Subgroups — C₁₉×#17385 #18023344

Order 4864.

988 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1472	C₂	1	4	yes	maximal
5	C₁₉×#1470	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1461	C₂	1	4	yes	maximal, complemented
7	C₁₉×#533	—	2	1	no	—
8	C₁₉×#533	—	2	1	no	—
9	C₁₉×#533	—	2	1	no	—
10	C₁₉×#533	—	2	1	no	—
11	C₁₉×#533	—	2	1	no	—
12	C₁₉×#533	—	2	1	no	—
13	C₁₉×#533	—	2	1	no	—
14	C₁₉×#533	—	2	1	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₄	1	2	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#432	—	2	1	no	—
25	C₁₉×#432	C₂²	1	2	yes	—
26	C₁₉×#431	—	2	1	no	—
27	C₁₉×#431	—	2	1	no	—
28	C₁₉×#431	—	2	1	no	—
29	C₁₉×#431	C₂²	1	2	yes	—
30	C₁₉×#431	C₂²	1	2	yes	—
31	C₁₉×#431	C₂²	1	2	yes	—
32	C₁₉×#423	—	2	1	no	—
33	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
34	C₁₉×#407	C₂²	1	2	yes	—
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₉	—	2	1	no	—
37	C₂×C₄×C₈×C₁₉	—	2	1	no	—
38	C₁₉×#324	C₂²	1	16	yes	—
39	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂²×C₈×C₁₉	—	2	2	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×#125	—	2	2	no	—
55	C₁₉×#125	—	2	2	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×C₂²⋊Q₈	—	2	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₄×Q₈×C₁₉	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	—	2	2	no	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₁₉×#117	—	2	2	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
85	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
86	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×C₄⋊C₈	—	2	2	no	—
99	C₁₉×C₄⋊C₈	—	2	2	no	—
100	C₁₉×C₄⋊C₈	—	2	2	no	—
101	C₁₉×C₄⋊C₈	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	2	2	no	—
103	C₁₉×C₂²⋊C₈	—	2	2	no	—
104	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
106	C₁₉×#97	—	2	2	no	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₄×C₈×C₁₉	—	2	2	no	—
109	C₄×C₈×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	8	no	—
116	C₂×Q₈×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	M₁₆×C₁₉	—	4	4	no	—
141	C₂×C₈×C₁₉	—	2	4	no	—
142	C₂×C₈×C₁₉	—	2	4	no	—
143	C₂×C₈×C₁₉	—	4	4	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₄²×C₁₉	—	2	4	no	—
159	C₄²×C₁₉	—	2	4	no	—
160	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
161	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
176	#17385	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
183	Q₈×C₁₉	—	4	4	no	—
184	Q₈×C₁₉	—	4	4	no	—
185	Q₈×C₁₉	—	4	4	no	—
186	Q₈×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	8	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	#101	1	4	yes	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#131	1	4	yes	—
219	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₈×C₁₉	—	4	4	no	—
222	C₈×C₁₉	—	4	4	no	—
223	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
224	#2920	C₂×C₁₉	1	1	yes	characteristic
225	C₂×#431	C₂×C₁₉	1	1	yes	characteristic
226	#1472	C₂×C₁₉	1	4	yes	—
227	#1470	C₂×C₁₉	1	4	yes	complemented
228	#1461	C₂×C₁₉	1	4	yes	complemented
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	C₂×#101	1	2	yes	—
238	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₁₉	C₂×#131	1	2	yes	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	4	no	—
249	C₄×C₁₉	#408	1	2	yes	—
250	C₄×C₁₉	#408	1	2	yes	—
251	C₄×C₁₉	#410	1	2	yes	—
252	C₄×C₁₉	C₂×#101	1	2	yes	—
253	C₄×C₁₉	C₂×#101	1	2	yes	—
254	#533	—	2	1	no	—
255	#533	—	2	1	no	—
256	#533	—	2	1	no	—
257	#533	—	2	1	no	—
258	#533	—	2	1	no	—
259	#533	—	2	1	no	—
260	#533	—	2	1	no	—
261	#533	—	2	1	no	—
262	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
264	C₂×#125	C₂²×C₁₉	1	2	yes	—
265	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
266	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
267	C₂×C₄×Q₈	C₄×C₁₉	1	2	yes	—
268	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
269	C₂×#117	C₄×C₁₉	1	2	yes	—
270	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
271	#432	—	2	1	no	—
272	#432	C₂²×C₁₉	1	2	yes	—
273	#431	—	2	1	no	—
274	#431	—	2	1	no	—
275	#431	—	2	1	no	—
276	#431	C₂²×C₁₉	1	2	yes	—
277	#431	C₂²×C₁₉	1	2	yes	—
278	#431	C₂²×C₁₉	1	2	yes	—
279	#423	—	2	1	no	—
280	C₂×C₄⋊C₈	—	2	1	no	—
281	#407	C₂²×C₁₉	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
283	C₄×M₁₆	—	2	1	no	—
284	C₂×C₄×C₈	—	2	1	no	—
285	#324	C₂²×C₁₉	1	16	yes	—
286	C₂×C₁₉	—	2	2	no	—
287	C₂×C₁₉	—	2	2	no	—
288	C₂×C₁₉	—	4	1	no	—
289	C₂×C₁₉	C₂×#408	1	1	yes	characteristic
290	C₂×C₁₉	C₂×#410	1	1	yes	characteristic
291	C₂×C₁₉	C₂²×#101	1	1	yes	characteristic
292	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
293	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
294	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
297	C₂×M₁₆	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	#125	—	2	2	no	—
308	#125	—	2	2	no	—
309	#125	—	2	2	no	—
310	#125	—	2	2	no	—
311	C₂²⋊Q₈	—	2	2	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	#117	—	2	2	no	—
328	#117	—	2	2	no	—
329	#117	—	2	2	no	—
330	#117	—	2	2	no	—
331	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
332	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
333	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
334	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
338	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
339	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
341	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
343	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
347	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	2	2	no	—
353	C₄⋊C₈	—	2	2	no	—
354	C₄⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₂²⋊C₈	—	2	2	no	—
357	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
358	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
359	#97	—	2	2	no	—
360	C₄×C₈	—	2	2	no	—
361	C₄×C₈	—	2	2	no	—
362	C₄×C₈	—	2	2	no	—
363	C₁₉	#17385	1	1	yes	characteristic, direct product factor, Sylow
364	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	8	no	—
370	C₂×Q₈	—	4	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
376	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
383	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
388	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
394	M₁₆	—	4	4	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	4	4	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	4	no	—
414	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
415	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
416	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
417	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
418	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
419	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
420	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
421	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
422	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
435	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
436	Q₈	—	4	4	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	4	4	no	—
439	Q₈	—	4	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	C₁₉×#101	1	4	yes	—
461	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
463	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
468	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
469	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
470	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₁₉×#131	1	4	yes	—
472	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
474	C₈	—	4	4	no	—
475	C₈	—	4	4	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	4	no	—
484	C₂²	C₂×C₁₉×#101	1	2	yes	—
485	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
486	C₂²	C₂×C₁₉×#131	1	2	yes	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	4	no	—
496	C₄	C₁₉×#408	1	2	yes	—
497	C₄	C₁₉×#408	1	2	yes	—
498	C₄	C₁₉×#410	1	2	yes	—
499	C₄	C₂×C₁₉×#101	1	2	yes	—
500	C₄	C₂×C₁₉×#101	1	2	yes	—
501	C₂	—	2	2	no	—
502	C₂	—	2	2	no	—
503	C₂	—	4	1	no	—
504	C₂	C₂×C₁₉×#408	1	1	yes	characteristic
505	C₂	C₂×C₁₉×#410	1	1	yes	characteristic
506	C₂	C₂²×C₁₉×#101	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₁₉×#1470	C₂	semidirect
6. C₁₉×#1461	C₂	semidirect
176. #17385	C₁₉	direct (N × H)
227. #1470	C₂×C₁₉	semidirect
228. #1461	C₂×C₁₉	semidirect
363. C₁₉	#17385	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#533	2
C₁₉×#2920	2
C₂×C₁₉×#431	2
C₁₉×#1472	2
C₁₉×#1470	2
C₁₉×#1461	2
#17385	19

Subgroups — C19×#17385 #18023344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17385 #18023344