Subgroups — C₁₉×#21814 #18027773

Order 4864.

1250 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1983	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1981	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1959	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1788	C₂	1	2	yes	maximal
11	C₁₉×#1787	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#536	—	2	4	no	—
15	C₁₉×#536	C₄	1	8	yes	complemented
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#123	—	2	2	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₁₉×#433	—	2	4	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×#103	C₂²	1	2	yes	—
30	C₂×C₁₉×#103	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₂×C₁₉×#102	C₂²	1	2	yes	—
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#388	—	2	2	no	—
37	C₁₉×#387	—	2	2	no	—
38	C₁₉×#384	C₂²	1	1	yes	characteristic
39	C₁₉×#382	C₂²	1	1	yes	characteristic
40	C₁₉×#380	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	4	2	no	—
44	C₂×#41×C₁₉	—	4	2	no	—
45	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	2	2	no	—
48	C₂²×Q₈×C₁₉	—	4	2	no	—
49	C₂²×Q₈×C₁₉	—	4	2	no	—
50	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
51	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	—	2	1	no	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
64	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#124	C₂×C₄	1	4	yes	—
68	C₁₉×#124	C₂×C₄	1	4	yes	—
69	C₁₉×#123	—	2	16	no	—
70	C₁₉×C₂²⋊Q₈	—	2	16	no	—
71	C₁₉×#117	C₂×C₄	1	4	yes	—
72	C₁₉×#117	D₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	—	2	4	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#103	—	4	2	no	—
89	C₁₉×#103	—	4	2	no	—
90	C₁₉×#103	—	4	2	no	—
91	C₁₉×#103	—	4	2	no	—
92	C₁₉×#103	—	4	2	no	—
93	C₁₉×#102	—	4	2	no	—
94	C₁₉×#102	—	4	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	4	no	—
96	C₁₉×#97	—	2	2	no	—
97	C₄×C₈×C₁₉	—	2	2	no	—
98	C₁₉×#95	—	2	2	no	—
99	C₁₉×#95	—	2	2	no	—
100	C₁₉×#95	—	2	2	no	—
101	C₂⁴×C₁₉	—	2	1	no	—
102	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
103	#41×C₁₉	—	4	8	no	—
104	#41×C₁₉	—	4	8	no	—
105	C₂×Q₈×C₁₉	—	2	4	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	4	8	no	—
116	C₂×Q₈×C₁₉	—	4	2	no	—
117	C₂×Q₈×C₁₉	—	4	2	no	—
118	C₂×Q₈×C₁₉	—	4	8	no	—
119	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
120	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	4	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	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	4	2	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	8	no	—
155	C₄⋊C₄×C₁₉	—	2	8	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	8	2	no	—
161	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
162	C₂²⋊C₄×C₁₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₉	—	8	2	no	—
165	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
166	C₄²×C₁₉	—	8	2	no	—
167	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
168	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
169	C₄²×C₁₉	C₂×D₄	1	2	yes	—
170	C₄²×C₁₉	C₂×D₄	1	2	yes	—
171	#21814	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	—	4	1	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₉	—	2	4	no	—
184	Q₈×C₁₉	—	2	4	no	—
185	Q₈×C₁₉	—	2	4	no	—
186	Q₈×C₁₉	—	4	8	no	—
187	Q₈×C₁₉	—	4	2	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	4	8	no	—
192	D₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	4	8	no	—
205	C₂×C₄×C₁₉	—	4	8	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
219	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
224	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
225	C₈×C₁₉	—	4	2	no	—
226	C₈×C₁₉	—	4	2	no	—
227	C₂×#536	C₂×C₁₉	1	1	yes	characteristic
228	C₂×#433	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#2314	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1983	C₂×C₁₉	1	2	yes	complemented
231	#1981	C₂×C₁₉	1	2	yes	complemented
232	#1960	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1959	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1958	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1956	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1788	C₂×C₁₉	1	2	yes	—
237	#1787	C₂×C₁₉	1	2	yes	complemented
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	2	4	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	4	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₁₉	#535	1	1	yes	characteristic
250	C₂²×C₁₉	#535	1	1	yes	characteristic
251	C₂²×C₁₉	#577	1	2	yes	—
252	C₂²×C₁₉	#578	1	2	yes	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	2	4	no	—
255	C₄×C₁₉	—	2	4	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	4	2	no	—
259	C₄×C₁₉	—	8	2	no	—
260	C₄×C₁₉	—	8	2	no	—
261	C₄×C₁₉	#518	1	2	yes	—
262	C₄×C₁₉	#535	1	2	yes	—
263	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
264	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
265	#536	—	2	4	no	—
266	#536	C₄×C₁₉	1	8	yes	complemented
267	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×#123	—	2	2	no	—
272	C₂×C₂²⋊Q₈	—	2	2	no	—
273	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
274	#433	—	2	4	no	—
275	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
276	C₂×#103	C₂²×C₁₉	1	2	yes	—
277	C₂×#103	C₂²×C₁₉	1	2	yes	—
278	C₂×#103	C₂²×C₁₉	1	2	yes	—
279	C₂×#103	C₂²×C₁₉	1	2	yes	—
280	C₂×#103	C₂²×C₁₉	1	2	yes	—
281	C₂×#103	C₂²×C₁₉	1	2	yes	—
282	C₂×#102	C₂²×C₁₉	1	2	yes	—
283	C₂×#102	C₂²×C₁₉	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
285	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
287	#388	—	2	2	no	—
288	#387	—	2	2	no	—
289	#384	C₂²×C₁₉	1	1	yes	characteristic
290	#382	C₂²×C₁₉	1	1	yes	characteristic
291	#380	C₂²×C₁₉	1	2	yes	—
292	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
293	C₂×C₁₉	—	4	2	no	—
294	C₂×C₁₉	—	8	2	no	—
295	C₂×C₁₉	#2309	1	1	yes	characteristic
296	C₂×C₁₉	#2898	1	2	yes	—
297	C₂×C₁₉	#3221	1	1	yes	characteristic
298	C₂×C₁₉	#3223	1	1	yes	characteristic
299	C₂×C₁₉	#3225	1	2	yes	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	4	2	no	—
302	C₂×#41	—	4	2	no	—
303	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	—	2	2	no	—
306	C₂²×Q₈	—	4	2	no	—
307	C₂²×Q₈	—	4	2	no	—
308	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
309	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
322	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
323	#124	—	2	2	no	—
324	#124	—	2	2	no	—
325	#124	C₂×C₄×C₁₉	1	4	yes	—
326	#124	C₂×C₄×C₁₉	1	4	yes	—
327	#123	—	2	16	no	—
328	C₂²⋊Q₈	—	2	16	no	—
329	#117	C₂×C₄×C₁₉	1	4	yes	—
330	#117	D₄×C₁₉	1	4	yes	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
344	C₄⋊C₈	—	2	4	no	—
345	#103	—	4	2	no	—
346	#103	—	4	2	no	—
347	#103	—	4	2	no	—
348	#103	—	4	2	no	—
349	#103	—	4	2	no	—
350	#103	—	4	2	no	—
351	#102	—	4	2	no	—
352	#102	—	4	2	no	—
353	C₂²⋊C₈	—	2	4	no	—
354	#97	—	2	2	no	—
355	C₄×C₈	—	2	2	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	C₁₉	#21814	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	—	2	1	no	—
361	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
362	#41	—	4	8	no	—
363	#41	—	4	8	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	4	8	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×Q₈	—	4	2	no	—
377	C₂×Q₈	—	4	8	no	—
378	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
379	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
380	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	8	2	no	—
420	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	8	2	no	—
424	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
425	C₄²	—	8	2	no	—
426	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
427	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
428	C₄²	C₂×D₄×C₁₉	1	2	yes	—
429	C₄²	C₂×D₄×C₁₉	1	2	yes	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
440	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
441	Q₈	—	2	4	no	—
442	Q₈	—	2	4	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	8	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	D₄	—	2	4	no	—
449	D₄	—	4	8	no	—
450	D₄	—	4	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
477	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
478	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
479	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
483	C₈	—	4	2	no	—
484	C₈	—	4	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	2	no	—
495	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
496	C₂²	C₁₉×#535	1	1	yes	characteristic
497	C₂²	C₁₉×#535	1	1	yes	characteristic
498	C₂²	C₁₉×#577	1	2	yes	—
499	C₂²	C₁₉×#578	1	2	yes	—
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	2	no	—
507	C₄	—	8	2	no	—
508	C₄	C₁₉×#518	1	2	yes	—
509	C₄	C₁₉×#535	1	2	yes	—
510	C₂	—	4	2	no	—
511	C₂	—	8	2	no	—
512	C₂	C₁₉×#2309	1	1	yes	characteristic
513	C₂	C₁₉×#2898	1	2	yes	—
514	C₂	C₁₉×#3221	1	1	yes	characteristic
515	C₂	C₁₉×#3223	1	1	yes	characteristic
516	C₂	C₁₉×#3225	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	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#433	C₂	semidirect
3. C₁₉×#2314	C₂	semidirect
4. C₁₉×#1983	C₂	semidirect
5. C₁₉×#1981	C₂	semidirect
6. C₁₉×#1960	C₂	semidirect
7. C₁₉×#1959	C₂	semidirect
8. C₁₉×#1958	C₂	semidirect
9. C₁₉×#1956	C₂	semidirect
11. C₁₉×#1787	C₂	semidirect
15. C₁₉×#536	C₄	semidirect
171. #21814	C₁₉	direct (N × H)
228. C₂×#433	C₂×C₁₉	semidirect
229. #2314	C₂×C₁₉	semidirect
230. #1983	C₂×C₁₉	semidirect
231. #1981	C₂×C₁₉	semidirect
232. #1960	C₂×C₁₉	semidirect
233. #1959	C₂×C₁₉	semidirect
234. #1958	C₂×C₁₉	semidirect
235. #1956	C₂×C₁₉	semidirect
237. #1787	C₂×C₁₉	semidirect
266. #536	C₄×C₁₉	semidirect
359. C₁₉	#21814	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×#536	2
C₂×C₁₉×#433	2
C₁₉×#2314	2
C₁₉×#1983	2
C₁₉×#1981	2
C₁₉×#1960	2
C₁₉×#1959	2
C₁₉×#1958	2
C₁₉×#1956	2
C₁₉×#1788	2
C₁₉×#1787	2
#21814	19

Subgroups — C19×#21814 #18027773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21814 #18027773