉	—	8	2	no	—
192	C₂³×C₁₉	—	8	2	no	—
193	C₂³×C₁₉	—	8	2	no	—
194	C₂³×C₁₉	—	8	4	no	—
195	C₂³×C₁₉	—	8	2	no	—
196	C₂³×C₁₉	—	8	2	no	—
197	C₂³×C₁₉	—	8	2	no	—
198	C₂³×C₁₉	—	8	4	no	—
199	C₂³×C₁₉	—	8	4	no	—
200	C₂³×C₁₉	—	8	4	no	—
201	C₂³×C₁₉	—	8	4	no	—
202	C₂³×C₁₉	#99	1	2	yes	—
203	C₂³×C₁₉	#99	1	2	yes	—
204	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₁₉	#120	1	2	yes	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	4	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	8	no	—
215	D₄×C₁₉	—	4	8	no	—
216	D₄×C₁₉	—	8	4	no	—
217	D₄×C₁₉	—	8	4	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	8	4	no	—
234	C₂×C₄×C₁₉	—	8	2	no	—
235	C₂×C₄×C₁₉	—	8	4	no	—
236	C₂×C₄×C₁₉	#120	1	2	yes	—
237	C₈×C₁₉	—	8	2	no	—
238	C₂×#534	C₂×C₁₉	1	1	yes	characteristic
239	C₂×#352	C₂×C₁₉	1	2	yes	complemented
240	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	2	yes	complemented
241	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1781	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	—	2	2	no	—
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	2	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	2	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	—	8	4	no	—
272	C₂²×C₁₉	—	8	4	no	—
273	C₂²×C₁₉	—	8	8	no	—
274	C₂²×C₁₉	—	8	4	no	—
275	C₂²×C₁₉	—	8	4	no	—
276	C₂²×C₁₉	—	8	2	no	—
277	C₂²×C₁₉	#379	1	1	yes	characteristic
278	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
279	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	16	2	no	—
286	C₂³×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
287	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
288	#534	—	2	4	no	—
289	#534	—	2	4	no	—
290	C₂×#123	—	2	1	no	—
291	C₂×#123	C₄×C₁₉	1	1	yes	characteristic, complemented
292	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#121	—	2	1	no	—
294	C₂×#121	—	2	1	no	—
295	C₂×#120	—	2	1	no	—
296	C₂×#120	C₄×C₁₉	1	1	yes	characteristic, complemented
297	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
298	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
299	C₂×#100	—	2	1	no	—
300	C₂×#100	C₂²×C₁₉	1	2	yes	—
301	C₂×#99	—	2	1	no	—
302	C₂×#99	C₂²×C₁₉	1	2	yes	—
303	#407	—	2	1	no	—
304	#379	—	2	1	no	—
305	#352	—	2	4	no	—
306	AΣL(1,𝔽₁₆)	—	2	4	no	—
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	4	2	no	—
310	C₂×C₁₉	—	4	2	no	—
311	C₂×C₁₉	—	4	2	no	—
312	C₂×C₁₉	—	4	1	no	—
313	C₂×C₁₉	—	4	1	no	—
314	C₂×C₁₉	—	8	1	no	—
315	C₂×C₁₉	—	8	2	no	—
316	C₂×C₁₉	#1781	1	1	yes	characteristic
317	C₂×C₁₉	#2121	1	2	yes	—
318	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
319	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
320	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	4	2	no	—
330	C₂²×D₄	—	4	2	no	—
331	C₂²×D₄	—	4	2	no	—
332	C₂²×D₄	—	4	2	no	—
333	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
334	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
335	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
336	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
339	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂×M₁₆	—	2	2	no	—
341	#123	—	2	8	no	—
342	#123	—	2	2	no	—
343	#123	—	2	2	no	—
344	#123	—	2	2	no	—
345	#123	D₄×C₁₉	1	4	yes	—
346	#121	—	2	8	no	—
347	#121	—	2	8	no	—
348	#120	—	2	8	no	—
349	#120	—	2	2	no	—
350	#120	—	2	2	no	—
351	#120	—	2	2	no	—
352	#120	D₄×C₁₉	1	4	yes	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	4	2	no	—
364	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
366	#100	—	2	2	no	—
367	#100	—	2	2	no	—
368	#100	—	4	2	no	—
369	#99	—	2	2	no	—
370	#99	—	2	2	no	—
371	#99	—	4	2	no	—
372	C₂²⋊C₈	—	4	2	no	—
373	C₁₉	#12690	1	1	yes	characteristic, direct product factor, Sylow
374	C₂⁴	—	2	1	no	—
375	C₂⁴	—	2	1	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	2	1	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	4	1	no	—
383	C₂⁴	—	4	1	no	—
384	C₂⁴	—	4	1	no	—
385	C₂⁴	—	8	2	no	—
386	C₂⁴	—	8	2	no	—
387	C₂⁴	—	8	2	no	—
388	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
389	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
391	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	complemented
392	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
393	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	8	no	—
411	C₂×D₄	—	4	8	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	8	2	no	—
419	C₂×D₄	—	8	2	no	—
420	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
421	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	8	2	no	—
434	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	M₁₆	—	4	2	no	—
438	M₁₆	—	4	2	no	—
439	C₂×C₈	—	4	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	8	4	no	—
452	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
453	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	complemented
454	C₂³	—	2	4	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	8	2	no	—
482	C₂³	—	8	2	no	—
483	C₂³	—	8	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	—	8	4	no	—
486	C₂³	—	8	2	no	—
487	C₂³	—	8	2	no	—
488	C₂³	—	8	2	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	—	8	4	no	—
493	C₂³	C₁₉×#99	1	2	yes	—
494	C₂³	C₁₉×#99	1	2	yes	—
495	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
496	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
497	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
498	C₂³	C₁₉×#120	1	2	yes	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	4	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	8	no	—
507	D₄	—	8	4	no	—
508	D₄	—	8	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	8	4	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	4	no	—
527	C₂×C₄	C₁₉×#120	1	2	yes	—
528	C₈	—	8	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	8	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	—	8	2	no	—
563	C₂²	C₁₉×#379	1	1	yes	characteristic
564	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
565	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	16	2	no	—
572	C₂	—	2	1	no	—
573	C₂	—	2	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	4	2	no	—
576	C₂	—	4	1	no	—
577	C₂	—	4	1	no	—
578	C₂	—	4	2	no	—
579	C₂	—	8	1	no	—
580	C₂	—	8	2	no	—
581	C₂	C₁₉×#1781	1	1	yes	characteristic
582	C₂	C₁₉×#2121	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#534	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂³×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#352	C₂	semidirect
3. C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	semidirect
4. C₁₉×#1783	C₂	semidirect
5. C₁₉×#1781	C₂	semidirect
6. C₂³×D₄×C₁₉	C₄	semidirect
11. C₂×C₁₉×#123	C₄	semidirect
16. C₂×C₁₉×#120	C₄	semidirect
18. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
99. C₂⁴×C₁₉	C₂²⋊C₄	semidirect
143. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
160. C₂²⋊C₄×C₁₉	C₂²⋊C₄	semidirect
161. C₂²⋊C₄×C₁₉	C₂²⋊C₄	semidirect
162. #12690	C₁₉	direct (N × H)
239. C₂×#352	C₂×C₁₉	semidirect
240. C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	semidirect
241. #1783	C₂×C₁₉	semidirect
242. #1781	C₂×C₁₉	semidirect
286. C₂³×D₄	C₄×C₁₉	semidirect
291. C₂×#123	C₄×C₁₉	semidirect
296. C₂×#120	C₄×C₁₉	semidirect
298. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
373. C₁₉	#12690	direct (N × H)
391. C₂⁴	C₂²⋊C₄×C₁₉	semidirect
435. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect
452. C₂²⋊C₄	C₂²⋊C₄×C₁₉	semidirect
453. C₂²⋊C₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#534	2
C₂×C₁₉×#352	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₁₉×#1783	2
C₁₉×#1781	2
#12690	19

Subgroups — C19×#12690 #18018649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12690 #18018649