Subgroups — C₁₉×#11021 #18016980

Order 4864.

1278 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#137	—	2	2	no	—
11	C₂×C₁₉×#137	—	2	2	no	—
12	C₂×C₁₉×#137	—	2	2	no	—
13	C₂×C₁₉×#137	—	2	2	no	—
14	C₂×C₁₉×#137	—	2	2	no	—
15	C₂×C₁₉×#137	C₄	1	4	yes	complemented
16	C₂²×Q₁₆×C₁₉	—	2	1	no	—
17	C₂²×SD₁₆×C₁₉	—	2	1	no	—
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#417	—	2	2	no	—
24	C₁₉×#417	—	2	2	no	—
25	C₂×C₁₉×#103	—	2	2	no	—
26	C₂×C₁₉×#103	—	2	1	no	—
27	C₂×C₁₉×#103	—	2	2	no	—
28	C₂×C₁₉×#103	—	2	2	no	—
29	C₂×C₁₉×#102	—	2	1	no	—
30	C₂×C₁₉×#101	—	2	2	no	—
31	C₂×C₁₉×#101	—	2	2	no	—
32	C₂×C₁₉×#101	—	2	2	no	—
33	C₁₉×#408	—	2	2	no	—
34	C₁₉×#408	—	2	2	no	—
35	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
36	C₁₉×#343	—	2	2	no	—
37	C₁₉×#341	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂×#41×C₁₉	—	2	1	no	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
49	C₂×#41×C₁₉	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂²×Q₈×C₁₉	—	2	1	no	—
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	—	2	1	no	—
59	C₂²×Q₈×C₁₉	—	2	1	no	—
60	C₂²×Q₈×C₁₉	—	2	1	no	—
61	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
62	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
63	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	—	2	1	no	—
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×#137	—	2	8	no	—
72	C₁₉×#137	—	2	8	no	—
73	C₁₉×#137	—	2	8	no	—
74	C₁₉×#137	—	2	8	no	—
75	C₂×Q₁₆×C₁₉	—	2	4	no	—
76	C₂×Q₁₆×C₁₉	—	2	4	no	—
77	C₂×Q₁₆×C₁₉	—	2	4	no	—
78	C₂×SD₁₆×C₁₉	—	2	4	no	—
79	C₂×SD₁₆×C₁₉	—	2	4	no	—
80	C₂×SD₁₆×C₁₉	—	2	4	no	—
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₂×M₁₆×C₁₉	—	2	1	no	—
83	C₂×M₁₆×C₁₉	—	2	1	no	—
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂×M₁₆×C₁₉	—	2	1	no	—
86	C₂×M₁₆×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂×M₁₆×C₁₉	—	2	1	no	—
89	C₂×M₁₆×C₁₉	—	2	1	no	—
90	C₂×M₁₆×C₁₉	—	2	1	no	—
91	C₂×M₁₆×C₁₉	—	2	1	no	—
92	C₂×M₁₆×C₁₉	—	2	1	no	—
93	C₂×M₁₆×C₁₉	—	2	1	no	—
94	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
95	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
96	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
97	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
98	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
99	C₂²×C₈×C₁₉	—	2	1	no	—
100	C₂²×C₈×C₁₉	—	2	1	no	—
101	C₂²×C₈×C₁₉	—	2	1	no	—
102	C₂²×C₈×C₁₉	—	2	1	no	—
103	C₂²×C₈×C₁₉	—	2	1	no	—
104	C₂²×C₈×C₁₉	—	2	1	no	—
105	C₂²×C₈×C₁₉	—	2	1	no	—
106	C₂²×C₈×C₁₉	—	2	1	no	—
107	C₂²×C₈×C₁₉	—	2	1	no	—
108	C₂²×C₈×C₁₉	D₄	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
115	C₁₉×#103	—	2	8	no	—
116	C₁₉×#103	—	2	4	no	—
117	C₁₉×#102	—	2	4	no	—
118	C₁₉×#101	—	2	8	no	—
119	C₁₉×C₂²⋊C₈	—	2	8	no	—
120	C₂⁴×C₁₉	—	2	1	no	—
121	C₂⁴×C₁₉	#41	1	1	yes	characteristic
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	2	2	no	—
127	#41×C₁₉	—	2	2	no	—
128	#41×C₁₉	—	2	2	no	—
129	#41×C₁₉	—	2	2	no	—
130	#41×C₁₉	—	4	1	no	—
131	#41×C₁₉	—	4	1	no	—
132	#41×C₁₉	—	4	1	no	—
133	#41×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	4	1	no	—
135	#41×C₁₉	—	4	1	no	—
136	#41×C₁₉	—	4	1	no	—
137	#41×C₁₉	—	4	1	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	2	no	—
143	C₂×Q₈×C₁₉	—	2	2	no	—
144	C₂×Q₈×C₁₉	—	2	2	no	—
145	C₂×Q₈×C₁₉	—	2	2	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	2	2	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	2	no	—
155	C₂×Q₈×C₁₉	—	2	2	no	—
156	C₂×Q₈×C₁₉	—	2	2	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	4	1	no	—
159	C₂×Q₈×C₁₉	—	4	1	no	—
160	C₂×Q₈×C₁₉	—	4	1	no	—
161	C₂×Q₈×C₁₉	—	4	1	no	—
162	C₂×Q₈×C₁₉	—	4	1	no	—
163	C₂×Q₈×C₁₉	—	4	1	no	—
164	C₂×Q₈×C₁₉	—	4	1	no	—
165	C₂×Q₈×C₁₉	—	4	1	no	—
166	C₂×Q₈×C₁₉	—	4	1	no	—
167	C₂×Q₈×C₁₉	—	4	1	no	—
168	C₂×Q₈×C₁₉	—	4	1	no	—
169	C₂×Q₈×C₁₉	—	4	1	no	—
170	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
171	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
172	C₂×D₄×C₁₉	—	2	2	no	—
173	C₂×D₄×C₁₉	—	2	2	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	1	no	—
176	C₂×D₄×C₁₉	—	2	1	no	—
177	C₂×D₄×C₁₉	—	2	1	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	4	1	no	—
180	C₂×D₄×C₁₉	—	4	1	no	—
181	C₂×D₄×C₁₉	—	4	1	no	—
182	C₂×D₄×C₁₉	—	4	1	no	—
183	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	2	2	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	—	4	1	no	—
192	C₂²×C₄×C₁₉	—	4	1	no	—
193	C₂²×C₄×C₁₉	—	4	1	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	4	1	no	—
196	C₂²×C₄×C₁₉	—	4	1	no	—
197	C₂²×C₄×C₁₉	—	4	1	no	—
198	C₂²×C₄×C₁₉	—	4	1	no	—
199	C₂²×C₄×C₁₉	—	4	1	no	—
200	C₂²×C₄×C₁₉	—	4	1	no	—
201	C₂²×C₄×C₁₉	—	8	2	no	—
202	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
214	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
216	Q₁₆×C₁₉	—	2	16	no	—
217	SD₁₆×C₁₉	—	2	16	no	—
218	M₁₆×C₁₉	—	2	2	no	—
219	M₁₆×C₁₉	—	2	2	no	—
220	M₁₆×C₁₉	—	2	2	no	—
221	M₁₆×C₁₉	—	2	2	no	—
222	M₁₆×C₁₉	—	2	2	no	—
223	M₁₆×C₁₉	—	2	2	no	—
224	M₁₆×C₁₉	—	2	2	no	—
225	M₁₆×C₁₉	—	4	1	no	—
226	M₁₆×C₁₉	—	4	1	no	—
227	M₁₆×C₁₉	—	4	1	no	—
228	M₁₆×C₁₉	—	4	1	no	—
229	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
230	C₂×C₈×C₁₉	—	2	2	no	—
231	C₂×C₈×C₁₉	—	2	2	no	—
232	C₂×C₈×C₁₉	—	2	2	no	—
233	C₂×C₈×C₁₉	—	2	2	no	—
234	C₂×C₈×C₁₉	—	2	2	no	—
235	C₂×C₈×C₁₉	—	2	2	no	—
236	C₂×C₈×C₁₉	—	2	2	no	—
237	C₂×C₈×C₁₉	—	2	2	no	—
238	C₂×C₈×C₁₉	—	4	1	no	—
239	C₂×C₈×C₁₉	—	4	1	no	—
240	C₂×C₈×C₁₉	—	4	1	no	—
241	C₂×C₈×C₁₉	—	4	1	no	—
242	C₂×C₈×C₁₉	—	4	1	no	—
243	C₂×C₈×C₁₉	—	4	1	no	—
244	C₂×C₈×C₁₉	—	4	1	no	—
245	C₂×C₈×C₁₉	—	4	1	no	—
246	C₄⋊C₄×C₁₉	—	2	2	no	—
247	C₄⋊C₄×C₁₉	—	2	2	no	—
248	C₄⋊C₄×C₁₉	—	4	1	no	—
249	C₄⋊C₄×C₁₉	—	4	1	no	—
250	#11021	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂³×C₁₉	—	2	2	no	—
252	C₂³×C₁₉	—	2	2	no	—
253	C₂³×C₁₉	—	2	2	no	—
254	C₂³×C₁₉	—	4	1	no	—
255	C₂³×C₁₉	—	4	1	no	—
256	C₂³×C₁₉	—	4	2	no	—
257	C₂³×C₁₉	—	4	2	no	—
258	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
259	C₂³×C₁₉	#121	1	1	yes	characteristic
260	C₂³×C₁₉	#121	1	1	yes	characteristic
261	C₂³×C₁₉	#121	1	1	yes	characteristic
262	C₂³×C₁₉	#123	1	1	yes	characteristic
263	C₂³×C₁₉	#123	1	1	yes	characteristic
264	C₂³×C₁₉	#124	1	1	yes	characteristic
265	Q₈×C₁₉	—	2	4	no	—
266	Q₈×C₁₉	—	2	2	no	—
267	Q₈×C₁₉	—	2	4	no	—
268	Q₈×C₁₉	—	2	2	no	—
269	Q₈×C₁₉	—	4	2	no	—
270	Q₈×C₁₉	—	4	2	no	—
271	Q₈×C₁₉	—	4	2	no	—
272	Q₈×C₁₉	—	4	2	no	—
273	Q₈×C₁₉	—	4	2	no	—
274	Q₈×C₁₉	—	4	1	no	—
275	Q₈×C₁₉	—	4	2	no	—
276	Q₈×C₁₉	—	4	1	no	—
277	D₄×C₁₉	—	2	2	no	—
278	D₄×C₁₉	—	2	2	no	—
279	D₄×C₁₉	—	4	2	no	—
280	D₄×C₁₉	—	4	2	no	—
281	D₄×C₁₉	—	4	2	no	—
282	D₄×C₁₉	—	4	2	no	—
283	D₄×C₁₉	—	4	1	no	—
284	D₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	4	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	2	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	2	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	2	no	—
293	C₂×C₄×C₁₉	—	4	2	no	—
294	C₂×C₄×C₁₉	—	4	2	no	—
295	C₂×C₄×C₁₉	—	4	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	—	4	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	8	2	no	—
301	C₂×C₄×C₁₉	—	8	2	no	—
302	C₂×C₄×C₁₉	—	8	2	no	—
303	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
310	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
311	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
312	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
313	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
314	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
315	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
316	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
317	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
318	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
319	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
320	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
321	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
322	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
323	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
324	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
325	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
326	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
327	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
328	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
329	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
330	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
331	C₈×C₁₉	—	2	4	no	—
332	C₈×C₁₉	—	4	2	no	—
333	C₈×C₁₉	—	4	2	no	—
334	C₈×C₁₉	—	4	2	no	—
335	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic
336	C₂×#417	C₂×C₁₉	1	1	yes	characteristic
337	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
338	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
339	C₂×#408	C₂×C₁₉	1	1	yes	characteristic
340	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
341	C₂×#341	C₂×C₁₉	1	1	yes	characteristic, complemented
342	C₂²×C₁₉	—	2	2	no	—
343	C₂²×C₁₉	—	2	2	no	—
344	C₂²×C₁₉	—	2	2	no	—
345	C₂²×C₁₉	—	2	2	no	—
346	C₂²×C₁₉	—	2	1	no	—
347	C₂²×C₁₉	—	2	1	no	—
348	C₂²×C₁₉	—	2	1	no	—
349	C₂²×C₁₉	—	2	1	no	—
350	C₂²×C₁₉	—	4	4	no	—
351	C₂²×C₁₉	—	4	2	no	—
352	C₂²×C₁₉	—	8	2	no	—
353	C₂²×C₁₉	—	8	1	no	—
354	C₂²×C₁₉	—	8	1	no	—
355	C₂²×C₁₉	#386	1	1	yes	characteristic
356	C₂²×C₁₉	#386	1	1	yes	characteristic
357	C₂²×C₁₉	#390	1	1	yes	characteristic
358	C₂²×C₁₉	#392	1	1	yes	characteristic
359	C₂²×C₁₉	#394	1	1	yes	characteristic
360	C₂²×C₁₉	#394	1	1	yes	characteristic
361	C₂²×C₁₉	#394	1	1	yes	characteristic
362	C₂²×C₁₉	#471	1	2	yes	—
363	C₂²×C₁₉	#473	1	2	yes	—
364	C₄×C₁₉	—	4	2	no	—
365	C₄×C₁₉	—	4	4	no	—
366	C₄×C₁₉	—	8	2	no	—
367	C₄×C₁₉	#379	1	1	yes	characteristic
368	C₄×C₁₉	#386	1	1	yes	characteristic
369	C₄×C₁₉	#386	1	1	yes	characteristic
370	C₄×C₁₉	#390	1	1	yes	characteristic
371	C₄×C₁₉	#392	1	1	yes	characteristic
372	C₄×C₁₉	#392	1	1	yes	characteristic
373	C₄×C₁₉	#392	1	1	yes	characteristic
374	C₄×C₁₉	#394	1	1	yes	characteristic
375	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
376	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#137	—	2	2	no	—
378	C₂×#137	—	2	2	no	—
379	C₂×#137	—	2	2	no	—
380	C₂×#137	—	2	2	no	—
381	C₂×#137	—	2	2	no	—
382	C₂×#137	C₄×C₁₉	1	4	yes	complemented
383	C₂²×Q₁₆	—	2	1	no	—
384	C₂²×SD₁₆	—	2	1	no	—
385	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
386	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
387	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
388	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
390	#417	—	2	2	no	—
391	#417	—	2	2	no	—
392	C₂×#103	—	2	2	no	—
393	C₂×#103	—	2	1	no	—
394	C₂×#103	—	2	2	no	—
395	C₂×#103	—	2	2	no	—
396	C₂×#102	—	2	1	no	—
397	C₂×#101	—	2	2	no	—
398	C₂×#101	—	2	2	no	—
399	C₂×#101	—	2	2	no	—
400	#408	—	2	2	no	—
401	#408	—	2	2	no	—
402	C₂×C₂²⋊C₈	—	2	2	no	—
403	#343	—	2	2	no	—
404	#341	—	2	2	no	—
405	C₂×C₁₉	—	2	1	no	—
406	C₂×C₁₉	—	2	1	no	—
407	C₂×C₁₉	—	2	1	no	—
408	C₂×C₁₉	—	2	1	no	—
409	C₂×C₁₉	—	8	2	no	—
410	C₂×C₁₉	#1438	1	1	yes	characteristic
411	C₂×C₁₉	#1908	1	2	yes	—
412	C₂×C₁₉	#2019	1	1	yes	characteristic
413	C₂×C₁₉	#2020	1	1	yes	characteristic
414	C₂×C₁₉	#2052	1	2	yes	—
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	1	no	—
421	C₂×#41	—	2	1	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	—	2	1	no	—
425	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
426	C₂×#41	D₄×C₁₉	1	2	yes	—
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	—	2	1	no	—
432	C₂²×Q₈	—	2	1	no	—
433	C₂²×Q₈	—	2	1	no	—
434	C₂²×Q₈	—	2	1	no	—
435	C₂²×Q₈	—	2	1	no	—
436	C₂²×Q₈	—	2	1	no	—
437	C₂²×Q₈	—	2	1	no	—
438	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
439	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
440	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
441	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
448	#137	—	2	8	no	—
449	#137	—	2	8	no	—
450	#137	—	2	8	no	—
451	#137	—	2	8	no	—
452	C₂×Q₁₆	—	2	4	no	—
453	C₂×Q₁₆	—	2	4	no	—
454	C₂×Q₁₆	—	2	4	no	—
455	C₂×SD₁₆	—	2	4	no	—
456	C₂×SD₁₆	—	2	4	no	—
457	C₂×SD₁₆	—	2	4	no	—
458	C₂×M₁₆	—	2	1	no	—
459	C₂×M₁₆	—	2	1	no	—
460	C₂×M₁₆	—	2	1	no	—
461	C₂×M₁₆	—	2	1	no	—
462	C₂×M₁₆	—	2	1	no	—
463	C₂×M₁₆	—	2	1	no	—
464	C₂×M₁₆	—	2	1	no	—
465	C₂×M₁₆	—	2	1	no	—
466	C₂×M₁₆	—	2	1	no	—
467	C₂×M₁₆	—	2	1	no	—
468	C₂×M₁₆	—	2	1	no	—
469	C₂×M₁₆	—	2	1	no	—
470	C₂×M₁₆	—	2	1	no	—
471	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
472	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
473	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
474	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
475	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
476	C₂²×C₈	—	2	1	no	—
477	C₂²×C₈	—	2	1	no	—
478	C₂²×C₈	—	2	1	no	—
479	C₂²×C₈	—	2	1	no	—
480	C₂²×C₈	—	2	1	no	—
481	C₂²×C₈	—	2	1	no	—
482	C₂²×C₈	—	2	1	no	—
483	C₂²×C₈	—	2	1	no	—
484	C₂²×C₈	—	2	1	no	—
485	C₂²×C₈	D₄×C₁₉	1	2	yes	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
492	#103	—	2	8	no	—
493	#103	—	2	4	no	—
494	#102	—	2	4	no	—
495	#101	—	2	8	no	—
496	C₂²⋊C₈	—	2	8	no	—
497	C₁₉	#11021	1	1	yes	characteristic, direct product factor, Sylow
498	C₂⁴	—	2	1	no	—
499	C₂⁴	#41×C₁₉	1	1	yes	characteristic
500	#41	—	2	2	no	—
501	#41	—	2	2	no	—
502	#41	—	2	2	no	—
503	#41	—	2	2	no	—
504	#41	—	2	2	no	—
505	#41	—	2	2	no	—
506	#41	—	2	2	no	—
507	#41	—	2	2	no	—
508	#41	—	4	1	no	—
509	#41	—	4	1	no	—
510	#41	—	4	1	no	—
511	#41	—	4	1	no	—
512	#41	—	4	1	no	—
513	#41	—	4	1	no	—
514	#41	—	4	1	no	—
515	#41	—	4	1	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	2	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	4	1	no	—
537	C₂×Q₈	—	4	1	no	—
538	C₂×Q₈	—	4	1	no	—
539	C₂×Q₈	—	4	1	no	—
540	C₂×Q₈	—	4	1	no	—
541	C₂×Q₈	—	4	1	no	—
542	C₂×Q₈	—	4	1	no	—
543	C₂×Q₈	—	4	1	no	—
544	C₂×Q₈	—	4	1	no	—
545	C₂×Q₈	—	4	1	no	—
546	C₂×Q₈	—	4	1	no	—
547	C₂×Q₈	—	4	1	no	—
548	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
549	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	4	1	no	—
558	C₂×D₄	—	4	1	no	—
559	C₂×D₄	—	4	1	no	—
560	C₂×D₄	—	4	1	no	—
561	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	4	1	no	—
570	C₂²×C₄	—	4	1	no	—
571	C₂²×C₄	—	4	1	no	—
572	C₂²×C₄	—	4	1	no	—
573	C₂²×C₄	—	4	1	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	—	4	1	no	—
577	C₂²×C₄	—	4	1	no	—
578	C₂²×C₄	—	4	1	no	—
579	C₂²×C₄	—	8	2	no	—
580	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
591	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
592	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
593	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
594	Q₁₆	—	2	16	no	—
595	SD₁₆	—	2	16	no	—
596	M₁₆	—	2	2	no	—
597	M₁₆	—	2	2	no	—
598	M₁₆	—	2	2	no	—
599	M₁₆	—	2	2	no	—
600	M₁₆	—	2	2	no	—
601	M₁₆	—	2	2	no	—
602	M₁₆	—	2	2	no	—
603	M₁₆	—	4	1	no	—
604	M₁₆	—	4	1	no	—
605	M₁₆	—	4	1	no	—
606	M₁₆	—	4	1	no	—
607	M₁₆	C₂²⋊C₄×C₁₉	1	4	yes	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	2	2	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	—	4	1	no	—
617	C₂×C₈	—	4	1	no	—
618	C₂×C₈	—	4	1	no	—
619	C₂×C₈	—	4	1	no	—
620	C₂×C₈	—	4	1	no	—
621	C₂×C₈	—	4	1	no	—
622	C₂×C₈	—	4	1	no	—
623	C₂×C₈	—	4	1	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	—	4	1	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	2	no	—
634	C₂³	—	4	2	no	—
635	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
636	C₂³	C₁₉×#121	1	1	yes	characteristic
637	C₂³	C₁₉×#121	1	1	yes	characteristic
638	C₂³	C₁₉×#121	1	1	yes	characteristic
639	C₂³	C₁₉×#123	1	1	yes	characteristic
640	C₂³	C₁₉×#123	1	1	yes	characteristic
641	C₂³	C₁₉×#124	1	1	yes	characteristic
642	Q₈	—	2	4	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	2	4	no	—
645	Q₈	—	2	2	no	—
646	Q₈	—	4	2	no	—
647	Q₈	—	4	2	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	4	2	no	—
650	Q₈	—	4	2	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	2	no	—
653	Q₈	—	4	1	no	—
654	D₄	—	2	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	4	2	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
681	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
682	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
683	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
684	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
685	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
686	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
687	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
688	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
689	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
690	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
691	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
692	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
693	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
694	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
695	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
696	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
697	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
698	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
699	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
700	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
701	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
702	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
703	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
704	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
705	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
706	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
707	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
708	C₈	—	2	4	no	—
709	C₈	—	4	2	no	—
710	C₈	—	4	2	no	—
711	C₈	—	4	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	8	1	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	2	no	—
725	C₂²	C₁₉×#386	1	1	yes	characteristic
726	C₂²	C₁₉×#386	1	1	yes	characteristic
727	C₂²	C₁₉×#390	1	1	yes	characteristic
728	C₂²	C₁₉×#392	1	1	yes	characteristic
729	C₂²	C₁₉×#394	1	1	yes	characteristic
730	C₂²	C₁₉×#394	1	1	yes	characteristic
731	C₂²	C₁₉×#394	1	1	yes	characteristic
732	C₂²	C₁₉×#471	1	2	yes	—
733	C₂²	C₁₉×#473	1	2	yes	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	8	2	no	—
737	C₄	C₁₉×#379	1	1	yes	characteristic
738	C₄	C₁₉×#386	1	1	yes	characteristic
739	C₄	C₁₉×#386	1	1	yes	characteristic
740	C₄	C₁₉×#390	1	1	yes	characteristic
741	C₄	C₁₉×#392	1	1	yes	characteristic
742	C₄	C₁₉×#392	1	1	yes	characteristic
743	C₄	C₁₉×#392	1	1	yes	characteristic
744	C₄	C₁₉×#394	1	1	yes	characteristic
745	C₂	—	2	1	no	—
746	C₂	—	2	1	no	—
747	C₂	—	2	1	no	—
748	C₂	—	2	1	no	—
749	C₂	—	8	2	no	—
750	C₂	C₁₉×#1438	1	1	yes	characteristic
751	C₂	C₁₉×#1908	1	2	yes	—
752	C₂	C₁₉×#2019	1	1	yes	characteristic
753	C₂	C₁₉×#2020	1	1	yes	characteristic
754	C₂	C₁₉×#2052	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
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
3. C₂²×C₁₉×#103	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
6. C₂×C₁₉×#343	C₂	semidirect
7. C₂×C₁₉×#341	C₂	semidirect
15. C₂×C₁₉×#137	C₄	semidirect
250. #11021	C₁₉	direct (N × H)
337. C₂²×#103	C₂×C₁₉	semidirect
338. C₂²×#101	C₂×C₁₉	semidirect
340. C₂×#343	C₂×C₁₉	semidirect
341. C₂×#341	C₂×C₁₉	semidirect
382. C₂×#137	C₄×C₁₉	semidirect
497. C₁₉	#11021	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#137	2
C₂×C₁₉×#417	2
C₂²×C₁₉×#103	2
C₂²×C₁₉×#101	2
C₂×C₁₉×#408	2
C₂×C₁₉×#343	2
C₂×C₁₉×#341	2
#11021	19

Subgroups — C19×#11021 #18016980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11021 #18016980