Subgroups — C₁₉×#21515 #18027474

Order 4864.

1044 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2328	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#460	C₄	1	8	yes	complemented
25	C₁₉×#440	—	2	4	no	—
26	C₄×SD₁₆×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#390	C₂²	1	1	yes	characteristic
42	C₁₉×#390	C₂²	1	1	yes	characteristic
43	C₁₉×#386	—	2	1	no	—
44	C₁₉×#386	—	2	1	no	—
45	C₁₉×#386	—	2	1	no	—
46	C₁₉×#386	—	2	1	no	—
47	C₁₉×#382	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#376	—	2	1	no	—
55	C₁₉×#376	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₁₉×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	—	2	1	no	—
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	—	2	1	no	—
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂×SD₁₆×C₁₉	—	2	2	no	—
70	C₂×SD₁₆×C₁₉	—	2	2	no	—
71	C₂×SD₁₆×C₁₉	—	2	2	no	—
72	C₂×SD₁₆×C₁₉	—	2	2	no	—
73	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
74	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#127	—	2	2	no	—
80	C₁₉×#127	C₂×C₄	1	4	yes	—
81	C₄×Q₈×C₁₉	—	2	2	no	—
82	C₄×Q₈×C₁₉	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
86	C₄×Q₈×C₁₉	D₄	1	4	yes	complemented
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	2	no	—
115	C₁₉×#106	—	2	2	no	—
116	C₁₉×C₄⋊C₈	—	2	2	no	—
117	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	C₂×C₄	1	4	yes	complemented
125	C₁₉×#102	C₂×C₄	1	4	yes	complemented
126	C₁₉×#97	—	2	2	no	—
127	C₄×C₈×C₁₉	—	2	2	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	D₄	1	1	yes	characteristic
134	C₁₉×#95	D₄	1	1	yes	characteristic
135	C₁₉×#95	D₄	1	1	yes	characteristic
136	C₁₉×#95	D₄	1	1	yes	characteristic
137	C₂⁴×C₁₉	—	2	1	no	—
138	C₂⁴×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₉	#41	1	2	yes	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	2	4	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	8	1	no	—
158	C₂×D₄×C₁₉	—	8	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
162	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	4	2	no	—
170	C₂²×C₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	—	8	1	no	—
172	C₂²×C₄×C₁₉	—	8	1	no	—
173	C₂²×C₄×C₁₉	—	8	1	no	—
174	C₂²×C₄×C₁₉	—	8	1	no	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
182	SD₁₆×C₁₉	—	2	8	no	—
183	SD₁₆×C₁₉	—	2	8	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
195	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
196	C₄⋊C₄×C₁₉	—	2	4	no	—
197	C₄⋊C₄×C₁₉	—	2	4	no	—
198	C₄⋊C₄×C₁₉	—	2	4	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₁₉	#41	1	2	yes	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	8	1	no	—
212	C₂²⋊C₄×C₁₉	—	8	1	no	—
213	C₂²⋊C₄×C₁₉	—	8	1	no	—
214	C₂²⋊C₄×C₁₉	—	8	1	no	—
215	C₄²×C₁₉	—	2	4	no	—
216	C₄²×C₁₉	—	2	4	no	—
217	C₄²×C₁₉	—	2	4	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	8	1	no	—
221	C₄²×C₁₉	—	8	1	no	—
222	C₄²×C₁₉	—	8	1	no	—
223	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
224	C₄²×C₁₉	C₂×D₄	1	2	yes	—
225	C₄²×C₁₉	#41	1	2	yes	—
226	C₄²×C₁₉	#41	1	2	yes	—
227	#21515	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₁₉	—	2	2	no	—
229	C₂³×C₁₉	—	2	2	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₁₉	—	2	2	no	—
244	Q₈×C₁₉	—	2	2	no	—
245	Q₈×C₁₉	—	2	2	no	—
246	Q₈×C₁₉	C₄×D₄	1	4	yes	—
247	D₄×C₁₉	—	2	2	no	—
248	D₄×C₁₉	—	2	2	no	—
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	4	1	no	—
254	D₄×C₁₉	—	4	1	no	—
255	D₄×C₁₉	—	8	4	no	—
256	D₄×C₁₉	—	8	4	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	8	4	no	—
290	C₂×C₄×C₁₉	—	8	4	no	—
291	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
292	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
293	C₂×C₄×C₁₉	#121	1	2	yes	—
294	C₂×C₄×C₁₉	#121	1	2	yes	—
295	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
301	C₈×C₁₉	—	2	2	no	—
302	C₈×C₁₉	—	2	2	no	—
303	C₈×C₁₉	—	4	1	no	—
304	C₈×C₁₉	—	4	1	no	—
305	C₂×#460	C₂×C₁₉	1	1	yes	characteristic
306	C₂×#440	C₂×C₁₉	1	1	yes	characteristic, complemented
307	C₂×C₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#2328	C₂×C₁₉	1	1	yes	characteristic
309	#2276	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1982	C₂×C₁₉	1	1	yes	characteristic
311	#1949	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1805	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1768	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1762	C₂×C₁₉	1	1	yes	characteristic, complemented
319	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	2	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	8	1	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	—	8	1	no	—
334	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
335	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
336	C₂²×C₁₉	#525	1	1	yes	characteristic
337	C₂²×C₁₉	#576	1	1	yes	characteristic
338	C₂²×C₁₉	#577	1	1	yes	characteristic
339	C₂²×C₁₉	#577	1	1	yes	characteristic
340	C₂²×C₁₉	#577	1	1	yes	characteristic
341	C₄×C₁₉	—	2	2	no	—
342	C₄×C₁₉	—	2	2	no	—
343	C₄×C₁₉	—	2	2	no	—
344	C₄×C₁₉	—	2	2	no	—
345	C₄×C₁₉	—	2	4	no	—
346	C₄×C₁₉	—	4	1	no	—
347	C₄×C₁₉	—	4	2	no	—
348	C₄×C₁₉	—	4	1	no	—
349	C₄×C₁₉	—	4	2	no	—
350	C₄×C₁₉	—	4	2	no	—
351	C₄×C₁₉	—	8	1	no	—
352	C₄×C₁₉	—	8	1	no	—
353	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
354	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
355	C₄×C₁₉	#529	1	1	yes	characteristic
356	C₄×C₁₉	#532	1	1	yes	characteristic
357	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
358	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
365	#460	C₄×C₁₉	1	8	yes	complemented
366	#440	—	2	4	no	—
367	C₄×SD₁₆	—	2	4	no	—
368	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
382	#390	C₂²×C₁₉	1	1	yes	characteristic
383	#390	C₂²×C₁₉	1	1	yes	characteristic
384	#386	—	2	1	no	—
385	#386	—	2	1	no	—
386	#386	—	2	1	no	—
387	#386	—	2	1	no	—
388	#382	C₂²×C₁₉	1	1	yes	characteristic
389	C₄×C₄⋊C₄	—	2	1	no	—
390	C₄×C₄⋊C₄	—	2	1	no	—
391	C₄×C₄⋊C₄	—	2	1	no	—
392	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
393	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
395	#376	—	2	1	no	—
396	#376	C₂²×C₁₉	1	1	yes	characteristic
397	#340	C₂²×C₁₉	1	1	yes	characteristic
398	#340	C₂²×C₁₉	1	1	yes	characteristic
399	#340	C₂²×C₁₉	1	1	yes	characteristic
400	#340	C₂²×C₁₉	1	1	yes	characteristic
401	#336	C₂²×C₁₉	1	1	yes	characteristic
402	#336	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×C₁₉	—	8	2	no	—
404	C₂×C₁₉	—	8	2	no	—
405	C₂×C₁₉	C₄×#121	1	1	yes	characteristic
406	C₂×C₁₉	#2946	1	1	yes	characteristic
407	C₂×C₁₉	#2949	1	1	yes	characteristic
408	C₂×C₁₉	#3043	1	1	yes	characteristic
409	C₂×C₁₉	#3045	1	1	yes	characteristic
410	C₂×C₁₉	#3119	1	1	yes	characteristic
411	C₂×C₁₉	#3126	1	1	yes	characteristic
412	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂³×C₄	—	2	1	no	—
418	C₂³×C₄	—	2	1	no	—
419	C₂×SD₁₆	—	2	2	no	—
420	C₂×SD₁₆	—	2	2	no	—
421	C₂×SD₁₆	—	2	2	no	—
422	C₂×SD₁₆	—	2	2	no	—
423	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
424	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
425	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	#127	—	2	2	no	—
430	#127	C₂×C₄×C₁₉	1	4	yes	—
431	C₄×Q₈	—	2	2	no	—
432	C₄×Q₈	—	2	2	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
436	C₄×Q₈	D₄×C₁₉	1	4	yes	complemented
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
464	#107	—	2	2	no	—
465	#106	—	2	2	no	—
466	C₄⋊C₈	—	2	2	no	—
467	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	complemented
468	#103	—	2	2	no	—
469	#103	—	2	2	no	—
470	#102	—	2	2	no	—
471	#102	—	2	2	no	—
472	#102	—	2	2	no	—
473	#102	—	2	2	no	—
474	#102	C₂×C₄×C₁₉	1	4	yes	complemented
475	#102	C₂×C₄×C₁₉	1	4	yes	complemented
476	#97	—	2	2	no	—
477	C₄×C₈	—	2	2	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	D₄×C₁₉	1	1	yes	characteristic
484	#95	D₄×C₁₉	1	1	yes	characteristic
485	#95	D₄×C₁₉	1	1	yes	characteristic
486	#95	D₄×C₁₉	1	1	yes	characteristic
487	C₁₉	#21515	1	1	yes	characteristic, direct product factor, Sylow
488	C₂⁴	—	2	1	no	—
489	C₂⁴	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
494	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
495	C₂×Q₈	#41×C₁₉	1	2	yes	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	8	1	no	—
509	C₂×D₄	—	8	1	no	—
510	C₂×D₄	—	8	1	no	—
511	C₂×D₄	—	8	1	no	—
512	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
513	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	8	1	no	—
523	C₂²×C₄	—	8	1	no	—
524	C₂²×C₄	—	8	1	no	—
525	C₂²×C₄	—	8	1	no	—
526	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
533	SD₁₆	—	2	8	no	—
534	SD₁₆	—	2	8	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
546	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
558	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
559	C₄⋊C₄	#41×C₁₉	1	2	yes	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	8	1	no	—
563	C₂²⋊C₄	—	8	1	no	—
564	C₂²⋊C₄	—	8	1	no	—
565	C₂²⋊C₄	—	8	1	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	8	1	no	—
572	C₄²	—	8	1	no	—
573	C₄²	—	8	1	no	—
574	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
575	C₄²	C₂×D₄×C₁₉	1	2	yes	—
576	C₄²	#41×C₁₉	1	2	yes	—
577	C₄²	#41×C₁₉	1	2	yes	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	2	2	no	—
596	Q₈	C₄×D₄×C₁₉	1	4	yes	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	2	no	—
600	D₄	—	2	2	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	8	4	no	—
606	D₄	—	8	4	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
642	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
643	C₂×C₄	C₁₉×#121	1	2	yes	—
644	C₂×C₄	C₁₉×#121	1	2	yes	—
645	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
647	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
648	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
649	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
650	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
651	C₈	—	2	2	no	—
652	C₈	—	2	2	no	—
653	C₈	—	4	1	no	—
654	C₈	—	4	1	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	8	1	no	—
662	C₂²	—	8	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
670	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
671	C₂²	C₁₉×#525	1	1	yes	characteristic
672	C₂²	C₁₉×#576	1	1	yes	characteristic
673	C₂²	C₁₉×#577	1	1	yes	characteristic
674	C₂²	C₁₉×#577	1	1	yes	characteristic
675	C₂²	C₁₉×#577	1	1	yes	characteristic
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	4	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	1	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
689	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
690	C₄	C₁₉×#529	1	1	yes	characteristic
691	C₄	C₁₉×#532	1	1	yes	characteristic
692	C₂	—	8	2	no	—
693	C₂	—	8	2	no	—
694	C₂	C₄×C₁₉×#121	1	1	yes	characteristic
695	C₂	C₁₉×#2946	1	1	yes	characteristic
696	C₂	C₁₉×#2949	1	1	yes	characteristic
697	C₂	C₁₉×#3043	1	1	yes	characteristic
698	C₂	C₁₉×#3045	1	1	yes	characteristic
699	C₂	C₁₉×#3119	1	1	yes	characteristic
700	C₂	C₁₉×#3126	1	1	yes	characteristic

	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×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#440	C₂	semidirect
3. C₂×C₄×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#2276	C₂	semidirect
7. C₁₉×#1949	C₂	semidirect
8. C₁₉×#1926	C₂	semidirect
9. C₁₉×#1925	C₂	semidirect
10. C₁₉×#1880	C₂	semidirect
11. C₁₉×#1880	C₂	semidirect
12. C₁₉×#1805	C₂	semidirect
13. C₁₉×#1768	C₂	semidirect
14. C₁₉×#1762	C₂	semidirect
15. C₄×C₁₉×#102	C₂	semidirect
24. C₁₉×#460	C₄	semidirect
73. C₂×SD₁₆×C₁₉	C₂×C₄	semidirect
74. C₂×SD₁₆×C₁₉	C₂×C₄	semidirect
85. C₄×Q₈×C₁₉	C₂×C₄	semidirect
86. C₄×Q₈×C₁₉	D₄	semidirect
117. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
124. C₁₉×#102	C₂×C₄	semidirect
125. C₁₉×#102	C₂×C₄	semidirect
227. #21515	C₁₉	direct (N × H)
306. C₂×#440	C₂×C₁₉	semidirect
307. C₂×C₄×SD₁₆	C₂×C₁₉	semidirect
309. #2276	C₂×C₁₉	semidirect
311. #1949	C₂×C₁₉	semidirect
312. #1926	C₂×C₁₉	semidirect
313. #1925	C₂×C₁₉	semidirect
314. #1880	C₂×C₁₉	semidirect
315. #1880	C₂×C₁₉	semidirect
316. #1805	C₂×C₁₉	semidirect
317. #1768	C₂×C₁₉	semidirect
318. #1762	C₂×C₁₉	semidirect
319. C₄×#102	C₂×C₁₉	semidirect
365. #460	C₄×C₁₉	semidirect
423. C₂×SD₁₆	C₂×C₄×C₁₉	semidirect
424. C₂×SD₁₆	C₂×C₄×C₁₉	semidirect
435. C₄×Q₈	C₂×C₄×C₁₉	semidirect
436. C₄×Q₈	D₄×C₁₉	semidirect
467. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
474. #102	C₂×C₄×C₁₉	semidirect
475. #102	C₂×C₄×C₁₉	semidirect
487. C₁₉	#21515	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×#460	2
C₂×C₁₉×#440	2
C₂×C₄×SD₁₆×C₁₉	2
C₁₉×#2328	2
C₁₉×#2276	2
C₁₉×#1982	2
C₁₉×#1949	2
C₁₉×#1926	2
C₁₉×#1925	2
C₁₉×#1880	2
C₁₉×#1805	2
C₁₉×#1768	2
C₁₉×#1762	2
C₄×C₁₉×#102	2
#21515	19

Subgroups — C19×#21515 #18027474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21515 #18027474