Subgroups — C₁₉×#21425 #18027384

Order 4864.

1100 conjugacy classes of subgroups.

The subgroup lattice has 522 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×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1997	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1966	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1901	C₂	1	4	yes	maximal
7	C₄×C₁₉×#101	C₂	1	4	yes	maximal, complemented
8	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
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	C₁₉×#533	—	2	1	no	—
16	C₁₉×#533	—	2	1	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#125	C₄	1	2	yes	—
20	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₁₉×#117	C₄	1	2	yes	—
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#432	—	2	1	no	—
27	C₁₉×#432	—	2	1	no	—
28	C₁₉×#431	—	2	1	no	—
29	C₁₉×#431	—	2	1	no	—
30	C₁₉×#423	C₂²	1	2	yes	—
31	C₂×C₁₉×#101	C₂²	1	8	yes	—
32	C₁₉×#407	C₂²	1	2	yes	—
33	C₄×M₁₆×C₁₉	—	2	1	no	—
34	C₄×M₁₆×C₁₉	—	2	1	no	—
35	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
37	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
38	C₂×C₁₉×#97	—	2	1	no	—
39	C₂×C₄×C₈×C₁₉	—	2	1	no	—
40	C₁₉×#343	C₂²	1	8	yes	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	8	no	—
48	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
49	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#125	—	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	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	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	C₄×Q₈×C₁₉	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
90	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
91	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂×C₄	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	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×C₄⋊C₈	—	2	2	no	—
104	C₁₉×C₄⋊C₈	—	2	2	no	—
105	C₁₉×#101	—	2	16	no	—
106	C₁₉×C₂²⋊C₈	—	2	2	no	—
107	C₁₉×C₂²⋊C₈	—	2	2	no	—
108	C₁₉×#97	—	2	2	no	—
109	C₁₉×#97	—	2	2	no	—
110	C₁₉×#97	—	2	2	no	—
111	C₄×C₈×C₁₉	—	2	2	no	—
112	C₄×C₈×C₁₉	—	2	2	no	—
113	C₄×C₈×C₁₉	—	2	2	no	—
114	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	8	no	—
120	C₂×Q₈×C₁₉	—	4	4	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
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	1	yes	characteristic
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	4	yes	—
133	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₁₉	—	2	8	no	—
145	M₁₆×C₁₉	—	2	4	no	—
146	M₁₆×C₁₉	—	2	8	no	—
147	M₁₆×C₁₉	#41	1	8	yes	—
148	C₂×C₈×C₁₉	—	2	8	no	—
149	C₂×C₈×C₁₉	—	2	4	no	—
150	C₂×C₈×C₁₉	—	2	4	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	2	no	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	4	no	—
165	C₄²×C₁₉	—	2	4	no	—
166	C₄²×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
183	#21425	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
190	Q₈×C₁₉	—	4	4	no	—
191	Q₈×C₁₉	—	4	4	no	—
192	Q₈×C₁₉	—	4	4	no	—
193	Q₈×C₁₉	—	4	4	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	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	8	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	4	no	—
214	C₂×C₄×C₁₉	#101	1	4	yes	complemented
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
228	C₈×C₁₉	—	2	8	no	—
229	C₈×C₁₉	—	4	4	no	—
230	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
231	#2920	C₂×C₁₉	1	1	yes	characteristic
232	C₂×C₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic
233	#1997	C₂×C₁₉	1	2	yes	complemented
234	#1966	C₂×C₁₉	1	2	yes	complemented
235	#1901	C₂×C₁₉	1	4	yes	—
236	C₄×#101	C₂×C₁₉	1	4	yes	complemented
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	4	4	no	—
245	C₂²×C₁₉	C₂×#101	1	2	yes	—
246	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₁₉	C₄×#41	1	2	yes	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	C₂×#101	1	2	yes	—
258	C₄×C₁₉	C₂×#101	1	2	yes	—
259	C₄×C₁₉	#413	1	2	yes	—
260	C₄×C₁₉	#525	1	2	yes	—
261	C₄×C₁₉	#532	1	2	yes	—
262	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
263	#533	—	2	1	no	—
264	#533	—	2	1	no	—
265	#533	—	2	1	no	—
266	#533	—	2	1	no	—
267	#533	—	2	1	no	—
268	#533	—	2	1	no	—
269	#533	—	2	1	no	—
270	#533	—	2	1	no	—
271	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#125	C₄×C₁₉	1	2	yes	—
274	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
275	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
276	C₂×C₄×Q₈	C₄×C₁₉	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
278	C₂×#117	C₄×C₁₉	1	2	yes	—
279	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
280	#432	—	2	1	no	—
281	#432	—	2	1	no	—
282	#431	—	2	1	no	—
283	#431	—	2	1	no	—
284	#423	C₂²×C₁₉	1	2	yes	—
285	C₂×#101	C₂²×C₁₉	1	8	yes	—
286	#407	C₂²×C₁₉	1	2	yes	—
287	C₄×M₁₆	—	2	1	no	—
288	C₄×M₁₆	—	2	1	no	—
289	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
290	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
291	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
292	C₂×#97	—	2	1	no	—
293	C₂×C₄×C₈	—	2	1	no	—
294	#343	C₂²×C₁₉	1	8	yes	—
295	C₂×C₁₉	—	2	2	no	—
296	C₂×C₁₉	—	2	2	no	—
297	C₂×C₁₉	—	4	1	no	—
298	C₂×C₁₉	#2297	1	1	yes	characteristic
299	C₂×C₁₉	C₂²×#101	1	1	yes	characteristic
300	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
301	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
302	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
303	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	8	no	—
308	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
309	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
310	C₂²×C₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	#125	—	2	2	no	—
320	#125	—	2	2	no	—
321	#125	—	2	2	no	—
322	#125	—	2	2	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	#117	—	2	2	no	—
340	#117	—	2	2	no	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
344	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
345	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
346	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
347	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
350	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
351	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
354	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
357	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
358	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
363	C₄⋊C₈	—	2	2	no	—
364	C₄⋊C₈	—	2	2	no	—
365	#101	—	2	16	no	—
366	C₂²⋊C₈	—	2	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	#97	—	2	2	no	—
369	#97	—	2	2	no	—
370	#97	—	2	2	no	—
371	C₄×C₈	—	2	2	no	—
372	C₄×C₈	—	2	2	no	—
373	C₄×C₈	—	2	2	no	—
374	C₁₉	#21425	1	1	yes	characteristic, direct product factor, Sylow
375	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	4	2	no	—
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	1	yes	characteristic
388	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
394	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
399	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
405	M₁₆	—	2	8	no	—
406	M₁₆	—	2	4	no	—
407	M₁₆	—	2	8	no	—
408	M₁₆	#41×C₁₉	1	8	yes	—
409	C₂×C₈	—	2	8	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	2	4	no	—
428	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
429	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
430	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
431	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
432	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
433	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
435	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
436	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
448	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
449	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
450	Q₈	—	4	4	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	4	4	no	—
453	Q₈	—	4	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	C₁₉×#101	1	4	yes	complemented
475	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
476	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
477	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
478	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
479	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
480	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
482	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
484	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
488	C₈	—	2	8	no	—
489	C₈	—	4	4	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	4	no	—
498	C₂²	C₂×C₁₉×#101	1	2	yes	—
499	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
500	C₂²	C₄×#41×C₁₉	1	2	yes	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	C₂×C₁₉×#101	1	2	yes	—
511	C₄	C₂×C₁₉×#101	1	2	yes	—
512	C₄	C₁₉×#413	1	2	yes	—
513	C₄	C₁₉×#525	1	2	yes	—
514	C₄	C₁₉×#532	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	2	2	no	—
517	C₂	—	4	1	no	—
518	C₂	C₁₉×#2297	1	1	yes	characteristic
519	C₂	C₂²×C₁₉×#101	1	1	yes	characteristic
520	C₂	C₂×C₁₉×#413	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
4. C₁₉×#1997	C₂	semidirect
5. C₁₉×#1966	C₂	semidirect
7. C₄×C₁₉×#101	C₂	semidirect
183. #21425	C₁₉	direct (N × H)
214. C₂×C₄×C₁₉	#101	semidirect
233. #1997	C₂×C₁₉	semidirect
234. #1966	C₂×C₁₉	semidirect
236. C₄×#101	C₂×C₁₉	semidirect
374. C₁₉	#21425	direct (N × H)
474. C₂×C₄	C₁₉×#101	semidirect

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×C₄×M₁₆×C₁₉	2
C₁₉×#1997	2
C₁₉×#1966	2
C₁₉×#1901	2
C₄×C₁₉×#101	2
#21425	19

Subgroups — C19×#21425 #18027384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21425 #18027384