Subgroups — C₂×C₁₉×#2065 #18029564

Order 4864.

1422 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2065	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	—	2	4	no	—
20	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
21	C₂×C₁₉×C₄⋊C₈	—	2	4	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	complemented
23	C₂×C₁₉×#102	—	2	4	no	—
24	C₂×C₁₉×#102	—	2	4	no	—
25	C₂×C₁₉×#102	C₂²	1	4	yes	—
26	C₂×C₁₉×#102	C₂²	1	4	yes	—
27	C₁₉×#390	—	2	2	no	—
28	C₁₉×#390	C₂²	1	4	yes	—
29	C₁₉×#389	—	2	2	no	—
30	C₁₉×#389	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#95	—	2	1	no	—
32	C₁₉×#340	C₂²	1	4	yes	complemented
33	C₂⁵×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
41	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	D₄	1	4	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	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	4	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
66	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
74	C₂×C₄²×C₁₉	—	2	2	no	—
75	C₂×C₄²×C₁₉	—	2	2	no	—
76	C₂×C₄²×C₁₉	D₄	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
78	C₁₉×#106	—	2	8	no	—
79	C₁₉×C₄⋊C₈	—	2	8	no	—
80	C₁₉×#102	—	2	8	no	—
81	C₁₉×#102	—	2	8	no	—
82	C₁₉×#95	—	2	4	no	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	2	no	—
85	C₂⁴×C₁₉	—	4	2	no	—
86	C₂⁴×C₁₉	—	4	2	no	—
87	C₂⁴×C₁₉	—	4	2	no	—
88	C₂⁴×C₁₉	—	4	2	no	—
89	C₂⁴×C₁₉	—	4	2	no	—
90	C₂⁴×C₁₉	—	4	2	no	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₁₉	—	2	8	no	—
93	C₂×D₄×C₁₉	—	2	8	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	4	4	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
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	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	#41	1	2	yes	—
131	C₂²×C₄×C₁₉	#41	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₁₉	—	2	8	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	4	4	no	—
140	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	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	—	4	8	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₄⋊C₄×C₁₉	—	4	2	no	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₂²⋊C₄×C₁₉	—	4	8	no	—
152	C₂²⋊C₄×C₁₉	—	4	8	no	—
153	C₄²×C₁₉	—	2	4	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₂×#2065	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	8	no	—
165	C₂³×C₁₉	—	4	8	no	—
166	C₂³×C₁₉	—	4	8	no	—
167	C₂³×C₁₉	—	8	4	no	—
168	C₂³×C₁₉	—	8	4	no	—
169	C₂³×C₁₉	—	8	4	no	—
170	C₂³×C₁₉	—	8	4	no	—
171	C₂³×C₁₉	#121	1	2	yes	—
172	C₂³×C₁₉	#121	1	2	yes	—
173	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
174	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
175	C₂³×C₁₉	#135	1	2	yes	—
176	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
177	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
178	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	8	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	8	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	8	4	no	—
202	C₂×C₄×C₁₉	—	8	4	no	—
203	C₂×C₄×C₁₉	#121	1	4	yes	—
204	C₂×C₄×C₁₉	#121	1	2	yes	—
205	C₂×C₄×C₁₉	#121	1	2	yes	—
206	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
207	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
208	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₁₉	#126	1	4	yes	—
210	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
217	C₈×C₁₉	—	2	4	no	—
218	C₈×C₁₉	—	4	2	no	—
219	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂²×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
221	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
222	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
223	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
224	C₂×#389	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2065	C₂×C₁₉	1	8	yes	direct product factor
226	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	4	4	no	—
229	C₂²×C₁₉	—	4	4	no	—
230	C₂²×C₁₉	—	8	16	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	—	8	2	no	—
233	C₂²×C₁₉	—	8	2	no	—
234	C₂²×C₁₉	—	8	2	no	—
235	C₂²×C₁₉	#396	1	4	yes	—
236	C₂²×C₁₉	#460	1	4	yes	—
237	C₂²×C₁₉	#463	1	4	yes	—
238	C₂²×C₁₉	#465	1	4	yes	—
239	C₂²×C₁₉	#469	1	4	yes	—
240	C₂²×C₁₉	#476	1	4	yes	—
241	C₂²×C₁₉	#478	1	4	yes	—
242	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
244	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
245	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
246	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
247	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₄×C₁₉	—	2	4	no	—
250	C₄×C₁₉	—	4	4	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	8	2	no	—
253	C₄×C₁₉	—	8	2	no	—
254	C₄×C₁₉	#396	1	4	yes	—
255	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
256	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
258	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
259	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
260	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
261	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	—	2	1	no	—
263	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	—	2	1	no	—
267	C₂²×C₂²⋊C₄	—	2	1	no	—
268	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×#106	—	2	4	no	—
270	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
271	C₂×C₄⋊C₈	—	2	4	no	—
272	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
273	C₂×#102	—	2	4	no	—
274	C₂×#102	—	2	4	no	—
275	C₂×#102	C₂²×C₁₉	1	4	yes	—
276	C₂×#102	C₂²×C₁₉	1	4	yes	—
277	#390	—	2	2	no	—
278	#390	C₂²×C₁₉	1	4	yes	—
279	#389	—	2	2	no	—
280	#389	C₂²×C₁₉	1	4	yes	complemented
281	C₂×#95	—	2	1	no	—
282	#340	C₂²×C₁₉	1	4	yes	complemented
283	C₂×C₁₉	—	8	4	no	—
284	C₂×C₁₉	#2065	1	8	yes	direct product factor
285	C₂×C₁₉	C₂×#396	1	1	yes	characteristic
286	C₂×C₁₉	C₂×#463	1	1	yes	characteristic
287	C₂×C₁₉	C₂×#460	1	1	yes	characteristic
288	C₂×C₁₉	C₂×#465	1	1	yes	characteristic
289	C₂×C₁₉	C₂×#469	1	1	yes	characteristic
290	C₂×C₁₉	C₂×#476	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#478	1	1	yes	characteristic
292	C₂⁵	—	2	1	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
300	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
305	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	D₄×C₁₉	1	4	yes	—
313	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
314	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	4	4	no	—
325	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	4	no	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₂²⋊C₄	—	4	4	no	—
332	C₂×C₂²⋊C₄	—	4	4	no	—
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	D₄×C₁₉	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
337	#106	—	2	8	no	—
338	C₄⋊C₈	—	2	8	no	—
339	#102	—	2	8	no	—
340	#102	—	2	8	no	—
341	#95	—	2	4	no	—
342	C₁₉	C₂×#2065	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	4	2	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	—	4	2	no	—
349	C₂⁴	—	4	2	no	—
350	C₂⁴	—	4	2	no	—
351	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	—
383	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
388	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
389	C₂²×C₄	#41×C₁₉	1	2	yes	—
390	C₂²×C₄	#41×C₁₉	1	2	yes	—
391	C₂²×C₄	#41×C₁₉	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
393	C₂×C₈	—	2	8	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	4	no	—
400	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	8	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
411	C₂²⋊C₄	—	4	8	no	—
412	C₂²⋊C₄	—	4	8	no	—
413	C₄²	—	2	4	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	8	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	8	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	8	4	no	—
427	C₂³	—	8	4	no	—
428	C₂³	—	8	4	no	—
429	C₂³	—	8	4	no	—
430	C₂³	C₁₉×#121	1	2	yes	—
431	C₂³	C₁₉×#121	1	2	yes	—
432	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
433	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
434	C₂³	C₁₉×#135	1	2	yes	—
435	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
436	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
437	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
438	D₄	—	2	4	no	—
439	D₄	—	2	4	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	4	no	—
462	C₂×C₄	C₁₉×#121	1	2	yes	—
463	C₂×C₄	C₁₉×#121	1	2	yes	—
464	C₂×C₄	C₁₉×#121	1	4	yes	—
465	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
466	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
467	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
468	C₂×C₄	C₁₉×#126	1	4	yes	—
469	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	4	2	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	16	no	—
486	C₂²	C₁₉×#396	1	4	yes	—
487	C₂²	C₁₉×#460	1	4	yes	—
488	C₂²	C₁₉×#463	1	4	yes	—
489	C₂²	C₁₉×#465	1	4	yes	—
490	C₂²	C₁₉×#469	1	4	yes	—
491	C₂²	C₁₉×#476	1	4	yes	—
492	C₂²	C₁₉×#478	1	4	yes	—
493	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
494	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
495	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
496	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
497	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
498	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
499	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
500	C₄	—	2	4	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	2	no	—
503	C₄	—	8	2	no	—
504	C₄	—	8	2	no	—
505	C₄	C₁₉×#396	1	4	yes	—
506	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
507	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
508	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
509	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
510	C₂	—	8	4	no	—
511	C₂	C₁₉×#2065	1	8	yes	direct product factor
512	C₂	C₂×C₁₉×#396	1	1	yes	characteristic
513	C₂	C₂×C₁₉×#463	1	1	yes	characteristic
514	C₂	C₂×C₁₉×#460	1	1	yes	characteristic
515	C₂	C₂×C₁₉×#465	1	1	yes	characteristic
516	C₂	C₂×C₁₉×#469	1	1	yes	characteristic
517	C₂	C₂×C₁₉×#476	1	1	yes	characteristic
518	C₂	C₂×C₁₉×#478	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#106	C₂	semidirect
2. C₂²×C₁₉×C₄⋊C₈	C₂	semidirect
6. C₂×C₁₉×#389	C₂	semidirect
7. C₁₉×#2065	C₂	direct (N × H)
8. C₂×C₁₉×#340	C₂	semidirect
20. C₂×C₁₉×#106	C₂²	semidirect
22. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
30. C₁₉×#389	C₂²	semidirect
32. C₁₉×#340	C₂²	semidirect
156. C₂×#2065	C₁₉	direct (N × H)
219. C₂²×#106	C₂×C₁₉	semidirect
220. C₂²×C₄⋊C₈	C₂×C₁₉	semidirect
224. C₂×#389	C₂×C₁₉	semidirect
225. #2065	C₂×C₁₉	direct (N × H)
226. C₂×#340	C₂×C₁₉	semidirect
270. C₂×#106	C₂²×C₁₉	semidirect
272. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
280. #389	C₂²×C₁₉	semidirect
282. #340	C₂²×C₁₉	semidirect
284. C₂×C₁₉	#2065	direct (N × H)
342. C₁₉	C₂×#2065	direct (N × H)
511. C₂	C₁₉×#2065	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×#106	2
C₂²×C₁₉×C₄⋊C₈	2
C₂²×C₁₉×#102	2
C₂×C₁₉×#390	2
C₂×C₁₉×#389	2
C₁₉×#2065	2
C₂×C₁₉×#340	2
C₂×#2065	19

Subgroups — C2×C19×#2065 #18029564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2065 #18029564