Subgroups — C₁₉×#62380 #18068339

Order 4864.

1608 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3555	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3393	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3383	C₂	1	2	yes	maximal, complemented
6	Q₈×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3380	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3377	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3372	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3369	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3258	C₂	1	4	yes	maximal, complemented
12	C₁₉×#3252	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3177	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3175	C₂	1	2	yes	maximal
15	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic
17	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#563	—	2	4	no	—
19	Q₈²×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#557	C₂²	1	2	yes	—
21	C₁₉×#557	C₂²	1	4	yes	—
22	C₁₉×#556	—	2	2	no	—
23	C₁₉×#556	C₂²	1	2	yes	—
24	C₁₉×#556	C₂²	1	4	yes	—
25	C₁₉×#554	C₂²	1	2	yes	—
26	C₁₉×#552	—	2	2	no	—
27	C₁₉×#544	—	2	2	no	—
28	C₁₉×#542	C₂²	1	4	yes	—
29	C₁₉×#541	—	2	2	no	—
30	C₁₉×#541	—	2	4	no	—
31	C₁₉×#541	C₂²	1	4	yes	—
32	C₁₉×#533	C₂²	1	2	yes	—
33	C₁₉×#533	C₂²	1	1	yes	characteristic
34	C₁₉×#529	C₂²	1	2	yes	—
35	C₁₉×#500	C₂²	1	1	yes	characteristic
36	C₁₉×#500	C₂²	1	2	yes	—
37	C₁₉×#499	C₂²	1	1	yes	characteristic
38	C₁₉×#499	C₂²	1	2	yes	—
39	C₁₉×#495	C₂²	1	1	yes	characteristic
40	C₁₉×#495	C₂²	1	2	yes	—
41	C₁₉×#494	C₂²	1	1	yes	characteristic
42	C₁₉×#494	C₂²	1	2	yes	—
43	C₁₉×#491	C₂²	1	4	yes	—
44	C₁₉×#489	C₂²	1	4	yes	—
45	C₁₉×#488	C₂²	1	2	yes	—
46	C₁₉×#487	C₂²	1	2	yes	—
47	C₁₉×#479	C₂²	1	4	yes	—
48	C₁₉×#479	C₂²	1	4	yes	—
49	C₁₉×#478	C₂²	1	4	yes	—
50	C₁₉×#477	C₂²	1	2	yes	—
51	C₁₉×#477	C₂²	1	4	yes	—
52	C₁₉×#476	C₂²	1	2	yes	—
53	C₁₉×#475	C₂²	1	4	yes	—
54	C₁₉×#470	C₂²	1	4	yes	—
55	C₁₉×#468	C₂²	1	4	yes	—
56	C₁₉×#467	C₂²	1	1	yes	characteristic
57	C₁₉×#467	C₂²	1	2	yes	—
58	C₁₉×#467	C₂²	1	2	yes	—
59	C₁₉×#466	C₂²	1	1	yes	characteristic
60	C₁₉×#465	C₂²	1	2	yes	—
61	C₁₉×#464	C₂²	1	4	yes	—
62	C₁₉×#464	C₂²	1	4	yes	—
63	C₁₉×#464	C₂²	1	4	yes	—
64	C₁₉×#462	C₂²	1	2	yes	—
65	C₁₉×#462	C₂²	1	4	yes	—
66	C₁₉×#461	C₂²	1	2	yes	—
67	C₁₉×#461	C₂²	1	4	yes	—
68	C₁₉×#446	C₂²	1	1	yes	characteristic
69	C₁₉×#446	C₂²	1	1	yes	characteristic
70	C₁₉×#446	C₂²	1	2	yes	—
71	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
72	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
73	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
74	C₁₉×#441	C₂²	1	4	yes	—
75	C₁₉×#440	C₂²	1	4	yes	—
76	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
77	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
81	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
83	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
84	C₄×D₈×C₁₉	C₂²	1	2	yes	—
85	C₁₉×#424	C₂²	1	2	yes	—
86	C₁₉×#423	C₂²	1	1	yes	characteristic
87	C₁₉×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
89	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
91	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
92	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
94	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
95	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
97	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×C₄⋊Q₈	—	2	4	no	—
100	C₁₉×C₄⋊Q₈	—	2	4	no	—
101	C₁₉×C₄⋊Q₈	—	2	2	no	—
102	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
103	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
104	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
107	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₁₉×#126	—	2	4	no	—
109	C₁₉×#126	—	2	4	no	—
110	C₁₉×#126	—	2	4	no	—
111	C₁₉×#126	—	2	4	no	—
112	C₁₉×#126	—	2	4	no	—
113	C₁₉×#126	—	2	4	no	—
114	C₁₉×#126	—	2	2	no	—
115	C₁₉×#125	—	2	4	no	—
116	C₁₉×#125	—	2	4	no	—
117	C₁₉×#125	—	2	4	no	—
118	C₁₉×#125	—	2	4	no	—
119	C₁₉×#125	—	2	4	no	—
120	C₁₉×#125	—	2	2	no	—
121	C₁₉×#125	—	2	2	no	—
122	C₁₉×#125	D₄	1	2	yes	—
123	C₁₉×#125	C₂³	1	4	yes	—
124	C₁₉×#125	C₂³	1	2	yes	—
125	C₁₉×#124	—	2	4	no	—
126	C₁₉×#124	C₂³	1	2	yes	—
127	C₁₉×#124	C₂³	1	4	yes	—
128	C₁₉×#123	—	2	2	no	—
129	C₁₉×#123	—	2	4	no	—
130	C₁₉×C₂²⋊Q₈	—	2	2	no	—
131	C₁₉×C₂²⋊Q₈	—	2	2	no	—
132	C₁₉×C₂²⋊Q₈	—	2	4	no	—
133	C₁₉×C₂²⋊Q₈	—	2	2	no	—
134	C₁₉×C₂²⋊Q₈	—	2	4	no	—
135	C₁₉×C₂²⋊Q₈	—	2	4	no	—
136	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
139	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₉×#121	C₂³	1	2	yes	—
142	C₄×Q₈×C₁₉	—	2	2	no	—
143	C₄×Q₈×C₁₉	—	2	2	no	—
144	C₄×Q₈×C₁₉	—	2	4	no	—
145	C₄×Q₈×C₁₉	—	2	2	no	—
146	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
147	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
148	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
149	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
150	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
152	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
154	C₄×D₄×C₁₉	—	2	2	no	—
155	C₄×D₄×C₁₉	C₂³	1	2	yes	—
156	C₄×D₄×C₁₉	C₂³	1	4	yes	—
157	C₁₉×#117	—	2	2	no	—
158	C₁₉×#117	—	2	4	no	—
159	C₁₉×#117	—	2	2	no	—
160	C₁₉×#117	—	2	2	no	—
161	C₁₉×#117	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
164	C₁₉×#107	C₂³	1	1	yes	characteristic
165	C₁₉×#107	C₂³	1	2	yes	—
166	C₁₉×#107	C₂³	1	1	yes	characteristic
167	C₁₉×#107	C₂³	1	2	yes	—
168	C₁₉×#107	C₂³	1	4	yes	—
169	C₁₉×#106	C₂³	1	2	yes	—
170	C₁₉×#106	C₂³	1	4	yes	—
171	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
172	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
173	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
174	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
175	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
176	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₉×#103	C₂³	1	2	yes	—
179	C₁₉×#103	C₂³	1	4	yes	—
180	C₁₉×#103	C₂³	1	4	yes	—
181	C₁₉×#103	C₂³	1	4	yes	—
182	C₁₉×#103	C₂³	1	4	yes	—
183	C₁₉×#103	C₂³	1	2	yes	—
184	C₁₉×#103	C₂³	1	4	yes	—
185	C₁₉×#102	C₂³	1	2	yes	—
186	C₁₉×#102	C₂³	1	4	yes	—
187	C₁₉×#102	C₂³	1	2	yes	—
188	C₁₉×#97	C₂³	1	2	yes	—
189	C₁₉×#97	C₂³	1	2	yes	—
190	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
191	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₉	C₂³	1	2	yes	—
195	C₄×C₈×C₁₉	C₂³	1	2	yes	—
196	C₂×Q₈×C₁₉	—	2	2	no	—
197	C₂×Q₈×C₁₉	—	2	4	no	—
198	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
201	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
203	C₂×D₄×C₁₉	—	2	2	no	—
204	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₉	—	2	2	no	—
206	C₂²×C₄×C₁₉	—	2	4	no	—
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
210	Q₁₆×C₁₉	—	2	2	no	—
211	Q₁₆×C₁₉	—	2	4	no	—
212	Q₁₆×C₁₉	—	4	2	no	—
213	Q₁₆×C₁₉	—	4	4	no	—
214	SD₁₆×C₁₉	—	4	2	no	—
215	SD₁₆×C₁₉	—	4	4	no	—
216	D₈×C₁₉	—	2	2	no	—
217	M₁₆×C₁₉	—	4	2	no	—
218	C₂×C₈×C₁₉	—	2	2	no	—
219	C₂×C₈×C₁₉	—	4	1	no	—
220	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
221	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
224	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
225	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₁₉	—	2	2	no	—
227	C₄⋊C₄×C₁₉	—	2	4	no	—
228	C₄⋊C₄×C₁₉	—	2	2	no	—
229	C₄⋊C₄×C₁₉	—	2	4	no	—
230	C₄⋊C₄×C₁₉	—	2	2	no	—
231	C₄⋊C₄×C₁₉	—	2	2	no	—
232	C₄⋊C₄×C₁₉	—	2	2	no	—
233	C₄⋊C₄×C₁₉	—	2	4	no	—
234	C₄⋊C₄×C₁₉	—	2	4	no	—
235	C₄⋊C₄×C₁₉	—	2	2	no	—
236	C₄⋊C₄×C₁₉	—	2	4	no	—
237	C₄⋊C₄×C₁₉	—	2	4	no	—
238	C₄⋊C₄×C₁₉	—	2	4	no	—
239	C₄⋊C₄×C₁₉	—	2	4	no	—
240	C₄⋊C₄×C₁₉	—	2	4	no	—
241	C₄⋊C₄×C₁₉	—	2	4	no	—
242	C₄⋊C₄×C₁₉	—	2	2	no	—
243	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
254	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
255	C₂²⋊C₄×C₁₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₉	—	2	2	no	—
257	C₂²⋊C₄×C₁₉	—	2	2	no	—
258	C₂²⋊C₄×C₁₉	—	2	2	no	—
259	C₂²⋊C₄×C₁₉	—	2	2	no	—
260	C₂²⋊C₄×C₁₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₉	—	2	2	no	—
263	C₂²⋊C₄×C₁₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
265	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
266	C₄²×C₁₉	—	2	4	no	—
267	C₄²×C₁₉	—	2	2	no	—
268	C₄²×C₁₉	—	2	4	no	—
269	C₄²×C₁₉	—	2	4	no	—
270	C₄²×C₁₉	—	2	4	no	—
271	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
274	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
275	C₄²×C₁₉	C₂⁴	1	2	yes	—
276	C₄²×C₁₉	C₂⁴	1	2	yes	—
277	#62380	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₁₉	—	2	2	no	—
279	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₁₉	—	2	2	no	—
281	Q₈×C₁₉	—	2	2	no	—
282	Q₈×C₁₉	—	2	2	no	—
283	Q₈×C₁₉	—	2	4	no	—
284	Q₈×C₁₉	—	2	2	no	—
285	Q₈×C₁₉	—	2	4	no	—
286	Q₈×C₁₉	—	4	2	no	—
287	Q₈×C₁₉	—	8	2	no	—
288	Q₈×C₁₉	—	8	4	no	—
289	D₄×C₁₉	—	2	2	no	—
290	D₄×C₁₉	—	2	2	no	—
291	D₄×C₁₉	—	8	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	4	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	4	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	4	no	—
302	C₂×C₄×C₁₉	—	8	4	no	—
303	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
313	C₈×C₁₉	—	2	1	no	—
314	C₈×C₁₉	—	2	1	no	—
315	C₈×C₁₉	—	2	1	no	—
316	C₈×C₁₉	—	2	2	no	—
317	C₈×C₁₉	—	2	2	no	—
318	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
319	#3555	C₂×C₁₉	1	2	yes	complemented
320	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#3393	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#3393	C₂×C₁₉	1	2	yes	complemented
323	#3383	C₂×C₁₉	1	2	yes	complemented
324	Q₈×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#3380	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#3377	C₂×C₁₉	1	4	yes	complemented
327	#3372	C₂×C₁₉	1	2	yes	complemented
328	#3369	C₂×C₁₉	1	2	yes	complemented
329	#3258	C₂×C₁₉	1	4	yes	complemented
330	#3252	C₂×C₁₉	1	2	yes	complemented
331	#3177	C₂×C₁₉	1	2	yes	complemented
332	#3175	C₂×C₁₉	1	2	yes	—
333	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#3168	C₂×C₁₉	1	1	yes	characteristic
335	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
336	C₂²×C₁₉	—	2	1	no	—
337	C₂²×C₁₉	—	2	1	no	—
338	C₂²×C₁₉	—	2	1	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	4	2	no	—
341	C₂²×C₁₉	—	4	2	no	—
342	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₁₉	—	2	1	no	—
344	C₄×C₁₉	—	2	1	no	—
345	C₄×C₁₉	—	2	2	no	—
346	C₄×C₁₉	—	2	2	no	—
347	C₄×C₁₉	—	2	1	no	—
348	C₄×C₁₉	—	2	1	no	—
349	C₄×C₁₉	—	2	2	no	—
350	C₄×C₁₉	—	2	2	no	—
351	C₄×C₁₉	—	4	4	no	—
352	C₄×C₁₉	—	4	2	no	—
353	C₄×C₁₉	—	4	4	no	—
354	C₄×C₁₉	—	4	2	no	—
355	C₄×C₁₉	—	4	2	no	—
356	C₄×C₁₉	#578	1	2	yes	—
357	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
358	C₄×C₁₉	#585	1	1	yes	characteristic
359	#563	—	2	4	no	—
360	Q₈²	C₂²×C₁₉	1	2	yes	—
361	#557	C₂²×C₁₉	1	2	yes	—
362	#557	C₂²×C₁₉	1	4	yes	—
363	#556	—	2	2	no	—
364	#556	C₂²×C₁₉	1	2	yes	—
365	#556	C₂²×C₁₉	1	4	yes	—
366	#554	C₂²×C₁₉	1	2	yes	—
367	#552	—	2	2	no	—
368	#544	—	2	2	no	—
369	#542	C₂²×C₁₉	1	4	yes	—
370	#541	—	2	2	no	—
371	#541	—	2	4	no	—
372	#541	C₂²×C₁₉	1	4	yes	—
373	#533	C₂²×C₁₉	1	2	yes	—
374	#533	C₂²×C₁₉	1	1	yes	characteristic
375	#529	C₂²×C₁₉	1	2	yes	—
376	#500	C₂²×C₁₉	1	1	yes	characteristic
377	#500	C₂²×C₁₉	1	2	yes	—
378	#499	C₂²×C₁₉	1	2	yes	—
379	#499	C₂²×C₁₉	1	1	yes	characteristic
380	#495	C₂²×C₁₉	1	1	yes	characteristic
381	#495	C₂²×C₁₉	1	2	yes	—
382	#494	C₂²×C₁₉	1	1	yes	characteristic
383	#494	C₂²×C₁₉	1	2	yes	—
384	#491	C₂²×C₁₉	1	4	yes	—
385	#489	C₂²×C₁₉	1	4	yes	—
386	#488	C₂²×C₁₉	1	2	yes	—
387	#487	C₂²×C₁₉	1	2	yes	—
388	#479	C₂²×C₁₉	1	4	yes	—
389	#479	C₂²×C₁₉	1	4	yes	—
390	#478	C₂²×C₁₉	1	4	yes	—
391	#477	C₂²×C₁₉	1	2	yes	—
392	#477	C₂²×C₁₉	1	4	yes	—
393	#476	C₂²×C₁₉	1	2	yes	—
394	#475	C₂²×C₁₉	1	4	yes	—
395	#470	C₂²×C₁₉	1	4	yes	—
396	#468	C₂²×C₁₉	1	4	yes	—
397	#467	C₂²×C₁₉	1	1	yes	characteristic
398	#467	C₂²×C₁₉	1	2	yes	—
399	#467	C₂²×C₁₉	1	2	yes	—
400	#466	C₂²×C₁₉	1	1	yes	characteristic
401	#465	C₂²×C₁₉	1	2	yes	—
402	#464	C₂²×C₁₉	1	4	yes	—
403	#464	C₂²×C₁₉	1	4	yes	—
404	#464	C₂²×C₁₉	1	4	yes	—
405	#462	C₂²×C₁₉	1	2	yes	—
406	#462	C₂²×C₁₉	1	4	yes	—
407	#461	C₂²×C₁₉	1	2	yes	—
408	#461	C₂²×C₁₉	1	4	yes	—
409	#446	C₂²×C₁₉	1	1	yes	characteristic
410	#446	C₂²×C₁₉	1	1	yes	characteristic
411	#446	C₂²×C₁₉	1	2	yes	—
412	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
413	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
414	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
415	#441	C₂²×C₁₉	1	4	yes	—
416	#440	C₂²×C₁₉	1	4	yes	—
417	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
418	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
419	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
420	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
421	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
422	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
423	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
424	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
425	C₄×D₈	C₂²×C₁₉	1	2	yes	—
426	#424	C₂²×C₁₉	1	2	yes	—
427	#423	C₂²×C₁₉	1	1	yes	characteristic
428	#405	C₂²×C₁₉	1	2	yes	—
429	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×C₁₉	—	4	1	no	—
431	C₂×C₁₉	—	8	2	no	—
432	C₂×C₁₉	#3497	1	1	yes	characteristic
433	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
434	C₂×C₁₉	#3584	1	1	yes	characteristic
435	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
436	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
437	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
438	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
439	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
440	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
441	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
443	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
445	C₄⋊Q₈	—	2	4	no	—
446	C₄⋊Q₈	—	2	4	no	—
447	C₄⋊Q₈	—	2	2	no	—
448	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
449	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
451	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
452	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
453	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
454	#126	—	2	4	no	—
455	#126	—	2	4	no	—
456	#126	—	2	4	no	—
457	#126	—	2	4	no	—
458	#126	—	2	4	no	—
459	#126	—	2	4	no	—
460	#126	—	2	2	no	—
461	#125	—	2	4	no	—
462	#125	—	2	4	no	—
463	#125	—	2	4	no	—
464	#125	—	2	4	no	—
465	#125	—	2	4	no	—
466	#125	—	2	2	no	—
467	#125	—	2	2	no	—
468	#125	D₄×C₁₉	1	2	yes	—
469	#125	C₂³×C₁₉	1	2	yes	—
470	#125	C₂³×C₁₉	1	4	yes	—
471	#124	—	2	4	no	—
472	#124	C₂³×C₁₉	1	2	yes	—
473	#124	C₂³×C₁₉	1	4	yes	—
474	#123	—	2	2	no	—
475	#123	—	2	4	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
483	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
484	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
485	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
486	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
487	#121	C₂³×C₁₉	1	2	yes	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	4	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
493	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
494	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
495	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
496	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
497	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
498	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
499	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	C₂³×C₁₉	1	2	yes	—
502	C₄×D₄	C₂³×C₁₉	1	4	yes	—
503	#117	—	2	2	no	—
504	#117	—	2	4	no	—
505	#117	—	2	2	no	—
506	#117	—	2	2	no	—
507	#117	C₂³×C₁₉	1	2	yes	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
510	#107	C₂³×C₁₉	1	1	yes	characteristic
511	#107	C₂³×C₁₉	1	2	yes	—
512	#107	C₂³×C₁₉	1	1	yes	characteristic
513	#107	C₂³×C₁₉	1	2	yes	—
514	#107	C₂³×C₁₉	1	4	yes	—
515	#106	C₂³×C₁₉	1	2	yes	—
516	#106	C₂³×C₁₉	1	4	yes	—
517	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
518	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
519	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
520	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
521	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
522	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
523	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
524	#103	C₂³×C₁₉	1	2	yes	—
525	#103	C₂³×C₁₉	1	4	yes	—
526	#103	C₂³×C₁₉	1	4	yes	—
527	#103	C₂³×C₁₉	1	4	yes	—
528	#103	C₂³×C₁₉	1	4	yes	—
529	#103	C₂³×C₁₉	1	2	yes	—
530	#103	C₂³×C₁₉	1	4	yes	—
531	#102	C₂³×C₁₉	1	2	yes	—
532	#102	C₂³×C₁₉	1	4	yes	—
533	#102	C₂³×C₁₉	1	2	yes	—
534	#97	C₂³×C₁₉	1	2	yes	—
535	#97	C₂³×C₁₉	1	2	yes	—
536	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
537	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
538	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
539	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
540	C₄×C₈	C₂³×C₁₉	1	2	yes	—
541	C₄×C₈	C₂³×C₁₉	1	2	yes	—
542	C₁₉	#62380	1	1	yes	characteristic, direct product factor, Sylow
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	4	no	—
545	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
548	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
549	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
557	Q₁₆	—	2	2	no	—
558	Q₁₆	—	2	4	no	—
559	Q₁₆	—	4	2	no	—
560	Q₁₆	—	4	4	no	—
561	SD₁₆	—	4	2	no	—
562	SD₁₆	—	4	4	no	—
563	D₈	—	2	2	no	—
564	M₁₆	—	4	2	no	—
565	C₂×C₈	—	2	2	no	—
566	C₂×C₈	—	4	1	no	—
567	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
568	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
569	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
570	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
571	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
572	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
591	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
592	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
594	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
595	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
596	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
597	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
598	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
599	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
601	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
612	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	4	no	—
618	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
619	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
620	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
621	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
622	C₄²	C₂⁴×C₁₉	1	2	yes	—
623	C₄²	C₂⁴×C₁₉	1	2	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
626	Q₈	—	2	2	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	4	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	2	4	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	8	2	no	—
634	Q₈	—	8	4	no	—
635	D₄	—	2	2	no	—
636	D₄	—	2	2	no	—
637	D₄	—	8	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	8	4	no	—
649	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
650	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
655	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
656	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
658	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
659	C₈	—	2	1	no	—
660	C₈	—	2	1	no	—
661	C₈	—	2	1	no	—
662	C₈	—	2	2	no	—
663	C₈	—	2	2	no	—
664	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	2	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	4	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	4	no	—
684	C₄	—	4	2	no	—
685	C₄	C₁₉×#578	1	2	yes	—
686	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
687	C₄	C₁₉×#585	1	1	yes	characteristic
688	C₂	—	4	1	no	—
689	C₂	—	8	2	no	—
690	C₂	C₁₉×#3497	1	1	yes	characteristic
691	C₂	C₂×C₁₉×#578	1	1	yes	characteristic
692	C₂	C₁₉×#3584	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 ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3555	C₂	semidirect
2. C₁₉×#3395	C₂	semidirect
3. C₁₉×#3393	C₂	semidirect
4. C₁₉×#3393	C₂	semidirect
5. C₁₉×#3383	C₂	semidirect
6. Q₈×Q₁₆×C₁₉	C₂	semidirect
7. C₁₉×#3380	C₂	semidirect
8. C₁₉×#3377	C₂	semidirect
9. C₁₉×#3372	C₂	semidirect
10. C₁₉×#3369	C₂	semidirect
11. C₁₉×#3258	C₂	semidirect
12. C₁₉×#3252	C₂	semidirect
13. C₁₉×#3177	C₂	semidirect
15. C₁₉×#3170	C₂	semidirect
17. C₁₉×#2960	C₂	semidirect
277. #62380	C₁₉	direct (N × H)
319. #3555	C₂×C₁₉	semidirect
320. #3395	C₂×C₁₉	semidirect
321. #3393	C₂×C₁₉	semidirect
322. #3393	C₂×C₁₉	semidirect
323. #3383	C₂×C₁₉	semidirect
324. Q₈×Q₁₆	C₂×C₁₉	semidirect
325. #3380	C₂×C₁₉	semidirect
326. #3377	C₂×C₁₉	semidirect
327. #3372	C₂×C₁₉	semidirect
328. #3369	C₂×C₁₉	semidirect
329. #3258	C₂×C₁₉	semidirect
330. #3252	C₂×C₁₉	semidirect
331. #3177	C₂×C₁₉	semidirect
333. #3170	C₂×C₁₉	semidirect
335. #2960	C₂×C₁₉	semidirect
542. C₁₉	#62380	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×#3555	2
C₁₉×#3395	2
C₁₉×#3393	2
C₁₉×#3383	2
Q₈×Q₁₆×C₁₉	2
C₁₉×#3380	2
C₁₉×#3377	2
C₁₉×#3372	2
C₁₉×#3369	2
C₁₉×#3258	2
C₁₉×#3252	2
C₁₉×#3177	2
C₁₉×#3175	2
C₁₉×#3170	2
C₁₉×#3168	2
C₁₉×#2960	2
#62380	19

Subgroups — C19×#62380 #18068339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62380 #18068339