Subgroups — C₁₉×#62369 #18068328

Order 4864.

1670 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3523	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3402	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3398	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3390	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3386	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3377	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3374	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3367	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3250	C₂	1	2	yes	maximal
10	C₁₉×#3249	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3248	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3181	C₂	1	4	yes	maximal, complemented
13	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic
15	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#557	C₂²	1	2	yes	—
17	C₁₉×#557	C₂²	1	2	yes	—
18	C₁₉×#557	C₂²	1	4	yes	—
19	C₁₉×#556	C₂²	1	2	yes	—
20	C₁₉×#556	C₂²	1	4	yes	—
21	C₁₉×#552	—	2	2	no	—
22	C₁₉×#552	—	2	4	no	—
23	D₄×Q₈×C₁₉	—	2	2	no	—
24	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#541	—	2	2	no	—
26	C₁₉×#541	—	2	4	no	—
27	C₁₉×#533	C₂²	1	2	yes	—
28	C₁₉×#533	C₂²	1	4	yes	—
29	C₁₉×#529	C₂²	1	2	yes	—
30	C₁₉×#529	C₂²	1	4	yes	—
31	C₁₉×#519	—	2	2	no	—
32	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#501	C₂²	1	4	yes	—
34	C₁₉×#500	C₂²	1	1	yes	characteristic
35	C₁₉×#499	C₂²	1	1	yes	characteristic
36	C₁₉×#497	C₂²	1	4	yes	—
37	C₁₉×#495	C₂²	1	1	yes	characteristic
38	C₁₉×#494	C₂²	1	1	yes	characteristic
39	C₁₉×#491	C₂²	1	4	yes	—
40	C₁₉×#489	C₂²	1	4	yes	—
41	C₁₉×#488	C₂²	1	2	yes	—
42	C₁₉×#487	C₂²	1	2	yes	—
43	C₁₉×#479	C₂²	1	4	yes	—
44	C₁₉×#479	C₂²	1	4	yes	—
45	C₁₉×#478	C₂²	1	4	yes	—
46	C₁₉×#477	C₂²	1	4	yes	—
47	C₁₉×#477	C₂²	1	4	yes	—
48	C₁₉×#475	C₂²	1	2	yes	—
49	C₁₉×#474	C₂²	1	2	yes	—
50	C₁₉×#467	C₂²	1	1	yes	characteristic
51	C₁₉×#467	C₂²	1	2	yes	—
52	C₁₉×#467	C₂²	1	2	yes	—
53	C₁₉×#467	C₂²	1	4	yes	—
54	C₁₉×#466	C₂²	1	1	yes	characteristic
55	C₁₉×#465	C₂²	1	2	yes	—
56	C₁₉×#465	C₂²	1	4	yes	—
57	C₁₉×#464	C₂²	1	4	yes	—
58	C₁₉×#464	C₂²	1	4	yes	—
59	C₁₉×#463	C₂²	1	4	yes	—
60	C₁₉×#462	C₂²	1	2	yes	—
61	C₁₉×#462	C₂²	1	4	yes	—
62	C₁₉×#462	C₂²	1	4	yes	—
63	C₁₉×#461	C₂²	1	2	yes	—
64	C₁₉×#446	C₂²	1	2	yes	—
65	C₁₉×#446	C₂²	1	2	yes	—
66	C₁₉×#446	C₂²	1	2	yes	—
67	C₁₉×#446	C₂²	1	2	yes	—
68	C₁₉×#441	C₂²	1	4	yes	—
69	C₁₉×#441	C₂²	1	4	yes	—
70	C₁₉×#440	C₂²	1	4	yes	—
71	C₁₉×#440	C₂²	1	4	yes	—
72	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
73	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
74	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
75	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
76	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
77	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
78	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
79	C₂×C₁₉×#97	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
81	C₂²×Q₈×C₁₉	—	2	2	no	—
82	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
83	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
84	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
86	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
87	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
88	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
89	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
93	C₁₉×C₄⋊Q₈	—	2	2	no	—
94	C₁₉×C₄⋊Q₈	—	2	4	no	—
95	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
97	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₁₉×#126	—	2	4	no	—
100	C₁₉×#126	—	2	4	no	—
101	C₁₉×#126	—	2	4	no	—
102	C₁₉×#126	—	2	4	no	—
103	C₁₉×#126	—	2	2	no	—
104	C₁₉×#125	—	2	4	no	—
105	C₁₉×#125	—	2	4	no	—
106	C₁₉×#125	—	2	4	no	—
107	C₁₉×#125	—	2	2	no	—
108	C₁₉×#125	—	2	4	no	—
109	C₁₉×#125	—	2	4	no	—
110	C₁₉×#125	—	2	2	no	—
111	C₁₉×#125	C₂³	1	4	yes	—
112	C₁₉×#125	C₂³	1	2	yes	—
113	C₁₉×#124	C₂³	1	4	yes	—
114	C₁₉×#124	C₂³	1	2	yes	—
115	C₁₉×#123	—	2	2	no	—
116	C₁₉×#123	—	2	4	no	—
117	C₁₉×C₂²⋊Q₈	—	2	2	no	—
118	C₁₉×C₂²⋊Q₈	—	2	4	no	—
119	C₁₉×C₂²⋊Q₈	—	2	2	no	—
120	C₁₉×C₂²⋊Q₈	—	2	4	no	—
121	C₁₉×C₂²⋊Q₈	—	2	2	no	—
122	C₁₉×C₂²⋊Q₈	—	2	4	no	—
123	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
124	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₉×#121	C₂³	1	2	yes	—
126	C₄×Q₈×C₁₉	—	2	2	no	—
127	C₄×Q₈×C₁₉	—	2	2	no	—
128	C₄×Q₈×C₁₉	—	2	4	no	—
129	C₄×Q₈×C₁₉	—	2	2	no	—
130	C₄×Q₈×C₁₉	—	2	4	no	—
131	C₄×Q₈×C₁₉	D₄	1	2	yes	—
132	C₄×Q₈×C₁₉	D₄	1	2	yes	—
133	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
134	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
135	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
136	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
137	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
138	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
139	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
140	C₄×D₄×C₁₉	—	2	2	no	—
141	C₄×D₄×C₁₉	—	2	4	no	—
142	C₄×D₄×C₁₉	C₂³	1	2	yes	—
143	C₄×D₄×C₁₉	C₂³	1	4	yes	—
144	C₁₉×#117	—	2	2	no	—
145	C₁₉×#117	—	2	4	no	—
146	C₁₉×#117	—	2	2	no	—
147	C₁₉×#117	—	2	4	no	—
148	C₁₉×#117	—	2	2	no	—
149	C₁₉×#117	—	2	4	no	—
150	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
152	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
154	C₁₉×#107	C₂³	1	1	yes	characteristic
155	C₁₉×#107	C₂³	1	2	yes	—
156	C₁₉×#107	C₂³	1	1	yes	characteristic
157	C₁₉×#107	C₂³	1	2	yes	—
158	C₁₉×#107	C₂³	1	4	yes	—
159	C₁₉×#106	C₂³	1	2	yes	—
160	C₁₉×#106	C₂³	1	4	yes	—
161	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
162	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
163	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
164	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
165	C₁₉×#103	C₂³	1	2	yes	—
166	C₁₉×#103	C₂³	1	4	yes	—
167	C₁₉×#103	C₂³	1	2	yes	—
168	C₁₉×#103	C₂³	1	4	yes	—
169	C₁₉×#103	C₂³	1	4	yes	—
170	C₁₉×#103	C₂³	1	4	yes	—
171	C₁₉×#103	C₂³	1	4	yes	—
172	C₁₉×#102	C₂³	1	2	yes	—
173	C₁₉×#102	C₂³	1	2	yes	—
174	C₁₉×#102	C₂³	1	4	yes	—
175	C₁₉×#97	C₂³	1	4	yes	—
176	C₁₉×#97	C₂³	1	4	yes	—
177	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
181	C₂×Q₈×C₁₉	—	2	4	no	—
182	C₂×Q₈×C₁₉	—	2	2	no	—
183	C₂×Q₈×C₁₉	—	4	2	no	—
184	C₂×Q₈×C₁₉	—	4	8	no	—
185	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
186	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
187	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
188	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
189	C₂×D₄×C₁₉	—	2	2	no	—
190	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₉	—	2	4	no	—
192	C₂²×C₄×C₁₉	—	2	2	no	—
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
198	Q₁₆×C₁₉	—	2	4	no	—
199	Q₁₆×C₁₉	—	4	1	no	—
200	Q₁₆×C₁₉	—	4	4	no	—
201	Q₁₆×C₁₉	—	4	2	no	—
202	SD₁₆×C₁₉	—	2	4	no	—
203	SD₁₆×C₁₉	—	4	4	no	—
204	D₈×C₁₉	—	4	1	no	—
205	C₂×C₈×C₁₉	—	2	2	no	—
206	C₂×C₈×C₁₉	—	4	1	no	—
207	C₂×C₈×C₁₉	—	4	2	no	—
208	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
210	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
211	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
212	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
213	C₄⋊C₄×C₁₉	—	2	4	no	—
214	C₄⋊C₄×C₁₉	—	2	2	no	—
215	C₄⋊C₄×C₁₉	—	2	2	no	—
216	C₄⋊C₄×C₁₉	—	2	4	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	4	no	—
219	C₄⋊C₄×C₁₉	—	2	4	no	—
220	C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₄⋊C₄×C₁₉	—	2	4	no	—
222	C₄⋊C₄×C₁₉	—	2	2	no	—
223	C₄⋊C₄×C₁₉	—	2	4	no	—
224	C₄⋊C₄×C₁₉	—	2	2	no	—
225	C₄⋊C₄×C₁₉	—	2	4	no	—
226	C₄⋊C₄×C₁₉	—	2	4	no	—
227	C₄⋊C₄×C₁₉	—	2	4	no	—
228	C₄⋊C₄×C₁₉	—	2	4	no	—
229	C₄⋊C₄×C₁₉	—	2	2	no	—
230	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
231	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
235	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
236	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
237	C₂²⋊C₄×C₁₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₉	—	2	2	no	—
240	C₂²⋊C₄×C₁₉	—	2	2	no	—
241	C₂²⋊C₄×C₁₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₉	—	2	2	no	—
246	C₄²×C₁₉	—	2	4	no	—
247	C₄²×C₁₉	—	2	4	no	—
248	C₄²×C₁₉	—	2	4	no	—
249	C₄²×C₁₉	—	2	4	no	—
250	C₄²×C₁₉	—	2	2	no	—
251	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₁₉	C₂×D₄	1	4	yes	—
253	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₄²×C₁₉	C₂⁴	1	4	yes	—
256	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
257	#62369	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₁₉	—	2	2	no	—
259	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₁₉	—	2	4	no	—
261	Q₈×C₁₉	—	2	2	no	—
262	Q₈×C₁₉	—	2	4	no	—
263	Q₈×C₁₉	—	2	4	no	—
264	Q₈×C₁₉	—	2	2	no	—
265	Q₈×C₁₉	—	4	2	no	—
266	Q₈×C₁₉	—	4	8	no	—
267	Q₈×C₁₉	—	4	4	no	—
268	D₄×C₁₉	—	2	2	no	—
269	D₄×C₁₉	—	2	2	no	—
270	D₄×C₁₉	—	4	4	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	4	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	4	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	4	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	8	no	—
283	C₂×C₄×C₁₉	—	4	4	no	—
284	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
287	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
292	C₈×C₁₉	—	2	1	no	—
293	C₈×C₁₉	—	2	1	no	—
294	C₈×C₁₉	—	2	4	no	—
295	C₈×C₁₉	—	2	1	no	—
296	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
297	#3523	C₂×C₁₉	1	2	yes	complemented
298	#3402	C₂×C₁₉	1	2	yes	complemented
299	#3398	C₂×C₁₉	1	2	yes	complemented
300	#3390	C₂×C₁₉	1	2	yes	complemented
301	#3386	C₂×C₁₉	1	2	yes	complemented
302	#3377	C₂×C₁₉	1	4	yes	complemented
303	#3374	C₂×C₁₉	1	2	yes	complemented
304	#3367	C₂×C₁₉	1	2	yes	complemented
305	#3250	C₂×C₁₉	1	2	yes	—
306	#3249	C₂×C₁₉	1	2	yes	complemented
307	#3248	C₂×C₁₉	1	2	yes	complemented
308	#3181	C₂×C₁₉	1	4	yes	complemented
309	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#3168	C₂×C₁₉	1	1	yes	characteristic
311	C₂×#446	C₂×C₁₉	1	1	yes	characteristic, complemented
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	4	2	no	—
315	C₂²×C₁₉	—	4	2	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	#578	1	2	yes	—
318	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	4	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	2	4	no	—
324	C₄×C₁₉	—	2	1	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	4	4	no	—
327	C₄×C₁₉	—	4	4	no	—
328	C₄×C₁₉	—	4	2	no	—
329	C₄×C₁₉	—	4	2	no	—
330	C₄×C₁₉	#575	1	2	yes	—
331	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
332	C₄×C₁₉	#585	1	1	yes	characteristic
333	#557	C₂²×C₁₉	1	2	yes	—
334	#557	C₂²×C₁₉	1	2	yes	—
335	#557	C₂²×C₁₉	1	4	yes	—
336	#556	C₂²×C₁₉	1	2	yes	—
337	#556	C₂²×C₁₉	1	4	yes	—
338	#552	—	2	2	no	—
339	#552	—	2	4	no	—
340	D₄×Q₈	—	2	2	no	—
341	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
342	#541	—	2	2	no	—
343	#541	—	2	4	no	—
344	#533	C₂²×C₁₉	1	2	yes	—
345	#533	C₂²×C₁₉	1	4	yes	—
346	#529	C₂²×C₁₉	1	2	yes	—
347	#529	C₂²×C₁₉	1	4	yes	—
348	#519	—	2	2	no	—
349	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
350	#501	C₂²×C₁₉	1	4	yes	—
351	#500	C₂²×C₁₉	1	1	yes	characteristic
352	#499	C₂²×C₁₉	1	1	yes	characteristic
353	#497	C₂²×C₁₉	1	4	yes	—
354	#495	C₂²×C₁₉	1	1	yes	characteristic
355	#494	C₂²×C₁₉	1	1	yes	characteristic
356	#491	C₂²×C₁₉	1	4	yes	—
357	#489	C₂²×C₁₉	1	4	yes	—
358	#488	C₂²×C₁₉	1	2	yes	—
359	#487	C₂²×C₁₉	1	2	yes	—
360	#479	C₂²×C₁₉	1	4	yes	—
361	#479	C₂²×C₁₉	1	4	yes	—
362	#478	C₂²×C₁₉	1	4	yes	—
363	#477	C₂²×C₁₉	1	4	yes	—
364	#477	C₂²×C₁₉	1	4	yes	—
365	#475	C₂²×C₁₉	1	2	yes	—
366	#474	C₂²×C₁₉	1	2	yes	—
367	#467	C₂²×C₁₉	1	1	yes	characteristic
368	#467	C₂²×C₁₉	1	2	yes	—
369	#467	C₂²×C₁₉	1	2	yes	—
370	#467	C₂²×C₁₉	1	4	yes	—
371	#466	C₂²×C₁₉	1	1	yes	characteristic
372	#465	C₂²×C₁₉	1	2	yes	—
373	#465	C₂²×C₁₉	1	4	yes	—
374	#464	C₂²×C₁₉	1	4	yes	—
375	#464	C₂²×C₁₉	1	4	yes	—
376	#463	C₂²×C₁₉	1	4	yes	—
377	#462	C₂²×C₁₉	1	2	yes	—
378	#462	C₂²×C₁₉	1	4	yes	—
379	#462	C₂²×C₁₉	1	4	yes	—
380	#461	C₂²×C₁₉	1	2	yes	—
381	#446	C₂²×C₁₉	1	2	yes	—
382	#446	C₂²×C₁₉	1	2	yes	—
383	#446	C₂²×C₁₉	1	2	yes	—
384	#446	C₂²×C₁₉	1	2	yes	—
385	#441	C₂²×C₁₉	1	4	yes	—
386	#441	C₂²×C₁₉	1	4	yes	—
387	#440	C₂²×C₁₉	1	4	yes	—
388	#440	C₂²×C₁₉	1	4	yes	—
389	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
390	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
391	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
392	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
393	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
396	C₂×#97	C₂²×C₁₉	1	2	yes	—
397	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×C₁₉	—	2	2	no	—
399	C₂×C₁₉	—	8	2	no	—
400	C₂×C₁₉	#3497	1	1	yes	characteristic
401	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
402	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
403	C₂²×Q₈	—	2	2	no	—
404	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
405	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
406	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
408	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
409	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
410	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
411	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
415	C₄⋊Q₈	—	2	2	no	—
416	C₄⋊Q₈	—	2	4	no	—
417	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
418	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
419	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
420	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
421	#126	—	2	4	no	—
422	#126	—	2	4	no	—
423	#126	—	2	4	no	—
424	#126	—	2	4	no	—
425	#126	—	2	2	no	—
426	#125	—	2	4	no	—
427	#125	—	2	4	no	—
428	#125	—	2	4	no	—
429	#125	—	2	2	no	—
430	#125	—	2	4	no	—
431	#125	—	2	4	no	—
432	#125	—	2	2	no	—
433	#125	C₂³×C₁₉	1	4	yes	—
434	#125	C₂³×C₁₉	1	2	yes	—
435	#124	C₂³×C₁₉	1	4	yes	—
436	#124	C₂³×C₁₉	1	2	yes	—
437	#123	—	2	2	no	—
438	#123	—	2	4	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	4	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	4	no	—
445	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
446	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
447	#121	C₂³×C₁₉	1	2	yes	—
448	C₄×Q₈	—	2	2	no	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×Q₈	—	2	4	no	—
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	—	2	4	no	—
453	C₄×Q₈	D₄×C₁₉	1	2	yes	—
454	C₄×Q₈	D₄×C₁₉	1	2	yes	—
455	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
456	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
457	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
458	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
459	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
460	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
461	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	4	no	—
464	C₄×D₄	C₂³×C₁₉	1	2	yes	—
465	C₄×D₄	C₂³×C₁₉	1	4	yes	—
466	#117	—	2	2	no	—
467	#117	—	2	4	no	—
468	#117	—	2	2	no	—
469	#117	—	2	4	no	—
470	#117	—	2	2	no	—
471	#117	—	2	4	no	—
472	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
474	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
476	#107	C₂³×C₁₉	1	1	yes	characteristic
477	#107	C₂³×C₁₉	1	2	yes	—
478	#107	C₂³×C₁₉	1	1	yes	characteristic
479	#107	C₂³×C₁₉	1	2	yes	—
480	#107	C₂³×C₁₉	1	4	yes	—
481	#106	C₂³×C₁₉	1	2	yes	—
482	#106	C₂³×C₁₉	1	4	yes	—
483	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
484	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
485	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
486	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
487	#103	C₂³×C₁₉	1	2	yes	—
488	#103	C₂³×C₁₉	1	4	yes	—
489	#103	C₂³×C₁₉	1	2	yes	—
490	#103	C₂³×C₁₉	1	4	yes	—
491	#103	C₂³×C₁₉	1	4	yes	—
492	#103	C₂³×C₁₉	1	4	yes	—
493	#103	C₂³×C₁₉	1	4	yes	—
494	#102	C₂³×C₁₉	1	2	yes	—
495	#102	C₂³×C₁₉	1	2	yes	—
496	#102	C₂³×C₁₉	1	4	yes	—
497	#97	C₂³×C₁₉	1	4	yes	—
498	#97	C₂³×C₁₉	1	4	yes	—
499	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
500	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
501	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
502	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
503	C₁₉	#62369	1	1	yes	characteristic, direct product factor, Sylow
504	C₂×Q₈	—	2	4	no	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	4	2	no	—
507	C₂×Q₈	—	4	8	no	—
508	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
509	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
510	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
511	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
518	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
521	Q₁₆	—	2	4	no	—
522	Q₁₆	—	4	1	no	—
523	Q₁₆	—	4	4	no	—
524	Q₁₆	—	4	2	no	—
525	SD₁₆	—	2	4	no	—
526	SD₁₆	—	4	4	no	—
527	D₈	—	4	1	no	—
528	C₂×C₈	—	2	2	no	—
529	C₂×C₈	—	4	1	no	—
530	C₂×C₈	—	4	2	no	—
531	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
532	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
533	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
534	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
535	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
554	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
555	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
556	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
557	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
558	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
559	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	4	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	4	no	—
571	C₄²	—	2	4	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	2	no	—
574	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
575	C₄²	C₂×D₄×C₁₉	1	4	yes	—
576	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
577	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
578	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
579	C₄²	C₂⁴×C₁₉	1	4	yes	—
580	C₂³	—	2	2	no	—
581	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
582	Q₈	—	2	4	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	2	4	no	—
585	Q₈	—	2	4	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	4	8	no	—
589	Q₈	—	4	4	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	8	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
608	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
609	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
612	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
613	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
614	C₈	—	2	1	no	—
615	C₈	—	2	1	no	—
616	C₈	—	2	4	no	—
617	C₈	—	2	1	no	—
618	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	C₁₉×#578	1	2	yes	—
625	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	4	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	4	no	—
631	C₄	—	2	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	4	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	C₁₉×#575	1	2	yes	—
638	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
639	C₄	C₁₉×#585	1	1	yes	characteristic
640	C₂	—	2	2	no	—
641	C₂	—	8	2	no	—
642	C₂	C₁₉×#3497	1	1	yes	characteristic
643	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
644	C₂	C₂×C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#466	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3523	C₂	semidirect
2. C₁₉×#3402	C₂	semidirect
3. C₁₉×#3398	C₂	semidirect
4. C₁₉×#3390	C₂	semidirect
5. C₁₉×#3386	C₂	semidirect
6. C₁₉×#3377	C₂	semidirect
7. C₁₉×#3374	C₂	semidirect
8. C₁₉×#3367	C₂	semidirect
10. C₁₉×#3249	C₂	semidirect
11. C₁₉×#3248	C₂	semidirect
12. C₁₉×#3181	C₂	semidirect
13. C₁₉×#3170	C₂	semidirect
15. C₂×C₁₉×#446	C₂	semidirect
257. #62369	C₁₉	direct (N × H)
297. #3523	C₂×C₁₉	semidirect
298. #3402	C₂×C₁₉	semidirect
299. #3398	C₂×C₁₉	semidirect
300. #3390	C₂×C₁₉	semidirect
301. #3386	C₂×C₁₉	semidirect
302. #3377	C₂×C₁₉	semidirect
303. #3374	C₂×C₁₉	semidirect
304. #3367	C₂×C₁₉	semidirect
306. #3249	C₂×C₁₉	semidirect
307. #3248	C₂×C₁₉	semidirect
308. #3181	C₂×C₁₉	semidirect
309. #3170	C₂×C₁₉	semidirect
311. C₂×#446	C₂×C₁₉	semidirect
503. C₁₉	#62369	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3523	2
C₁₉×#3402	2
C₁₉×#3398	2
C₁₉×#3390	2
C₁₉×#3386	2
C₁₉×#3377	2
C₁₉×#3374	2
C₁₉×#3367	2
C₁₉×#3250	2
C₁₉×#3249	2
C₁₉×#3248	2
C₁₉×#3181	2
C₁₉×#3170	2
C₁₉×#3168	2
C₂×C₁₉×#446	2
#62369	19

Subgroups — C19×#62369 #18068328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62369 #18068328