Subgroups — C₁₉×#21765 #18027724

Order 4864.

1538 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1894	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1872	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1823	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1787	C₂	1	2	yes	maximal, complemented
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₉×C₂²⋊Q₈	C₄	1	8	yes	complemented
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
22	C₂×C₁₉×#103	C₂²	1	8	yes	complemented
23	C₁₉×#407	—	2	4	no	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₁₉×#380	—	2	1	no	—
27	C₁₉×#380	—	2	1	no	—
28	C₁₉×#380	C₂²	1	2	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	—	2	1	no	—
31	C₁₉×#340	C₂²	1	8	yes	complemented
32	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×Q₈×C₁₉	—	2	2	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	4	4	no	—
36	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
37	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	4	4	no	—
42	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	D₄	1	4	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₉	—	2	4	no	—
51	C₂×M₁₆×C₁₉	—	4	4	no	—
52	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
53	C₁₉×C₂²⋊Q₈	—	2	8	no	—
54	C₁₉×C₂²⋊Q₈	—	2	8	no	—
55	C₁₉×C₂²⋊Q₈	—	2	4	no	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
58	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
59	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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	—	4	4	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
75	C₁₉×#103	—	4	8	no	—
76	C₁₉×C₂²⋊C₈	—	2	4	no	—
77	C₁₉×C₂²⋊C₈	—	2	4	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	2	no	—
82	C₂⁴×C₁₉	—	2	4	no	—
83	C₂⁴×C₁₉	—	4	2	no	—
84	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
85	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₁₉	—	2	4	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	8	no	—
91	C₂×Q₈×C₁₉	—	4	8	no	—
92	C₂×Q₈×C₁₉	—	4	4	no	—
93	C₂×Q₈×C₁₉	—	4	8	no	—
94	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	4	8	no	—
104	C₂²×C₄×C₁₉	—	4	8	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	4	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	4	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₁₉	—	4	8	no	—
128	C₂×C₈×C₁₉	—	2	4	no	—
129	C₂×C₈×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	8	no	—
135	C₄⋊C₄×C₁₉	—	4	4	no	—
136	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
137	C₂²⋊C₄×C₁₉	—	2	8	no	—
138	C₂²⋊C₄×C₁₉	—	2	8	no	—
139	C₂²⋊C₄×C₁₉	—	4	4	no	—
140	C₂²⋊C₄×C₁₉	—	4	4	no	—
141	#21765	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	—	2	8	no	—
152	C₂³×C₁₉	—	2	8	no	—
153	C₂³×C₁₉	—	4	4	no	—
154	C₂³×C₁₉	—	4	8	no	—
155	C₂³×C₁₉	—	4	8	no	—
156	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
160	C₂³×C₁₉	#137	1	2	yes	—
161	C₂³×C₁₉	#137	1	4	yes	—
162	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₁₉	—	2	8	no	—
164	Q₈×C₁₉	—	4	8	no	—
165	Q₈×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	4	4	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	8	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	8	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	8	8	no	—
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
195	C₈×C₁₉	—	4	4	no	—
196	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
197	C₂×#407	C₂×C₁₉	1	1	yes	characteristic
198	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
199	#1894	C₂×C₁₉	1	4	yes	complemented
200	#1872	C₂×C₁₉	1	4	yes	complemented
201	#1823	C₂×C₁₉	1	2	yes	complemented
202	#1787	C₂×C₁₉	1	2	yes	complemented
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	2	4	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	4	16	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	#417	1	4	yes	—
218	C₂²×C₁₉	#419	1	4	yes	—
219	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×C₁₉	#534	1	2	yes	—
221	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₂²×C₁₉	C₂×#137	1	2	yes	—
223	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	8	4	no	—
230	C₄×C₁₉	#518	1	2	yes	—
231	C₄×C₁₉	#534	1	2	yes	—
232	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
235	C₂×C₂²⋊Q₈	—	2	4	no	—
236	C₂×C₂²⋊Q₈	—	2	1	no	—
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×C₂²⋊Q₈	C₄×C₁₉	1	8	yes	complemented
239	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
240	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
241	C₂²×C₄⋊C₄	—	2	1	no	—
242	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
244	C₂²×C₂²⋊C₄	—	2	1	no	—
245	C₂²×C₂²⋊C₄	—	2	1	no	—
246	C₂×#103	C₂²×C₁₉	1	8	yes	complemented
247	#407	—	2	4	no	—
248	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
250	#380	—	2	1	no	—
251	#380	—	2	1	no	—
252	#380	C₂²×C₁₉	1	2	yes	—
253	#380	C₂²×C₁₉	1	2	yes	—
254	C₂×#95	—	2	1	no	—
255	#340	C₂²×C₁₉	1	8	yes	complemented
256	C₂×C₁₉	—	2	4	no	—
257	C₂×C₁₉	—	2	4	no	—
258	C₂×C₁₉	—	4	2	no	—
259	C₂×C₁₉	#2308	1	1	yes	characteristic
260	C₂×C₁₉	C₂×#419	1	1	yes	characteristic
261	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
262	C₂×C₁₉	#3193	1	2	yes	—
263	C₂×C₁₉	#3195	1	2	yes	—
264	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
265	C₂²×Q₈	—	2	2	no	—
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×Q₈	—	4	4	no	—
268	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
269	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	—	4	4	no	—
274	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
275	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	D₄×C₁₉	1	4	yes	—
279	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×M₁₆	—	2	4	no	—
283	C₂×M₁₆	—	4	4	no	—
284	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
285	C₂²⋊Q₈	—	2	8	no	—
286	C₂²⋊Q₈	—	2	8	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
290	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
291	C₂×C₄⋊C₄	—	2	8	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	4	4	no	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
299	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	8	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	4	4	no	—
307	#103	—	4	8	no	—
308	C₂²⋊C₈	—	2	4	no	—
309	C₂²⋊C₈	—	2	4	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₁₉	#21765	1	1	yes	characteristic, direct product factor, Sylow
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
318	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	—	4	8	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×Q₈	—	4	8	no	—
327	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	8	no	—
337	C₂²×C₄	—	4	8	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
348	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
349	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
350	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×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	C₂⁴×C₁₉	1	1	yes	characteristic
360	M₁₆	—	4	8	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	8	no	—
380	C₂³	—	2	8	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	8	no	—
387	C₂³	—	4	8	no	—
388	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
389	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
390	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
391	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
392	C₂³	C₁₉×#137	1	2	yes	—
393	C₂³	C₁₉×#137	1	4	yes	—
394	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
395	Q₈	—	2	8	no	—
396	Q₈	—	4	8	no	—
397	Q₈	—	4	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	8	8	no	—
421	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
427	C₈	—	4	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	C₁₉×#417	1	4	yes	—
443	C₂²	C₁₉×#419	1	4	yes	—
444	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
445	C₂²	C₁₉×#534	1	2	yes	—
446	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
447	C₂²	C₂×C₁₉×#137	1	2	yes	—
448	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	8	4	no	—
455	C₄	C₁₉×#518	1	2	yes	—
456	C₄	C₁₉×#534	1	2	yes	—
457	C₂	—	2	4	no	—
458	C₂	—	2	4	no	—
459	C₂	—	4	2	no	—
460	C₂	C₁₉×#2308	1	1	yes	characteristic
461	C₂	C₂×C₁₉×#419	1	1	yes	characteristic
462	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
463	C₂	C₁₉×#3193	1	2	yes	—
464	C₂	C₁₉×#3195	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1894	C₂	semidirect
5. C₁₉×#1872	C₂	semidirect
6. C₁₉×#1823	C₂	semidirect
7. C₁₉×#1787	C₂	semidirect
14. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
22. C₂×C₁₉×#103	C₂²	semidirect
31. C₁₉×#340	C₂²	semidirect
36. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
58. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
66. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
141. #21765	C₁₉	direct (N × H)
199. #1894	C₂×C₁₉	semidirect
200. #1872	C₂×C₁₉	semidirect
201. #1823	C₂×C₁₉	semidirect
202. #1787	C₂×C₁₉	semidirect
238. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
246. C₂×#103	C₂²×C₁₉	semidirect
255. #340	C₂²×C₁₉	semidirect
268. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
290. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
298. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
312. C₁₉	#21765	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₂×C₁₉×#407	2
C₂×C₁₉×#380	2
C₁₉×#1894	2
C₁₉×#1872	2
C₁₉×#1823	2
C₁₉×#1787	2
#21765	19

Subgroups — C19×#21765 #18027724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21765 #18027724