Subgroups — C₁₉×#11064 #18017023

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#419	—	2	2	no	—
16	C₁₉×#419	—	2	2	no	—
17	C₁₉×#419	—	2	2	no	—
18	C₁₉×#419	C₄	1	4	yes	complemented
19	C₂×C₁₉×#103	—	2	1	no	—
20	C₂×C₁₉×#103	—	2	1	no	—
21	C₂×C₁₉×#103	—	2	2	no	—
22	C₁₉×#391	—	2	2	no	—
23	C₁₉×#391	—	2	2	no	—
24	C₁₉×#389	—	2	2	no	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#384	—	2	1	no	—
27	C₁₉×#382	—	2	1	no	—
28	C₂×C₁₉×#95	—	2	2	no	—
29	C₁₉×#343	—	2	2	no	—
30	C₁₉×#339	—	2	2	no	—
31	C₁₉×#339	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
44	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
45	C₂²×Q₈×C₁₉	Q₈	1	2	yes	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	D₄	1	2	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₁₉×#117	—	2	1	no	—
70	C₁₉×#117	C₂×C₄	1	2	yes	—
71	C₁₉×#117	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	D₄	1	2	yes	—
92	C₁₉×#103	—	2	4	no	—
93	C₁₉×#103	—	2	4	no	—
94	C₁₉×#103	—	2	8	no	—
95	C₁₉×#95	—	2	8	no	—
96	C₁₉×#95	—	2	4	no	—
97	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	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	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	—	4	1	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂×Q₈×C₁₉	—	4	1	no	—
125	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
126	C₂²×C₄×C₁₉	—	2	4	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	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	4	2	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	C₂²×C₄×C₁₉	—	4	4	no	—
145	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
159	M₁₆×C₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	4	1	no	—
164	M₁₆×C₁₉	—	4	1	no	—
165	M₁₆×C₁₉	—	4	1	no	—
166	M₁₆×C₁₉	—	4	1	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	4	1	no	—
170	C₂×C₈×C₁₉	—	4	1	no	—
171	C₂×C₈×C₁₉	—	4	1	no	—
172	C₂×C₈×C₁₉	—	4	1	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	1	no	—
180	C₄⋊C₄×C₁₉	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	8	4	no	—
183	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	4	1	no	—
187	C₂²⋊C₄×C₁₉	—	4	1	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	4	1	no	—
193	C₄²×C₁₉	—	4	1	no	—
194	C₄²×C₁₉	—	4	1	no	—
195	C₄²×C₁₉	—	4	1	no	—
196	#11064	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
200	C₂³×C₁₉	#120	1	1	yes	characteristic
201	C₂³×C₁₉	#120	1	1	yes	characteristic
202	C₂³×C₁₉	#121	1	1	yes	characteristic
203	C₂³×C₁₉	#121	1	1	yes	characteristic
204	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂³×C₁₉	#124	1	1	yes	characteristic
206	Q₈×C₁₉	—	2	4	no	—
207	Q₈×C₁₉	—	2	4	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	Q₈×C₁₉	—	4	2	no	—
213	Q₈×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	4	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	4	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	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	4	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
265	C₈×C₁₉	—	4	2	no	—
266	C₈×C₁₉	—	4	2	no	—
267	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
268	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
269	#2317	C₂×C₁₉	1	1	yes	characteristic
270	C₂×#391	C₂×C₁₉	1	1	yes	characteristic
271	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
272	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
273	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	2	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	#385	1	1	yes	characteristic
283	C₂²×C₁₉	#386	1	1	yes	characteristic
284	C₂²×C₁₉	#388	1	1	yes	characteristic
285	C₂²×C₁₉	#392	1	1	yes	characteristic
286	C₂²×C₁₉	#393	1	1	yes	characteristic
287	C₂²×C₁₉	#394	1	1	yes	characteristic
288	C₂²×C₁₉	#396	1	1	yes	characteristic
289	C₂²×C₁₉	#455	1	2	yes	—
290	C₂²×C₁₉	#456	1	2	yes	—
291	C₄×C₁₉	—	4	4	no	—
292	C₄×C₁₉	—	4	4	no	—
293	C₄×C₁₉	—	4	4	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	—	8	2	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	#380	1	1	yes	characteristic
298	C₄×C₁₉	#385	1	1	yes	characteristic
299	C₄×C₁₉	#388	1	1	yes	characteristic
300	C₄×C₁₉	#390	1	1	yes	characteristic
301	C₄×C₁₉	#394	1	1	yes	characteristic
302	C₄×C₁₉	#396	1	1	yes	characteristic
303	C₄×C₁₉	#397	1	1	yes	characteristic
304	C₄×C₁₉	#399	1	1	yes	characteristic
305	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
306	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
307	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
311	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
312	#419	—	2	2	no	—
313	#419	—	2	2	no	—
314	#419	—	2	2	no	—
315	#419	C₄×C₁₉	1	4	yes	complemented
316	C₂×#103	—	2	1	no	—
317	C₂×#103	—	2	1	no	—
318	C₂×#103	—	2	2	no	—
319	#391	—	2	2	no	—
320	#391	—	2	2	no	—
321	#389	—	2	2	no	—
322	#385	—	2	2	no	—
323	#384	—	2	1	no	—
324	#382	—	2	1	no	—
325	C₂×#95	—	2	2	no	—
326	#343	—	2	2	no	—
327	#339	—	2	2	no	—
328	#339	—	2	2	no	—
329	C₂×C₁₉	—	2	1	no	—
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	#1439	1	1	yes	characteristic
334	C₂×C₁₉	#1882	1	2	yes	—
335	C₂×C₁₉	#2004	1	1	yes	characteristic
336	C₂×C₁₉	#2005	1	1	yes	characteristic
337	C₂×C₁₉	#2028	1	2	yes	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	—	2	1	no	—
340	C₂²×Q₈	—	2	1	no	—
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×Q₈	—	2	1	no	—
343	C₂²×Q₈	—	2	1	no	—
344	C₂²×Q₈	—	2	1	no	—
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×Q₈	—	2	1	no	—
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
350	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
351	C₂²×Q₈	Q₈×C₁₉	1	2	yes	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	D₄×C₁₉	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
367	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	C₂×C₄×C₁₉	1	2	yes	—
377	#117	D₄×C₁₉	1	2	yes	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	4	no	—
385	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	D₄×C₁₉	1	2	yes	—
398	#103	—	2	4	no	—
399	#103	—	2	4	no	—
400	#103	—	2	8	no	—
401	#95	—	2	8	no	—
402	#95	—	2	4	no	—
403	C₁₉	#11064	1	1	yes	characteristic, direct product factor, Sylow
404	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	—	4	1	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×Q₈	—	4	1	no	—
428	C₂×Q₈	—	4	1	no	—
429	C₂×Q₈	—	4	1	no	—
430	C₂×Q₈	—	4	1	no	—
431	C₂×Q₈	—	4	1	no	—
432	C₂×Q₈	C₄⋊C₄×C₁₉	1	4	yes	complemented
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
463	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	4	1	no	—
473	M₁₆	—	4	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	8	4	no	—
490	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	4	1	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	—	4	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
506	C₂³	C₁₉×#120	1	1	yes	characteristic
507	C₂³	C₁₉×#120	1	1	yes	characteristic
508	C₂³	C₁₉×#121	1	1	yes	characteristic
509	C₂³	C₁₉×#121	1	1	yes	characteristic
510	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂³	C₁₉×#124	1	1	yes	characteristic
512	Q₈	—	2	4	no	—
513	Q₈	—	2	4	no	—
514	Q₈	—	4	2	no	—
515	Q₈	—	4	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	4	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
546	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
548	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
549	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
550	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
551	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
552	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
553	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
554	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
555	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
556	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
557	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
558	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
559	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
560	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
561	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
562	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
563	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
564	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
565	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
566	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
567	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
568	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
569	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
570	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
571	C₈	—	4	2	no	—
572	C₈	—	4	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	C₁₉×#385	1	1	yes	characteristic
582	C₂²	C₁₉×#386	1	1	yes	characteristic
583	C₂²	C₁₉×#388	1	1	yes	characteristic
584	C₂²	C₁₉×#392	1	1	yes	characteristic
585	C₂²	C₁₉×#393	1	1	yes	characteristic
586	C₂²	C₁₉×#394	1	1	yes	characteristic
587	C₂²	C₁₉×#396	1	1	yes	characteristic
588	C₂²	C₁₉×#455	1	2	yes	—
589	C₂²	C₁₉×#456	1	2	yes	—
590	C₄	—	4	4	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	—	8	2	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	C₁₉×#380	1	1	yes	characteristic
597	C₄	C₁₉×#385	1	1	yes	characteristic
598	C₄	C₁₉×#388	1	1	yes	characteristic
599	C₄	C₁₉×#390	1	1	yes	characteristic
600	C₄	C₁₉×#394	1	1	yes	characteristic
601	C₄	C₁₉×#396	1	1	yes	characteristic
602	C₄	C₁₉×#397	1	1	yes	characteristic
603	C₄	C₁₉×#399	1	1	yes	characteristic
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	C₁₉×#1439	1	1	yes	characteristic
609	C₂	C₁₉×#1882	1	2	yes	—
610	C₂	C₁₉×#2004	1	1	yes	characteristic
611	C₂	C₁₉×#2005	1	1	yes	characteristic
612	C₂	C₁₉×#2028	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
18. C₁₉×#419	C₄	semidirect
125. C₂×Q₈×C₁₉	C₄⋊C₄	semidirect
196. #11064	C₁₉	direct (N × H)
315. #419	C₄×C₁₉	semidirect
403. C₁₉	#11064	direct (N × H)
432. C₂×Q₈	C₄⋊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×#419	2
C₁₉×#2317	2
C₂×C₁₉×#391	2
C₂×C₁₉×#343	2
C₂×C₁₉×#339	2
#11064	19

Subgroups — C19×#11064 #18017023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11064 #18017023