Subgroups — C₁₉×#22521 #18028480

Order 4864.

1010 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1991	C₂	1	2	yes	maximal
5	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1989	C₂	1	2	yes	maximal
7	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1805	C₂	1	2	yes	maximal
9	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₉×#103	C₂	1	2	yes	maximal
11	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#557	—	2	4	no	—
13	C₁₉×#557	C₄	1	8	yes	complemented
14	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#125	—	2	2	no	—
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₈×Q₈×C₁₉	—	2	4	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
30	C₁₉×#391	—	2	1	no	—
31	C₁₉×#387	—	2	2	no	—
32	C₁₉×#384	C₂²	1	1	yes	characteristic
33	C₁₉×#382	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×C₄⋊Q₈	—	2	8	no	—
51	C₁₉×C₄⋊Q₈	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
53	C₁₉×#125	—	2	16	no	—
54	C₁₉×#125	—	2	4	no	—
55	C₁₉×#125	C₂×C₄	1	8	yes	—
56	C₄×Q₈×C₁₉	—	2	8	no	—
57	C₄×Q₈×C₁₉	—	2	4	no	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
60	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
62	C₄×Q₈×C₁₉	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	D₄	1	2	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	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	—	2	2	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	—	2	4	no	—
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×#103	—	2	4	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	Q₈	1	4	yes	complemented
88	C₄×C₈×C₁₉	—	2	4	no	—
89	C₄×C₈×C₁₉	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	—	2	1	no	—
100	C₂×Q₈×C₁₉	—	4	2	no	—
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
103	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
105	C₂×Q₈×C₁₉	#41	1	2	yes	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₁₉	—	2	8	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	8	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	—	8	1	no	—
140	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
141	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
142	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
144	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
145	C₄²×C₁₉	—	2	8	no	—
146	C₄²×C₁₉	—	2	4	no	—
147	C₄²×C₁₉	—	4	2	no	—
148	C₄²×C₁₉	—	8	2	no	—
149	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
150	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₁₉	C₂×D₄	1	4	yes	—
152	C₄²×C₁₉	C₂×D₄	1	2	yes	—
153	#22521	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	2	no	—
156	Q₈×C₁₉	—	2	2	no	—
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	8	no	—
159	Q₈×C₁₉	—	4	8	no	—
160	Q₈×C₁₉	C₄×Q₈	1	4	yes	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
186	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₁₉	#135	1	2	yes	—
190	C₂×C₄×C₁₉	#135	1	2	yes	—
191	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
197	C₈×C₁₉	—	2	2	no	—
198	C₈×C₁₉	—	4	2	no	—
199	C₈×C₁₉	—	4	1	no	—
200	C₂×#557	C₂×C₁₉	1	1	yes	characteristic
201	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic
202	#2355	C₂×C₁₉	1	1	yes	characteristic
203	#1991	C₂×C₁₉	1	2	yes	—
204	#1990	C₂×C₁₉	1	1	yes	characteristic
205	#1989	C₂×C₁₉	1	2	yes	—
206	#1988	C₂×C₁₉	1	1	yes	characteristic
207	#1805	C₂×C₁₉	1	2	yes	—
208	#1803	C₂×C₁₉	1	1	yes	characteristic
209	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
210	C₄×#103	C₂×C₁₉	1	2	yes	—
211	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₉	#548	1	1	yes	characteristic
213	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
216	C₂²×C₁₉	#577	1	1	yes	characteristic
217	C₂²×C₁₉	#578	1	1	yes	characteristic
218	C₄×C₁₉	—	2	4	no	—
219	C₄×C₁₉	—	2	4	no	—
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	—	8	2	no	—
227	C₄×C₁₉	#416	1	4	yes	—
228	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
229	C₄×C₁₉	#519	1	1	yes	characteristic
230	C₄×C₁₉	#548	1	1	yes	characteristic
231	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
232	#557	—	2	4	no	—
233	#557	C₄×C₁₉	1	8	yes	complemented
234	C₂×C₄⋊Q₈	—	2	1	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#125	—	2	2	no	—
237	C₂×#125	C₂²×C₁₉	1	2	yes	—
238	C₂×C₄×Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
241	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₈×Q₈	—	2	4	no	—
243	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
245	C₂×#103	C₂²×C₁₉	1	2	yes	—
246	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
250	#391	—	2	1	no	—
251	#387	—	2	2	no	—
252	#384	C₂²×C₁₉	1	1	yes	characteristic
253	#382	C₂²×C₁₉	1	2	yes	—
254	C₄×C₄⋊C₄	—	2	1	no	—
255	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
257	#340	C₂²×C₁₉	1	2	yes	—
258	#340	C₂²×C₁₉	1	2	yes	—
259	#340	C₂²×C₁₉	1	2	yes	—
260	#340	C₂²×C₁₉	1	2	yes	—
261	#340	C₂²×C₁₉	1	1	yes	characteristic
262	#340	C₂²×C₁₉	1	2	yes	—
263	#340	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×C₁₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₁₉	C₂×#416	1	1	yes	characteristic
266	C₂×C₁₉	#2898	1	1	yes	characteristic
267	C₂×C₁₉	#3364	1	1	yes	characteristic
268	C₂×C₁₉	#3365	1	1	yes	characteristic
269	C₂×C₁₉	#3381	1	1	yes	characteristic
270	C₂×C₁₉	#3383	1	1	yes	characteristic
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
273	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	8	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
280	#125	—	2	16	no	—
281	#125	—	2	4	no	—
282	#125	C₂×C₄×C₁₉	1	8	yes	—
283	C₄×Q₈	—	2	8	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
287	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
288	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
289	C₄×Q₈	D₄×C₁₉	1	4	yes	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
309	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
310	C₄⋊C₈	—	2	4	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	4	no	—
313	#103	—	2	2	no	—
314	#103	Q₈×C₁₉	1	4	yes	complemented
315	C₄×C₈	—	2	4	no	—
316	C₄×C₈	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	C₁₉	#22521	1	1	yes	characteristic, direct product factor, Sylow
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
331	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
332	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
333	C₂×Q₈	#41×C₁₉	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	8	1	no	—
368	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
369	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
370	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
371	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
372	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	4	2	no	—
376	C₄²	—	8	2	no	—
377	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
378	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
379	C₄²	C₂×D₄×C₁₉	1	4	yes	—
380	C₄²	C₂×D₄×C₁₉	1	2	yes	—
381	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	Q₈	—	2	8	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	8	no	—
387	Q₈	C₄×Q₈×C₁₉	1	4	yes	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
413	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
414	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
415	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
416	C₂×C₄	C₁₉×#135	1	2	yes	—
417	C₂×C₄	C₁₉×#135	1	2	yes	—
418	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	1	no	—
427	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
428	C₂²	C₁₉×#548	1	1	yes	characteristic
429	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
430	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
431	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
432	C₂²	C₁₉×#577	1	1	yes	characteristic
433	C₂²	C₁₉×#578	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	C₁₉×#416	1	4	yes	—
444	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
445	C₄	C₁₉×#519	1	1	yes	characteristic
446	C₄	C₁₉×#548	1	1	yes	characteristic
447	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
448	C₂	Q₈×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
449	C₂	C₂×C₁₉×#416	1	1	yes	characteristic
450	C₂	C₁₉×#2898	1	1	yes	characteristic
451	C₂	C₁₉×#3364	1	1	yes	characteristic
452	C₂	C₁₉×#3365	1	1	yes	characteristic
453	C₂	C₁₉×#3381	1	1	yes	characteristic
454	C₂	C₁₉×#3383	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₉×#557	C₄	semidirect
87. C₁₉×#103	Q₈	semidirect
153. #22521	C₁₉	direct (N × H)
233. #557	C₄×C₁₉	semidirect
314. #103	Q₈×C₁₉	semidirect
321. C₁₉	#22521	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×#557	2
C₂×C₈×Q₈×C₁₉	2
C₁₉×#2355	2
C₁₉×#1991	2
C₁₉×#1990	2
C₁₉×#1989	2
C₁₉×#1988	2
C₁₉×#1805	2
C₁₉×#1803	2
C₄×C₁₉×#103	2
#22521	19

Subgroups — C19×#22521 #18028480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22521 #18028480