Subgroups — C₁₉×#17996 #18023955

Order 4864.

618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3102	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1591	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#529	C₂²	1	1	yes	characteristic
17	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#485	C₄	1	1	yes	characteristic
19	C₁₉×#482	C₄	1	1	yes	characteristic
20	C₁₉×#479	C₄	1	1	yes	characteristic
21	C₁₉×#478	C₄	1	1	yes	characteristic
22	C₁₉×#464	C₄	1	1	yes	characteristic
23	C₁₉×#463	C₄	1	1	yes	characteristic
24	C₁₉×#452	C₄	1	1	yes	characteristic
25	C₁₉×#449	C₄	1	1	yes	characteristic
26	C₁₉×#446	C₂²	1	1	yes	characteristic
27	C₁₉×#446	C₂²	1	1	yes	characteristic
28	C₁₉×#446	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#436	—	2	1	no	—
35	C₁₉×#436	C₂²	1	1	yes	characteristic
36	C₁₉×#435	—	2	1	no	—
37	C₁₉×#435	—	2	1	no	—
38	C₁₉×#435	—	2	1	no	—
39	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#433	—	2	1	no	—
43	C₁₉×#432	—	2	1	no	—
44	C₁₉×#432	C₂²	1	1	yes	characteristic
45	C₁₉×#431	C₂²	1	1	yes	characteristic
46	C₁₉×#431	C₂²	1	1	yes	characteristic
47	C₁₉×#405	—	2	1	no	—
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#97	—	2	1	no	—
50	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#335	C₂²	1	1	yes	characteristic
52	C₁₉×#335	C₂²	1	1	yes	characteristic
53	C₁₉×#334	C₂²	1	1	yes	characteristic
54	C₁₉×#334	C₂²	1	1	yes	characteristic
55	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×#322	C₂²	1	1	yes	characteristic
64	C₁₉×#322	C₂²	1	1	yes	characteristic
65	C₈²×C₁₉	C₂²	1	1	yes	characteristic
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	—	2	1	no	—
76	C₂²×C₈×C₁₉	—	2	1	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₁₉×#126	—	2	1	no	—
80	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
81	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
82	C₁₉×#123	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#117	—	2	1	no	—
95	C₁₉×#117	—	2	1	no	—
96	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
100	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
101	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
102	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
103	C₁₉×C₄⋊C₈	—	2	1	no	—
104	C₁₉×C₄⋊C₈	—	2	1	no	—
105	C₁₉×C₄⋊C₈	—	2	1	no	—
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
114	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
115	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
118	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
119	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
120	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
121	C₁₉×C₂²⋊C₈	—	2	1	no	—
122	C₁₉×C₂²⋊C₈	—	2	1	no	—
123	C₁₉×C₂²⋊C₈	—	2	1	no	—
124	C₁₉×C₂²⋊C₈	—	2	1	no	—
125	C₁₉×C₂²⋊C₈	—	2	1	no	—
126	C₁₉×C₂²⋊C₈	—	2	1	no	—
127	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
128	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₁₉×#97	—	2	1	no	—
130	C₁₉×#97	—	2	1	no	—
131	C₁₉×#97	—	2	1	no	—
132	C₁₉×#97	—	2	1	no	—
133	C₁₉×#97	D₄	1	1	yes	characteristic
134	C₁₉×#97	D₄	1	1	yes	characteristic
135	C₄×C₈×C₁₉	—	2	1	no	—
136	C₄×C₈×C₁₉	—	2	1	no	—
137	C₄×C₈×C₁₉	—	2	1	no	—
138	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	2	2	no	—
145	#41×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
159	Q₁₆×C₁₉	—	4	1	no	—
160	SD₁₆×C₁₉	—	2	2	no	—
161	SD₁₆×C₁₉	—	4	1	no	—
162	D₈×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	—	4	2	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	4	2	no	—
173	C₂×C₈×C₁₉	—	4	2	no	—
174	C₂×C₈×C₁₉	—	4	2	no	—
175	C₂×C₈×C₁₉	—	4	2	no	—
176	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	#41	1	1	yes	characteristic
209	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
210	#17996	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
214	Q₈×C₁₉	—	2	1	no	—
215	Q₈×C₁₉	—	2	1	no	—
216	Q₈×C₁₉	—	2	1	no	—
217	Q₈×C₁₉	—	2	1	no	—
218	D₄×C₁₉	—	2	1	no	—
219	D₄×C₁₉	—	2	1	no	—
220	D₄×C₁₉	—	2	1	no	—
221	D₄×C₁₉	—	4	2	no	—
222	D₄×C₁₉	—	8	1	no	—
223	D₄×C₁₉	#131	1	2	yes	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	8	1	no	—
241	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
247	C₈×C₁₉	—	2	2	no	—
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	—	2	1	no	—
250	C₈×C₁₉	—	2	1	no	—
251	C₈×C₁₉	—	2	1	no	—
252	C₈×C₁₉	—	2	1	no	—
253	C₈×C₁₉	—	2	1	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	C₈×C₁₉	—	4	1	no	—
257	C₈×C₁₉	—	4	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	#135	1	2	yes	—
260	C₈×C₁₉	#135	1	2	yes	—
261	#3102	C₂×C₁₉	1	1	yes	characteristic
262	#2970	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#2969	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1591	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1590	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
270	C₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1476	C₂×C₁₉	1	1	yes	characteristic, complemented
275	C₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
286	C₄×C₁₉	—	2	1	no	—
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	4	1	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	C₂×#131	1	1	yes	characteristic
297	C₄×C₁₉	#568	1	1	yes	characteristic
298	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
299	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
300	#529	C₂²×C₁₉	1	1	yes	characteristic
301	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
302	#485	C₄×C₁₉	1	1	yes	characteristic
303	#482	C₄×C₁₉	1	1	yes	characteristic
304	#479	C₄×C₁₉	1	1	yes	characteristic
305	#478	C₄×C₁₉	1	1	yes	characteristic
306	#464	C₄×C₁₉	1	1	yes	characteristic
307	#463	C₄×C₁₉	1	1	yes	characteristic
308	#452	C₄×C₁₉	1	1	yes	characteristic
309	#449	C₄×C₁₉	1	1	yes	characteristic
310	#446	C₂²×C₁₉	1	1	yes	characteristic
311	#446	C₂²×C₁₉	1	1	yes	characteristic
312	#446	C₂²×C₁₉	1	1	yes	characteristic
313	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
316	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
317	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
318	#436	—	2	1	no	—
319	#436	C₂²×C₁₉	1	1	yes	characteristic
320	#435	—	2	1	no	—
321	#435	—	2	1	no	—
322	#435	—	2	1	no	—
323	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
324	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
325	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
326	#433	—	2	1	no	—
327	#432	—	2	1	no	—
328	#432	C₂²×C₁₉	1	1	yes	characteristic
329	#431	C₂²×C₁₉	1	1	yes	characteristic
330	#431	C₂²×C₁₉	1	1	yes	characteristic
331	#405	—	2	1	no	—
332	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#97	—	2	1	no	—
334	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
335	#335	C₂²×C₁₉	1	1	yes	characteristic
336	#335	C₂²×C₁₉	1	1	yes	characteristic
337	#334	C₂²×C₁₉	1	1	yes	characteristic
338	#334	C₂²×C₁₉	1	1	yes	characteristic
339	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
341	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
342	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
343	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
344	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
345	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
346	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
347	#322	C₂²×C₁₉	1	1	yes	characteristic
348	#322	C₂²×C₁₉	1	1	yes	characteristic
349	C₈²	C₂²×C₁₉	1	1	yes	characteristic
350	C₈²	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×C₁₉	—	4	1	no	—
352	C₂×C₁₉	—	4	2	no	—
353	C₂×C₁₉	—	8	1	no	—
354	C₂×C₁₉	#2933	1	1	yes	characteristic
355	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
356	C₂×C₁₉	#2956	1	1	yes	characteristic
357	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
358	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
359	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
361	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
364	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	#126	—	2	1	no	—
370	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
371	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
372	#123	—	2	1	no	—
373	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
374	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
382	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
383	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
389	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
390	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
391	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
392	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
403	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
404	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
405	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
406	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
407	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
408	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
409	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
410	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
418	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
419	#97	—	2	1	no	—
420	#97	—	2	1	no	—
421	#97	—	2	1	no	—
422	#97	—	2	1	no	—
423	#97	D₄×C₁₉	1	1	yes	characteristic
424	#97	D₄×C₁₉	1	1	yes	characteristic
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
434	C₁₉	#17996	1	1	yes	characteristic, direct product factor, Sylow
435	#41	—	2	2	no	—
436	#41	—	4	1	no	—
437	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
438	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
442	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
450	Q₁₆	—	4	1	no	—
451	SD₁₆	—	2	2	no	—
452	SD₁₆	—	4	1	no	—
453	D₈	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	4	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	4	2	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	—	4	2	no	—
466	C₂×C₈	—	4	2	no	—
467	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
468	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
469	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
470	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₄²	#41×C₁₉	1	1	yes	characteristic
500	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	4	2	no	—
512	D₄	—	8	1	no	—
513	D₄	C₁₉×#131	1	2	yes	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
532	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
536	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
537	C₈	—	2	2	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	C₁₉×#135	1	2	yes	—
550	C₈	C₁₉×#135	1	2	yes	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	C₂×C₁₉×#131	1	1	yes	characteristic
572	C₄	C₁₉×#568	1	1	yes	characteristic
573	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
574	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	1	no	—
578	C₂	C₁₉×#2933	1	1	yes	characteristic
579	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
580	C₂	C₁₉×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₁₉×#449	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2970	C₂	semidirect
3. C₁₉×#2969	C₂	semidirect
4. C₁₉×#1591	C₂	semidirect
5. C₁₉×#1590	C₂	semidirect
6. C₁₉×#1584	C₂	semidirect
7. C₁₉×#1582	C₂	semidirect
8. C₁₉×#1582	C₂	semidirect
9. C₁₉×#1581	C₂	semidirect
10. C₈×SD₁₆×C₁₉	C₂	semidirect
11. C₈×D₈×C₁₉	C₂	semidirect
12. C₁₉×#1572	C₂	semidirect
13. C₁₉×#1494	C₂	semidirect
14. C₁₉×#1476	C₂	semidirect
15. C₈×M₁₆×C₁₉	C₂	semidirect
210. #17996	C₁₉	direct (N × H)
262. #2970	C₂×C₁₉	semidirect
263. #2969	C₂×C₁₉	semidirect
264. #1591	C₂×C₁₉	semidirect
265. #1590	C₂×C₁₉	semidirect
266. #1584	C₂×C₁₉	semidirect
267. #1582	C₂×C₁₉	semidirect
268. #1582	C₂×C₁₉	semidirect
269. #1581	C₂×C₁₉	semidirect
270. C₈×SD₁₆	C₂×C₁₉	semidirect
271. C₈×D₈	C₂×C₁₉	semidirect
272. #1572	C₂×C₁₉	semidirect
273. #1494	C₂×C₁₉	semidirect
274. #1476	C₂×C₁₉	semidirect
275. C₈×M₁₆	C₂×C₁₉	semidirect
434. C₁₉	#17996	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×#3102	2
C₁₉×#2970	2
C₁₉×#2969	2
C₁₉×#1591	2
C₁₉×#1590	2
C₁₉×#1584	2
C₁₉×#1582	2
C₁₉×#1581	2
C₈×SD₁₆×C₁₉	2
C₈×D₈×C₁₉	2
C₁₉×#1572	2
C₁₉×#1494	2
C₁₉×#1476	2
C₈×M₁₆×C₁₉	2
#17996	19

Subgroups — C19×#17996 #18023955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17996 #18023955