Subgroups — C₁₉×#11318 #18017277

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#342	—	2	2	no	—
16	C₁₉×#342	—	2	2	no	—
17	C₁₉×#342	—	2	2	no	—
18	C₁₉×#342	—	2	2	no	—
19	C₁₉×#342	—	2	2	no	—
20	C₁₉×#342	—	2	2	no	—
21	C₁₉×#342	C₄	1	4	yes	complemented
22	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	—	2	1	no	—
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
72	C₂⁴×C₁₉	—	8	2	no	—
73	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
78	C₂⁴×C₁₉	#41	1	1	yes	characteristic
79	C₂⁴×C₁₉	#41	1	1	yes	characteristic
80	C₂⁴×C₁₉	#41	1	1	yes	characteristic
81	C₂⁴×C₁₉	#41	1	1	yes	characteristic
82	C₂⁴×C₁₉	#41	1	1	yes	characteristic
83	C₂⁴×C₁₉	#41	1	1	yes	characteristic
84	C₂⁴×C₁₉	#41	1	1	yes	characteristic
85	C₂⁴×C₁₉	#41	1	1	yes	characteristic
86	C₂⁴×C₁₉	#41	1	1	yes	characteristic
87	C₂⁴×C₁₉	#41	1	1	yes	characteristic
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	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	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	—	8	2	no	—
110	C₂²×C₄×C₁₉	—	8	2	no	—
111	C₂²×C₄×C₁₉	—	8	2	no	—
112	C₂²×C₄×C₁₉	—	8	2	no	—
113	C₂²×C₄×C₁₉	—	8	2	no	—
114	C₂²×C₄×C₁₉	—	8	2	no	—
115	C₂²×C₄×C₁₉	—	8	2	no	—
116	C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₂²⋊C₄×C₁₉	—	2	2	no	—
120	C₂²⋊C₄×C₁₉	—	2	2	no	—
121	C₂²⋊C₄×C₁₉	—	2	2	no	—
122	C₂²⋊C₄×C₁₉	—	2	2	no	—
123	C₂²⋊C₄×C₁₉	—	2	2	no	—
124	C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂²⋊C₄×C₁₉	—	2	2	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	—	4	1	no	—
134	C₂²⋊C₄×C₁₉	—	4	1	no	—
135	C₂²⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₉	—	4	1	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	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	#11318	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	—	8	1	no	—
153	C₂³×C₁₉	—	8	1	no	—
154	C₂³×C₁₉	—	8	1	no	—
155	C₂³×C₁₉	—	8	1	no	—
156	C₂³×C₁₉	—	8	1	no	—
157	C₂³×C₁₉	—	8	1	no	—
158	C₂³×C₁₉	—	8	1	no	—
159	C₂³×C₁₉	—	8	1	no	—
160	C₂³×C₁₉	#117	1	1	yes	characteristic
161	C₂³×C₁₉	#117	1	1	yes	characteristic
162	C₂³×C₁₉	#117	1	1	yes	characteristic
163	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
165	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
166	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
167	C₂³×C₁₉	#121	1	1	yes	characteristic
168	C₂³×C₁₉	#121	1	1	yes	characteristic
169	C₂³×C₁₉	#121	1	1	yes	characteristic
170	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂³×C₁₉	#123	1	1	yes	characteristic
174	C₂³×C₁₉	#123	1	1	yes	characteristic
175	C₂³×C₁₉	#123	1	1	yes	characteristic
176	C₂³×C₁₉	#123	1	1	yes	characteristic
177	C₂³×C₁₉	#123	1	1	yes	characteristic
178	C₂³×C₁₉	#123	1	1	yes	characteristic
179	C₂³×C₁₉	#124	1	1	yes	characteristic
180	C₂³×C₁₉	#124	1	1	yes	characteristic
181	C₂³×C₁₉	#124	1	1	yes	characteristic
182	C₂³×C₁₉	#125	1	1	yes	characteristic
183	C₂³×C₁₉	#125	1	1	yes	characteristic
184	C₂³×C₁₉	#125	1	1	yes	characteristic
185	C₂³×C₁₉	#126	1	1	yes	characteristic
186	C₂³×C₁₉	#126	1	1	yes	characteristic
187	C₂³×C₁₉	#126	1	1	yes	characteristic
188	C₂³×C₁₉	#126	1	1	yes	characteristic
189	C₂³×C₁₉	#126	1	1	yes	characteristic
190	C₂³×C₁₉	#126	1	1	yes	characteristic
191	C₂³×C₁₉	#126	1	1	yes	characteristic
192	C₂³×C₁₉	#126	1	1	yes	characteristic
193	C₂³×C₁₉	#126	1	1	yes	characteristic
194	C₂³×C₁₉	#126	1	1	yes	characteristic
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	—	8	2	no	—
204	C₂×C₄×C₁₉	—	8	2	no	—
205	C₂×C₄×C₁₉	—	8	2	no	—
206	C₂×C₄×C₁₉	—	8	2	no	—
207	C₂×C₄×C₁₉	—	8	2	no	—
208	C₂×C₄×C₁₉	—	8	2	no	—
209	C₂×C₄×C₁₉	—	8	2	no	—
210	C₂×C₄×C₁₉	—	8	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	8	2	no	—
216	C₂×C₄×C₁₉	—	8	2	no	—
217	C₂×C₄×C₁₉	—	8	2	no	—
218	C₂×C₄×C₁₉	—	8	2	no	—
219	C₂×C₄×C₁₉	—	8	2	no	—
220	C₂×C₄×C₁₉	—	8	2	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
224	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
225	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
226	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
227	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
228	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
229	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	1	no	—
239	C₂²×C₁₉	—	4	1	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	4	1	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	1	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	—	4	1	no	—
259	C₂²×C₁₉	—	4	1	no	—
260	C₂²×C₁₉	—	4	1	no	—
261	C₂²×C₁₉	—	4	1	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	#383	1	1	yes	characteristic
266	C₂²×C₁₉	#387	1	1	yes	characteristic
267	C₂²×C₁₉	#387	1	1	yes	characteristic
268	C₂²×C₁₉	#387	1	1	yes	characteristic
269	C₂²×C₁₉	#388	1	1	yes	characteristic
270	C₂²×C₁₉	#388	1	1	yes	characteristic
271	C₂²×C₁₉	#388	1	1	yes	characteristic
272	C₂²×C₁₉	#396	1	1	yes	characteristic
273	C₂²×C₁₉	#397	1	1	yes	characteristic
274	C₂²×C₁₉	#397	1	1	yes	characteristic
275	C₂²×C₁₉	#397	1	1	yes	characteristic
276	C₂²×C₁₉	#400	1	1	yes	characteristic
277	C₂²×C₁₉	#400	1	1	yes	characteristic
278	C₂²×C₁₉	#400	1	1	yes	characteristic
279	C₂²×C₁₉	#401	1	1	yes	characteristic
280	C₄×C₁₉	—	8	2	no	—
281	C₄×C₁₉	—	8	2	no	—
282	C₄×C₁₉	—	8	2	no	—
283	C₄×C₁₉	—	8	2	no	—
284	C₄×C₁₉	—	8	2	no	—
285	C₄×C₁₉	—	8	2	no	—
286	C₄×C₁₉	—	8	2	no	—
287	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
288	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
291	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
292	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
294	#342	—	2	2	no	—
295	#342	—	2	2	no	—
296	#342	—	2	2	no	—
297	#342	—	2	2	no	—
298	#342	—	2	2	no	—
299	#342	—	2	2	no	—
300	#342	C₄×C₁₉	1	4	yes	complemented
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	2	1	no	—
304	C₂×C₁₉	—	2	1	no	—
305	C₂×C₁₉	—	2	1	no	—
306	C₂×C₁₉	—	2	1	no	—
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	2	1	no	—
310	C₂×C₁₉	—	2	1	no	—
311	C₂×C₁₉	—	2	1	no	—
312	C₂×C₁₉	—	2	1	no	—
313	C₂×C₁₉	—	2	1	no	—
314	C₂×C₁₉	—	2	1	no	—
315	C₂×C₁₉	#1443	1	1	yes	characteristic
316	C₂×C₁₉	#2104	1	2	yes	—
317	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊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	C₂×C₄×C₁₉	1	2	yes	—
361	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
363	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
364	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
365	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
366	C₂×C₂²⋊C₄	Q₈×C₁₉	1	2	yes	—
367	C₁₉	#11318	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	—	8	2	no	—
369	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
370	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
374	C₂⁴	#41×C₁₉	1	1	yes	characteristic
375	C₂⁴	#41×C₁₉	1	1	yes	characteristic
376	C₂⁴	#41×C₁₉	1	1	yes	characteristic
377	C₂⁴	#41×C₁₉	1	1	yes	characteristic
378	C₂⁴	#41×C₁₉	1	1	yes	characteristic
379	C₂⁴	#41×C₁₉	1	1	yes	characteristic
380	C₂⁴	#41×C₁₉	1	1	yes	characteristic
381	C₂⁴	#41×C₁₉	1	1	yes	characteristic
382	C₂⁴	#41×C₁₉	1	1	yes	characteristic
383	C₂⁴	#41×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	8	2	no	—
406	C₂²×C₄	—	8	2	no	—
407	C₂²×C₄	—	8	2	no	—
408	C₂²×C₄	—	8	2	no	—
409	C₂²×C₄	—	8	2	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	—	8	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	4	1	no	—
430	C₂²⋊C₄	—	4	1	no	—
431	C₂²⋊C₄	—	4	1	no	—
432	C₂²⋊C₄	—	4	1	no	—
433	C₂²⋊C₄	—	4	1	no	—
434	C₂²⋊C₄	—	4	1	no	—
435	C₂²⋊C₄	—	4	1	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₂²⋊C₄	—	4	1	no	—
438	C₂²⋊C₄	—	4	1	no	—
439	C₂²⋊C₄	—	4	1	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	8	1	no	—
448	C₂³	—	8	1	no	—
449	C₂³	—	8	1	no	—
450	C₂³	—	8	1	no	—
451	C₂³	—	8	1	no	—
452	C₂³	—	8	1	no	—
453	C₂³	—	8	1	no	—
454	C₂³	—	8	1	no	—
455	C₂³	C₁₉×#117	1	1	yes	characteristic
456	C₂³	C₁₉×#117	1	1	yes	characteristic
457	C₂³	C₁₉×#117	1	1	yes	characteristic
458	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
459	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
460	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
461	C₂³	C₄×Q₈×C₁₉	1	1	yes	characteristic
462	C₂³	C₁₉×#121	1	1	yes	characteristic
463	C₂³	C₁₉×#121	1	1	yes	characteristic
464	C₂³	C₁₉×#121	1	1	yes	characteristic
465	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
466	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
467	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
468	C₂³	C₁₉×#123	1	1	yes	characteristic
469	C₂³	C₁₉×#123	1	1	yes	characteristic
470	C₂³	C₁₉×#123	1	1	yes	characteristic
471	C₂³	C₁₉×#123	1	1	yes	characteristic
472	C₂³	C₁₉×#123	1	1	yes	characteristic
473	C₂³	C₁₉×#123	1	1	yes	characteristic
474	C₂³	C₁₉×#124	1	1	yes	characteristic
475	C₂³	C₁₉×#124	1	1	yes	characteristic
476	C₂³	C₁₉×#124	1	1	yes	characteristic
477	C₂³	C₁₉×#125	1	1	yes	characteristic
478	C₂³	C₁₉×#125	1	1	yes	characteristic
479	C₂³	C₁₉×#125	1	1	yes	characteristic
480	C₂³	C₁₉×#126	1	1	yes	characteristic
481	C₂³	C₁₉×#126	1	1	yes	characteristic
482	C₂³	C₁₉×#126	1	1	yes	characteristic
483	C₂³	C₁₉×#126	1	1	yes	characteristic
484	C₂³	C₁₉×#126	1	1	yes	characteristic
485	C₂³	C₁₉×#126	1	1	yes	characteristic
486	C₂³	C₁₉×#126	1	1	yes	characteristic
487	C₂³	C₁₉×#126	1	1	yes	characteristic
488	C₂³	C₁₉×#126	1	1	yes	characteristic
489	C₂³	C₁₉×#126	1	1	yes	characteristic
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	—	8	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	—	8	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	8	2	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	C₁₉×#383	1	1	yes	characteristic
554	C₂²	C₁₉×#387	1	1	yes	characteristic
555	C₂²	C₁₉×#387	1	1	yes	characteristic
556	C₂²	C₁₉×#387	1	1	yes	characteristic
557	C₂²	C₁₉×#388	1	1	yes	characteristic
558	C₂²	C₁₉×#388	1	1	yes	characteristic
559	C₂²	C₁₉×#388	1	1	yes	characteristic
560	C₂²	C₁₉×#396	1	1	yes	characteristic
561	C₂²	C₁₉×#397	1	1	yes	characteristic
562	C₂²	C₁₉×#397	1	1	yes	characteristic
563	C₂²	C₁₉×#397	1	1	yes	characteristic
564	C₂²	C₁₉×#400	1	1	yes	characteristic
565	C₂²	C₁₉×#400	1	1	yes	characteristic
566	C₂²	C₁₉×#400	1	1	yes	characteristic
567	C₂²	C₁₉×#401	1	1	yes	characteristic
568	C₄	—	8	2	no	—
569	C₄	—	8	2	no	—
570	C₄	—	8	2	no	—
571	C₄	—	8	2	no	—
572	C₄	—	8	2	no	—
573	C₄	—	8	2	no	—
574	C₄	—	8	2	no	—
575	C₂	—	2	1	no	—
576	C₂	—	2	1	no	—
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	C₁₉×#1443	1	1	yes	characteristic
590	C₂	C₁₉×#2104	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#401
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
21. C₁₉×#342	C₄	semidirect
144. #11318	C₁₉	direct (N × H)
300. #342	C₄×C₁₉	semidirect
367. C₁₉	#11318	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×#342	2
#11318	19

Subgroups — C19×#11318 #18017277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11318 #18017277