Subgroups — C₁₉×#18589 #18024548

Order 4864.

878 conjugacy classes of subgroups.

The subgroup lattice has 612 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	1	yes	maximal, characteristic
2	C₁₉×#3218	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1653	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1651	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1650	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1648	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1483	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#557	—	2	1	no	—
13	C₁₉×#557	C₂²	1	1	yes	characteristic
14	C₁₉×#557	C₂²	1	1	yes	characteristic
15	C₁₉×#556	—	2	1	no	—
16	C₁₉×#556	C₂²	1	1	yes	characteristic
17	C₁₉×#552	—	2	2	no	—
18	C₁₉×#552	—	2	1	no	—
19	D₄×Q₈×C₁₉	—	2	1	no	—
20	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#541	—	2	2	no	—
22	C₁₉×#541	—	2	1	no	—
23	C₁₉×#533	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₉×#529	—	2	1	no	—
27	C₁₉×#529	C₂²	1	1	yes	characteristic
28	C₁₉×#519	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#501	—	2	2	no	—
31	C₁₉×#500	C₂²	1	2	yes	—
32	C₁₉×#498	C₂²	1	2	yes	—
33	C₁₉×#497	—	2	1	no	—
34	C₁₉×#491	—	2	1	no	—
35	C₁₉×#475	—	2	1	no	—
36	C₁₉×#475	—	2	1	no	—
37	C₁₉×#475	C₂²	1	2	yes	—
38	C₁₉×#475	C₂²	1	2	yes	—
39	C₁₉×#462	C₂²	1	2	yes	—
40	C₁₉×#461	C₂²	1	2	yes	—
41	C₁₉×#451	—	2	1	no	—
42	C₁₉×#448	—	2	1	no	—
43	C₁₉×#432	C₂²	1	1	yes	characteristic
44	C₁₉×#428	—	2	2	no	—
45	C₂×C₁₉×#106	—	2	1	no	—
46	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#103	—	2	1	no	—
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#332	C₂²	1	2	yes	—
50	C₁₉×#332	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂²×Q₈×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
58	C₂×Q₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	—	2	2	no	—
82	C₁₉×#125	—	2	2	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	D₄	1	1	yes	characteristic
85	C₁₉×#125	D₄	1	2	yes	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	D₄	1	1	yes	characteristic
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₉×#121	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	—	2	2	no	—
100	C₄×Q₈×C₁₉	—	2	2	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×Q₈×C₁₉	—	2	1	no	—
104	C₄×Q₈×C₁₉	—	2	1	no	—
105	C₄×Q₈×C₁₉	—	2	1	no	—
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×Q₈×C₁₉	—	2	1	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
111	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
112	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₁₉	—	2	2	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	1	no	—
118	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₁₉×#117	—	2	2	no	—
120	C₁₉×#117	—	2	2	no	—
121	C₁₉×#117	—	2	2	no	—
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	—	2	1	no	—
124	C₁₉×#117	D₄	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₉	—	2	1	no	—
130	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
131	C₁₉×#107	—	2	4	no	—
132	C₁₉×#106	—	2	2	no	—
133	C₁₉×#106	—	2	2	no	—
134	C₁₉×#106	—	2	4	no	—
135	C₁₉×C₄⋊C₈	—	2	1	no	—
136	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
137	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×#103	—	2	2	no	—
140	C₁₉×#103	—	2	2	no	—
141	C₁₉×#103	—	2	2	no	—
142	C₁₉×C₂²⋊C₈	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₁₉×#97	—	2	1	no	—
145	C₄×C₈×C₁₉	C₂³	1	2	yes	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	1	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	—	4	1	no	—
153	C₂×Q₈×C₁₉	—	4	2	no	—
154	C₂×Q₈×C₁₉	—	4	2	no	—
155	C₂×Q₈×C₁₉	—	4	1	no	—
156	C₂×Q₈×C₁₉	—	8	2	no	—
157	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	Q₁₆×C₁₉	—	8	2	no	—
171	SD₁₆×C₁₉	—	8	2	no	—
172	M₁₆×C₁₉	—	2	4	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	4	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	4	1	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₄²×C₁₉	—	2	2	no	—
218	C₄²×C₁₉	—	2	2	no	—
219	C₄²×C₁₉	—	2	2	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	1	no	—
225	C₄²×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
230	#18589	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	#120	1	1	yes	characteristic
233	Q₈×C₁₉	—	2	1	no	—
234	Q₈×C₁₉	—	2	1	no	—
235	Q₈×C₁₉	—	2	1	no	—
236	Q₈×C₁₉	—	2	2	no	—
237	Q₈×C₁₉	—	4	2	no	—
238	Q₈×C₁₉	—	4	4	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	Q₈×C₁₉	—	4	1	no	—
241	Q₈×C₁₉	—	4	2	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	4	2	no	—
244	Q₈×C₁₉	—	8	2	no	—
245	Q₈×C₁₉	#137	1	2	yes	—
246	D₄×C₁₉	—	2	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	4	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₈×C₁₉	—	2	4	no	—
275	C₈×C₁₉	—	4	2	no	—
276	C₈×C₁₉	—	4	2	no	—
277	#3523	C₂×C₁₉	1	1	yes	characteristic
278	#3218	C₂×C₁₉	1	1	yes	characteristic
279	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
280	C₂×#475	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1653	C₂×C₁₉	1	2	yes	complemented
282	#1651	C₂×C₁₉	1	2	yes	complemented
283	#1650	C₂×C₁₉	1	2	yes	complemented
284	#1648	C₂×C₁₉	1	2	yes	complemented
285	#1552	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1483	C₂×C₁₉	1	1	yes	characteristic
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	#456	1	2	yes	—
294	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	8	2	no	—
309	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
310	C₄×C₁₉	#575	1	1	yes	characteristic
311	C₄×C₁₉	#577	1	2	yes	—
312	#557	—	2	1	no	—
313	#557	C₂²×C₁₉	1	1	yes	characteristic
314	#557	C₂²×C₁₉	1	1	yes	characteristic
315	#556	—	2	1	no	—
316	#556	C₂²×C₁₉	1	1	yes	characteristic
317	#552	—	2	2	no	—
318	#552	—	2	1	no	—
319	D₄×Q₈	—	2	1	no	—
320	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	#541	—	2	2	no	—
322	#541	—	2	1	no	—
323	#533	—	2	1	no	—
324	#533	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	#529	—	2	1	no	—
327	#529	C₂²×C₁₉	1	1	yes	characteristic
328	#519	—	2	1	no	—
329	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
330	#501	—	2	2	no	—
331	#500	C₂²×C₁₉	1	2	yes	—
332	#498	C₂²×C₁₉	1	2	yes	—
333	#497	—	2	1	no	—
334	#491	—	2	1	no	—
335	#475	—	2	1	no	—
336	#475	—	2	1	no	—
337	#475	C₂²×C₁₉	1	2	yes	—
338	#475	C₂²×C₁₉	1	2	yes	—
339	#462	C₂²×C₁₉	1	2	yes	—
340	#461	C₂²×C₁₉	1	2	yes	—
341	#451	—	2	1	no	—
342	#448	—	2	1	no	—
343	#432	C₂²×C₁₉	1	1	yes	characteristic
344	#428	—	2	2	no	—
345	C₂×#106	—	2	1	no	—
346	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×#103	—	2	1	no	—
348	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
349	#332	C₂²×C₁₉	1	2	yes	—
350	#332	C₂²×C₁₉	1	2	yes	—
351	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
352	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
353	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
354	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
355	C₂×C₁₉	—	2	2	no	—
356	C₂×C₁₉	—	8	1	no	—
357	C₂×C₁₉	#3007	1	1	yes	characteristic
358	C₂×C₁₉	#3010	1	1	yes	characteristic
359	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
360	C₂²×Q₈	—	2	1	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
363	C₂×Q₁₆	—	2	2	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	2	no	—
368	C₄⋊Q₈	—	2	1	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
375	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#126	—	2	2	no	—
380	#126	—	2	2	no	—
381	#126	—	2	1	no	—
382	#125	—	2	2	no	—
383	#125	—	2	2	no	—
384	#125	—	2	2	no	—
385	#125	—	2	1	no	—
386	#125	—	2	2	no	—
387	#125	—	2	2	no	—
388	#125	—	2	1	no	—
389	#125	D₄×C₁₉	1	1	yes	characteristic
390	#125	D₄×C₁₉	1	2	yes	—
391	#124	—	2	1	no	—
392	#124	D₄×C₁₉	1	1	yes	characteristic
393	#123	—	2	2	no	—
394	#123	—	2	1	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	1	no	—
399	C₂²⋊Q₈	—	2	1	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
403	#121	D₄×C₁₉	1	1	yes	characteristic
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
416	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
417	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
424	#117	—	2	2	no	—
425	#117	—	2	2	no	—
426	#117	—	2	2	no	—
427	#117	—	2	1	no	—
428	#117	—	2	1	no	—
429	#117	D₄×C₁₉	1	2	yes	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
436	#107	—	2	4	no	—
437	#106	—	2	2	no	—
438	#106	—	2	2	no	—
439	#106	—	2	4	no	—
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
442	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	#97	—	2	1	no	—
449	#97	—	2	1	no	—
450	C₄×C₈	C₂³×C₁₉	1	2	yes	—
451	C₁₉	#18589	1	1	yes	characteristic, direct product factor, Sylow
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	4	1	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	—	4	1	no	—
462	C₂×Q₈	—	8	2	no	—
463	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	Q₁₆	—	8	2	no	—
477	SD₁₆	—	8	2	no	—
478	M₁₆	—	2	4	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	4	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
513	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
536	C₂³	—	2	1	no	—
537	C₂³	C₁₉×#120	1	1	yes	characteristic
538	Q₈	—	2	1	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	4	2	no	—
543	Q₈	—	4	4	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	2	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	4	2	no	—
549	Q₈	—	8	2	no	—
550	Q₈	C₁₉×#137	1	2	yes	—
551	D₄	—	2	2	no	—
552	D₄	—	4	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
574	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
575	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
579	C₈	—	2	4	no	—
580	C₈	—	4	2	no	—
581	C₈	—	4	2	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	C₁₉×#456	1	2	yes	—
588	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	8	2	no	—
603	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
604	C₄	C₁₉×#575	1	1	yes	characteristic
605	C₄	C₁₉×#577	1	2	yes	—
606	C₂	—	2	2	no	—
607	C₂	—	8	1	no	—
608	C₂	C₁₉×#3007	1	1	yes	characteristic
609	C₂	C₁₉×#3010	1	1	yes	characteristic
610	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3165	C₂	semidirect
4. C₂×C₁₉×#475	C₂	semidirect
5. C₁₉×#1653	C₂	semidirect
6. C₁₉×#1651	C₂	semidirect
7. C₁₉×#1650	C₂	semidirect
8. C₁₉×#1648	C₂	semidirect
9. C₁₉×#1552	C₂	semidirect
10. C₁₉×#1491	C₂	semidirect
230. #18589	C₁₉	direct (N × H)
279. #3165	C₂×C₁₉	semidirect
280. C₂×#475	C₂×C₁₉	semidirect
281. #1653	C₂×C₁₉	semidirect
282. #1651	C₂×C₁₉	semidirect
283. #1650	C₂×C₁₉	semidirect
284. #1648	C₂×C₁₉	semidirect
285. #1552	C₂×C₁₉	semidirect
286. #1491	C₂×C₁₉	semidirect
451. C₁₉	#18589	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×#3218	2
C₁₉×#3165	2
C₂×C₁₉×#475	2
C₁₉×#1653	2
C₁₉×#1651	2
C₁₉×#1650	2
C₁₉×#1648	2
C₁₉×#1552	2
C₁₉×#1491	2
C₁₉×#1483	2
#18589	19

Subgroups — C19×#18589 #18024548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18589 #18024548