Subgroups — C₁₉×#21175 #18027134

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2274	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1949	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1949	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1948	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1947	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#428	—	2	4	no	—
20	C₁₉×#427	—	2	4	no	—
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#107	C₂²	1	2	yes	—
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	2	yes	—
26	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
27	C₁₉×#424	C₄	1	8	yes	complemented
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
30	C₁₉×#389	—	2	1	no	—
31	C₁₉×#389	—	2	1	no	—
32	C₁₉×#385	—	2	2	no	—
33	C₁₉×#384	C₂²	1	2	yes	—
34	C₁₉×#382	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
39	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#340	C₂²	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₁₉×#117	—	2	2	no	—
57	C₁₉×#117	—	2	2	no	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	C₂×C₄	1	4	yes	—
60	C₁₉×#117	D₄	1	4	yes	—
61	C₁₉×#117	Q₈	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₁₉×#107	—	2	2	no	—
87	C₁₉×#107	—	2	2	no	—
88	C₁₉×#107	—	2	4	no	—
89	C₁₉×#106	—	2	2	no	—
90	C₁₉×#106	—	2	2	no	—
91	C₁₉×#106	—	2	4	no	—
92	C₁₉×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
93	C₁₉×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	—	2	2	no	—
97	C₁₉×#95	—	2	2	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	8	1	no	—
108	C₂²×C₄×C₁₉	—	8	1	no	—
109	C₂²×C₄×C₁₉	—	8	1	no	—
110	C₂²×C₄×C₁₉	—	8	1	no	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₉	#41	1	2	yes	—
119	C₂²×C₄×C₁₉	#41	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	M₁₆×C₁₉	—	2	8	no	—
122	C₂×C₈×C₁₉	—	2	8	no	—
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	4	2	no	—
143	C₄⋊C₄×C₁₉	—	8	2	no	—
144	C₄⋊C₄×C₁₉	—	8	2	no	—
145	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
146	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
147	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	4	2	no	—
152	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	8	yes	—
153	C₄²×C₁₉	—	2	4	no	—
154	C₄²×C₁₉	—	4	2	no	—
155	C₄²×C₁₉	—	8	2	no	—
156	C₄²×C₁₉	—	8	2	no	—
157	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
158	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
159	#21175	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
165	C₂³×C₁₉	#121	1	2	yes	—
166	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
167	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	8	4	no	—
191	C₂×C₄×C₁₉	—	8	4	no	—
192	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
193	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
194	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
196	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
197	C₂×C₄×C₁₉	#121	1	2	yes	—
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
199	C₂×C₄×C₁₉	#125	1	4	yes	—
200	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
201	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
207	C₈×C₁₉	—	2	2	no	—
208	C₈×C₁₉	—	2	2	no	—
209	C₈×C₁₉	—	2	4	no	—
210	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
211	C₂×#427	C₂×C₁₉	1	1	yes	characteristic
212	C₂×#424	C₂×C₁₉	1	1	yes	characteristic
213	#2317	C₂×C₁₉	1	1	yes	characteristic
214	#2274	C₂×C₁₉	1	1	yes	characteristic
215	#1949	C₂×C₁₉	1	2	yes	complemented
216	#1949	C₂×C₁₉	1	2	yes	complemented
217	#1948	C₂×C₁₉	1	2	yes	complemented
218	#1947	C₂×C₁₉	1	2	yes	complemented
219	#1736	C₂×C₁₉	1	1	yes	characteristic
220	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	#389	1	4	yes	—
228	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
231	C₂²×C₁₉	#576	1	1	yes	characteristic
232	C₂²×C₁₉	#577	1	1	yes	characteristic
233	C₂²×C₁₉	#577	1	1	yes	characteristic
234	C₂²×C₁₉	#578	1	1	yes	characteristic
235	C₄×C₁₉	—	2	4	no	—
236	C₄×C₁₉	—	2	4	no	—
237	C₄×C₁₉	—	4	4	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	#389	1	4	yes	—
244	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
246	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
247	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
255	#428	—	2	4	no	—
256	#427	—	2	4	no	—
257	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
259	C₂×#107	C₂²×C₁₉	1	2	yes	—
260	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#106	C₂²×C₁₉	1	2	yes	—
263	#424	C₄×C₁₉	1	8	yes	complemented
264	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
266	#389	—	2	1	no	—
267	#389	—	2	1	no	—
268	#385	—	2	2	no	—
269	#384	C₂²×C₁₉	1	2	yes	—
270	#382	C₂²×C₁₉	1	2	yes	—
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	—	2	1	no	—
273	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
274	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
275	C₄×C₂²⋊C₄	—	2	2	no	—
276	#340	C₂²×C₁₉	1	2	yes	—
277	#340	C₂²×C₁₉	1	2	yes	—
278	#340	C₂²×C₁₉	1	2	yes	—
279	#340	C₂²×C₁₉	1	2	yes	—
280	C₂×C₁₉	—	2	4	no	—
281	C₂×C₁₉	C₂×#389	1	1	yes	characteristic
282	C₂×C₁₉	#2912	1	1	yes	characteristic
283	C₂×C₁₉	#2913	1	1	yes	characteristic
284	C₂×C₁₉	#3045	1	1	yes	characteristic
285	C₂×C₁₉	#3046	1	1	yes	characteristic
286	C₂×C₁₉	#3081	1	1	yes	characteristic
287	C₂×C₁₉	#3082	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
297	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	C₂×C₄×C₁₉	1	4	yes	—
304	#117	D₄×C₁₉	1	4	yes	—
305	#117	Q₈×C₁₉	1	4	yes	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
330	#107	—	2	2	no	—
331	#107	—	2	2	no	—
332	#107	—	2	4	no	—
333	#106	—	2	2	no	—
334	#106	—	2	2	no	—
335	#106	—	2	4	no	—
336	C₄⋊C₈	C₂×C₄×C₁₉	1	8	yes	complemented
337	C₄⋊C₈	C₂×C₄×C₁₉	1	8	yes	complemented
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	—	2	2	no	—
342	C₁₉	#21175	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	8	1	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	—	8	1	no	—
355	C₂²×C₄	—	8	1	no	—
356	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
363	C₂²×C₄	#41×C₁₉	1	2	yes	—
364	C₂²×C₄	#41×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
366	M₁₆	—	2	8	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
375	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
376	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	8	2	no	—
389	C₄⋊C₄	—	8	2	no	—
390	C₄⋊C₄	C₄⋊C₄×C₁₉	1	4	yes	—
391	C₄⋊C₄	C₄⋊C₄×C₁₉	1	4	yes	—
392	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
393	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
394	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	8	yes	—
398	C₄²	—	2	4	no	—
399	C₄²	—	4	2	no	—
400	C₄²	—	8	2	no	—
401	C₄²	—	8	2	no	—
402	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
403	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
409	C₂³	C₁₉×#121	1	2	yes	—
410	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
411	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	8	4	no	—
435	C₂×C₄	—	8	4	no	—
436	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
437	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
438	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
439	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
440	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
441	C₂×C₄	C₁₉×#121	1	2	yes	—
442	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
443	C₂×C₄	C₁₉×#125	1	4	yes	—
444	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
445	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	2	4	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	C₁₉×#389	1	4	yes	—
461	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
462	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
463	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
464	C₂²	C₁₉×#576	1	1	yes	characteristic
465	C₂²	C₁₉×#577	1	1	yes	characteristic
466	C₂²	C₁₉×#577	1	1	yes	characteristic
467	C₂²	C₁₉×#578	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	C₁₉×#389	1	4	yes	—
477	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
478	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
479	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
480	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
481	C₂	—	2	4	no	—
482	C₂	C₂×C₁₉×#389	1	1	yes	characteristic
483	C₂	C₁₉×#2912	1	1	yes	characteristic
484	C₂	C₁₉×#2913	1	1	yes	characteristic
485	C₂	C₁₉×#3045	1	1	yes	characteristic
486	C₂	C₁₉×#3046	1	1	yes	characteristic
487	C₂	C₁₉×#3081	1	1	yes	characteristic
488	C₂	C₁₉×#3082	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₉×#1949	C₂	semidirect
7. C₁₉×#1949	C₂	semidirect
8. C₁₉×#1948	C₂	semidirect
9. C₁₉×#1947	C₂	semidirect
27. C₁₉×#424	C₄	semidirect
92. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
93. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
159. #21175	C₁₉	direct (N × H)
215. #1949	C₂×C₁₉	semidirect
216. #1949	C₂×C₁₉	semidirect
217. #1948	C₂×C₁₉	semidirect
218. #1947	C₂×C₁₉	semidirect
263. #424	C₄×C₁₉	semidirect
336. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
337. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
342. C₁₉	#21175	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×#428	2
C₂×C₁₉×#427	2
C₂×C₁₉×#424	2
C₁₉×#2317	2
C₁₉×#2274	2
C₁₉×#1949	2
C₁₉×#1948	2
C₁₉×#1947	2
C₁₉×#1736	2
C₂×C₁₉×#340	2
#21175	19

Subgroups — C19×#21175 #18027134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21175 #18027134