Subgroups — C₁₉×#18453 #18024412

Order 4864.

970 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3536	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3196	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3189	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2816	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1614	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1606	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1602	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1516	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1511	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1471	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	—	2	2	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#548	—	2	1	no	—
15	C₁₉×#547	—	2	1	no	—
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	1	no	—
18	C₁₉×#543	C₂²	1	2	yes	—
19	C₁₉×#542	—	2	1	no	—
20	C₁₉×#539	—	2	1	no	—
21	C₁₉×#538	C₂²	1	2	yes	—
22	C₁₉×#537	—	2	1	no	—
23	C₁₉×#537	—	2	1	no	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₁₉×#485	—	2	1	no	—
29	C₁₉×#484	—	2	1	no	—
30	C₁₉×#484	C₂²	1	2	yes	—
31	C₁₉×#484	C₂²	1	1	yes	characteristic
32	C₁₉×#481	C₂²	1	1	yes	characteristic
33	C₁₉×#470	—	2	1	no	—
34	C₁₉×#468	—	2	1	no	—
35	C₁₉×#467	—	2	2	no	—
36	C₁₉×#452	—	2	1	no	—
37	C₁₉×#451	—	2	1	no	—
38	C₁₉×#451	C₂²	1	2	yes	—
39	C₁₉×#451	C₂²	1	1	yes	characteristic
40	C₁₉×#448	C₂²	1	1	yes	characteristic
41	C₁₉×#407	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₉×#399	C₂²	1	2	yes	—
44	C₁₉×#398	—	2	1	no	—
45	C₁₉×#394	—	2	2	no	—
46	C₁₉×#394	—	2	1	no	—
47	C₁₉×#393	C₂²	1	2	yes	—
48	C₁₉×#381	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#328	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#323	C₂²	1	2	yes	—
54	C₁₉×#323	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	D₄	1	2	yes	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₁₉	—	2	2	no	—
64	C₂×Q₁₆×C₁₉	—	2	1	no	—
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#124	—	2	1	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	1	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
93	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
95	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	D₄	1	1	yes	characteristic
107	C₁₉×#121	C₂³	1	1	yes	characteristic
108	C₁₉×#120	—	2	1	no	—
109	C₁₉×#120	—	2	2	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	—	2	2	no	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	—	2	1	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	2	no	—
116	C₁₉×#117	D₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
131	C₁₉×#107	—	2	2	no	—
132	C₁₉×#107	—	2	1	no	—
133	C₁₉×#106	—	2	1	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
143	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
144	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
145	C₁₉×#95	—	2	1	no	—
146	C₁₉×#95	—	2	2	no	—
147	C₁₉×#95	C₂³	1	2	yes	—
148	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
149	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
150	#41×C₁₉	—	8	1	no	—
151	#41×C₁₉	—	8	4	no	—
152	#41×C₁₉	—	8	2	no	—
153	C₂×Q₈×C₁₉	—	2	2	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	8	1	no	—
158	C₂×Q₈×C₁₉	—	8	1	no	—
159	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	2	2	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	8	1	no	—
171	C₂×D₄×C₁₉	—	8	2	no	—
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	8	1	no	—
183	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
190	Q₁₆×C₁₉	—	8	2	no	—
191	Q₁₆×C₁₉	—	8	1	no	—
192	SD₁₆×C₁₉	—	8	1	no	—
193	M₁₆×C₁₉	—	8	1	no	—
194	C₂×C₈×C₁₉	—	2	2	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	8	1	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	2	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	4	1	no	—
212	C₄⋊C₄×C₁₉	—	4	1	no	—
213	C₄⋊C₄×C₁₉	—	8	2	no	—
214	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₉	—	2	1	no	—
231	C₂²⋊C₄×C₁₉	—	4	1	no	—
232	C₂²⋊C₄×C₁₉	—	4	1	no	—
233	C₂²⋊C₄×C₁₉	—	8	1	no	—
234	C₂²⋊C₄×C₁₉	—	8	2	no	—
235	C₂²⋊C₄×C₁₉	—	8	2	no	—
236	C₄²×C₁₉	—	2	2	no	—
237	C₄²×C₁₉	—	2	1	no	—
238	#18453	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	2	no	—
240	C₂³×C₁₉	—	2	2	no	—
241	C₂³×C₁₉	—	2	1	no	—
242	C₂³×C₁₉	—	2	4	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	2	no	—
246	C₂³×C₁₉	—	4	2	no	—
247	C₂³×C₁₉	#120	1	1	yes	characteristic
248	C₂³×C₁₉	#120	1	1	yes	characteristic
249	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	Q₈×C₁₉	—	4	2	no	—
251	Q₈×C₁₉	—	4	1	no	—
252	Q₈×C₁₉	—	4	2	no	—
253	Q₈×C₁₉	—	4	1	no	—
254	Q₈×C₁₉	—	4	1	no	—
255	Q₈×C₁₉	—	4	2	no	—
256	Q₈×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	4	1	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	4	no	—
260	D₄×C₁₉	—	4	2	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	8	1	no	—
263	D₄×C₁₉	—	8	2	no	—
264	D₄×C₁₉	—	8	1	no	—
265	D₄×C₁₉	—	8	2	no	—
266	D₄×C₁₉	—	8	2	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	2	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	2	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	2	no	—
290	C₂×C₄×C₁₉	—	8	1	no	—
291	C₂×C₄×C₁₉	—	8	2	no	—
292	C₂×C₄×C₁₉	—	8	2	no	—
293	C₂×C₄×C₁₉	—	8	2	no	—
294	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
298	C₈×C₁₉	—	4	2	no	—
299	C₈×C₁₉	—	4	1	no	—
300	C₈×C₁₉	—	4	1	no	—
301	#3536	C₂×C₁₉	1	1	yes	characteristic
302	#3196	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#3189	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#2816	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1618	C₂×C₁₉	1	2	yes	complemented
306	#1614	C₂×C₁₉	1	2	yes	complemented
307	#1606	C₂×C₁₉	1	2	yes	complemented
308	#1602	C₂×C₁₉	1	2	yes	complemented
309	#1516	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1511	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1471	C₂×C₁₉	1	1	yes	characteristic, complemented
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	2	1	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	2	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	4	2	no	—
326	C₂²×C₁₉	—	8	2	no	—
327	C₂²×C₁₉	—	8	4	no	—
328	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
329	C₂²×C₁₉	#578	1	2	yes	—
330	C₄×C₁₉	—	2	1	no	—
331	C₄×C₁₉	—	2	1	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	2	1	no	—
334	C₄×C₁₉	—	4	1	no	—
335	C₄×C₁₉	—	4	2	no	—
336	C₄×C₁₉	—	4	2	no	—
337	C₄×C₁₉	—	4	1	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	4	2	no	—
340	C₄×C₁₉	—	8	2	no	—
341	C₄×C₁₉	—	8	1	no	—
342	C₄×C₁₉	—	8	1	no	—
343	#562	—	2	2	no	—
344	#554	—	2	1	no	—
345	#548	—	2	1	no	—
346	#547	—	2	1	no	—
347	#546	—	2	2	no	—
348	#546	—	2	1	no	—
349	#543	C₂²×C₁₉	1	2	yes	—
350	#542	—	2	1	no	—
351	#539	—	2	1	no	—
352	#538	C₂²×C₁₉	1	2	yes	—
353	#537	—	2	1	no	—
354	#537	—	2	1	no	—
355	#525	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
359	#485	—	2	1	no	—
360	#484	—	2	1	no	—
361	#484	C₂²×C₁₉	1	1	yes	characteristic
362	#484	C₂²×C₁₉	1	2	yes	—
363	#481	C₂²×C₁₉	1	1	yes	characteristic
364	#470	—	2	1	no	—
365	#468	—	2	1	no	—
366	#467	—	2	2	no	—
367	#452	—	2	1	no	—
368	#451	—	2	1	no	—
369	#451	C₂²×C₁₉	1	1	yes	characteristic
370	#451	C₂²×C₁₉	1	2	yes	—
371	#448	C₂²×C₁₉	1	1	yes	characteristic
372	#407	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
374	#399	C₂²×C₁₉	1	2	yes	—
375	#398	—	2	1	no	—
376	#394	—	2	1	no	—
377	#394	—	2	2	no	—
378	#393	C₂²×C₁₉	1	2	yes	—
379	#381	C₂²×C₁₉	1	1	yes	characteristic
380	#328	C₂²×C₁₉	1	2	yes	—
381	#328	C₂²×C₁₉	1	2	yes	—
382	#328	C₂²×C₁₉	1	2	yes	—
383	#327	C₂²×C₁₉	1	2	yes	—
384	#323	C₂²×C₁₉	1	2	yes	—
385	#323	C₂²×C₁₉	1	2	yes	—
386	C₂×C₁₉	—	2	2	no	—
387	C₂×C₁₉	—	4	1	no	—
388	C₂×C₁₉	—	4	1	no	—
389	C₂×C₁₉	—	8	1	no	—
390	C₂×C₁₉	—	8	2	no	—
391	C₂×C₁₉	#3011	1	1	yes	characteristic
392	C₂×C₁₉	#3019	1	1	yes	characteristic
393	C₂×C₁₉	#3026	1	1	yes	characteristic
394	C₂×#41	—	2	2	no	—
395	C₂×#41	—	2	1	no	—
396	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
397	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₂²×D₄	D₄×C₁₉	1	2	yes	—
400	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×Q₁₆	—	2	2	no	—
403	C₂×Q₁₆	—	2	1	no	—
404	C₂×SD₁₆	—	2	1	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₄⋊Q₈	—	2	1	no	—
408	#126	—	2	2	no	—
409	#125	—	2	2	no	—
410	#124	—	2	1	no	—
411	#124	—	2	2	no	—
412	#124	—	2	2	no	—
413	#123	—	2	2	no	—
414	#123	—	2	2	no	—
415	#123	—	2	2	no	—
416	#123	—	2	1	no	—
417	#123	—	2	2	no	—
418	C₂²⋊Q₈	—	2	1	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	2	no	—
426	C₂²⋊Q₈	—	2	2	no	—
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	D₄×C₁₉	1	2	yes	—
432	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
433	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
434	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
435	#121	—	2	1	no	—
436	#121	—	2	2	no	—
437	#121	—	2	2	no	—
438	#121	—	2	2	no	—
439	#121	—	2	2	no	—
440	#121	—	2	2	no	—
441	#121	—	2	1	no	—
442	#121	—	2	1	no	—
443	#121	—	2	1	no	—
444	#121	—	2	1	no	—
445	#121	D₄×C₁₉	1	1	yes	characteristic
446	#121	C₂³×C₁₉	1	1	yes	characteristic
447	#120	—	2	1	no	—
448	#120	—	2	2	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	2	no	—
455	#117	D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	2	no	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
470	#107	—	2	2	no	—
471	#107	—	2	1	no	—
472	#106	—	2	1	no	—
473	#103	—	2	2	no	—
474	#103	—	2	1	no	—
475	#103	—	2	1	no	—
476	#103	—	2	2	no	—
477	#103	—	2	1	no	—
478	#102	—	2	1	no	—
479	C₂²⋊C₈	—	2	1	no	—
480	C₂²⋊C₈	—	2	1	no	—
481	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
482	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
483	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
484	#95	—	2	1	no	—
485	#95	—	2	2	no	—
486	#95	C₂³×C₁₉	1	2	yes	—
487	C₁₉	#18453	1	1	yes	characteristic, direct product factor, Sylow
488	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
489	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
490	#41	—	8	1	no	—
491	#41	—	8	4	no	—
492	#41	—	8	2	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	8	1	no	—
498	C₂×Q₈	—	8	1	no	—
499	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	8	1	no	—
511	C₂×D₄	—	8	2	no	—
512	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂²×C₄	—	2	1	no	—
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	1	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	8	1	no	—
523	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
530	Q₁₆	—	8	2	no	—
531	Q₁₆	—	8	1	no	—
532	SD₁₆	—	8	1	no	—
533	M₁₆	—	8	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	2	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	8	1	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	—	4	1	no	—
553	C₄⋊C₄	—	8	2	no	—
554	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
556	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	8	1	no	—
574	C₂²⋊C₄	—	8	2	no	—
575	C₂²⋊C₄	—	8	2	no	—
576	C₄²	—	2	2	no	—
577	C₄²	—	2	1	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	C₁₉×#120	1	1	yes	characteristic
587	C₂³	C₁₉×#120	1	1	yes	characteristic
588	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
589	Q₈	—	4	2	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	2	no	—
592	Q₈	—	4	1	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	2	no	—
595	Q₈	—	8	2	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	4	no	—
599	D₄	—	4	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	8	1	no	—
602	D₄	—	8	2	no	—
603	D₄	—	8	1	no	—
604	D₄	—	8	2	no	—
605	D₄	—	8	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	8	1	no	—
630	C₂×C₄	—	8	2	no	—
631	C₂×C₄	—	8	2	no	—
632	C₂×C₄	—	8	2	no	—
633	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
634	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
637	C₈	—	4	2	no	—
638	C₈	—	4	1	no	—
639	C₈	—	4	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	8	2	no	—
655	C₂²	—	8	4	no	—
656	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
657	C₂²	C₁₉×#578	1	2	yes	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	2	no	—
668	C₄	—	8	2	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₂	—	2	2	no	—
672	C₂	—	4	1	no	—
673	C₂	—	4	1	no	—
674	C₂	—	8	2	no	—
675	C₂	—	8	1	no	—
676	C₂	C₁₉×#3011	1	1	yes	characteristic
677	C₂	C₁₉×#3019	1	1	yes	characteristic
678	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3536	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3196	C₂	semidirect
3. C₁₉×#3189	C₂	semidirect
4. C₁₉×#2816	C₂	semidirect
5. C₁₉×#1618	C₂	semidirect
6. C₁₉×#1614	C₂	semidirect
7. C₁₉×#1606	C₂	semidirect
8. C₁₉×#1602	C₂	semidirect
9. C₁₉×#1516	C₂	semidirect
10. C₁₉×#1511	C₂	semidirect
11. C₁₉×#1471	C₂	semidirect
238. #18453	C₁₉	direct (N × H)
302. #3196	C₂×C₁₉	semidirect
303. #3189	C₂×C₁₉	semidirect
304. #2816	C₂×C₁₉	semidirect
305. #1618	C₂×C₁₉	semidirect
306. #1614	C₂×C₁₉	semidirect
307. #1606	C₂×C₁₉	semidirect
308. #1602	C₂×C₁₉	semidirect
309. #1516	C₂×C₁₉	semidirect
310. #1511	C₂×C₁₉	semidirect
311. #1471	C₂×C₁₉	semidirect
487. C₁₉	#18453	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×#3536	2
C₁₉×#3196	2
C₁₉×#3189	2
C₁₉×#2816	2
C₁₉×#1618	2
C₁₉×#1614	2
C₁₉×#1606	2
C₁₉×#1602	2
C₁₉×#1516	2
C₁₉×#1511	2
C₁₉×#1471	2
#18453	19

Subgroups — C19×#18453 #18024412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18453 #18024412