Subgroups — C₄×C₁₉×#447 #18027405

Order 4864.

1964 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₈×C₁₉	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1879	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1862	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₉×#102	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	—	2	1	no	—
14	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	—	2	8	no	—
17	C₂×C₄×D₄×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#447	C₄	1	8	yes	direct product factor
27	C₄×D₈×C₁₉	—	2	8	no	—
28	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	complemented
36	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#388	—	2	1	no	—
39	C₁₉×#386	—	2	1	no	—
40	C₁₉×#380	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₁₉×#336	C₂²	1	2	yes	complemented
46	C₂⁵×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	4	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
53	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₉	—	2	8	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	—	2	2	no	—
58	C₂³×C₄×C₁₉	—	2	2	no	—
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	—	4	4	no	—
61	C₂³×C₄×C₁₉	—	4	4	no	—
62	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×D₈×C₁₉	—	2	4	no	—
66	C₂×D₈×C₁₉	—	2	4	no	—
67	C₂×D₈×C₁₉	C₂×C₄	1	8	yes	complemented
68	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#121	—	2	2	no	—
71	C₁₉×#121	C₂×C₄	1	4	yes	complemented
72	C₄×D₄×C₁₉	—	2	8	no	—
73	C₄×D₄×C₁₉	—	2	8	no	—
74	C₄×D₄×C₁₉	—	2	4	no	—
75	C₄×D₄×C₁₉	—	2	4	no	—
76	C₄×D₄×C₁₉	—	2	4	no	—
77	C₄×D₄×C₁₉	—	2	4	no	—
78	C₄×D₄×C₁₉	—	4	4	no	—
79	C₄×D₄×C₁₉	D₄	1	8	yes	complemented
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	4	no	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	4	no	—
102	C₁₉×#102	—	2	4	no	—
103	C₁₉×#102	—	2	4	no	—
104	C₁₉×#102	—	2	4	no	—
105	C₁₉×#102	C₂×C₄	1	8	yes	complemented
106	C₁₉×C₂²⋊C₈	—	2	2	no	—
107	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
108	C₄×C₈×C₁₉	—	2	4	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₂⁴×C₁₉	—	2	4	no	—
113	C₂⁴×C₁₉	—	2	4	no	—
114	C₂⁴×C₁₉	—	2	4	no	—
115	C₂⁴×C₁₉	—	2	2	no	—
116	C₂⁴×C₁₉	—	2	1	no	—
117	C₂⁴×C₁₉	—	4	2	no	—
118	C₂⁴×C₁₉	—	4	2	no	—
119	C₂⁴×C₁₉	—	4	2	no	—
120	C₂⁴×C₁₉	—	4	2	no	—
121	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	16	no	—
125	C₂×D₄×C₁₉	—	2	16	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	4	2	no	—
136	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
137	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	complemented
138	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
139	C₂×D₄×C₁₉	#41	1	4	yes	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	8	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	8	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	4	1	no	—
154	C₂²×C₄×C₁₉	—	4	4	no	—
155	C₂²×C₄×C₁₉	—	4	32	no	—
156	C₂²×C₄×C₁₉	—	4	2	no	—
157	C₂²×C₄×C₁₉	—	4	2	no	—
158	C₂²×C₄×C₁₉	—	4	4	no	—
159	C₂²×C₄×C₁₉	—	4	4	no	—
160	C₂²×C₄×C₁₉	—	4	4	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
165	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	#41	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	D₈×C₁₉	—	2	16	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₂×C₈×C₁₉	—	2	2	no	—
179	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	complemented
180	C₄⋊C₄×C₁₉	—	2	4	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	4	2	no	—
186	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	complemented
187	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
188	C₂²⋊C₄×C₁₉	—	2	8	no	—
189	C₂²⋊C₄×C₁₉	—	2	4	no	—
190	C₂²⋊C₄×C₁₉	—	2	8	no	—
191	C₂²⋊C₄×C₁₉	—	4	2	no	—
192	C₂²⋊C₄×C₁₉	—	4	2	no	—
193	C₂²⋊C₄×C₁₉	—	4	2	no	—
194	C₂²⋊C₄×C₁₉	—	4	2	no	—
195	C₄²×C₁₉	—	2	2	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	4	2	no	—
199	C₄²×C₁₉	C₂×D₄	1	4	yes	—
200	C₄×#447	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	16	no	—
206	C₂³×C₁₉	—	2	4	no	—
207	C₂³×C₁₉	—	2	4	no	—
208	C₂³×C₁₉	—	2	4	no	—
209	C₂³×C₁₉	—	2	2	no	—
210	C₂³×C₁₉	—	4	8	no	—
211	C₂³×C₁₉	—	4	8	no	—
212	C₂³×C₁₉	—	4	8	no	—
213	C₂³×C₁₉	—	4	8	no	—
214	C₂³×C₁₉	—	4	8	no	—
215	C₂³×C₁₉	—	4	2	no	—
216	C₂³×C₁₉	—	4	2	no	—
217	C₂³×C₁₉	—	4	2	no	—
218	C₂³×C₁₉	—	4	2	no	—
219	C₂³×C₁₉	—	4	8	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	C₄×D₄	1	2	yes	—
227	C₂³×C₁₉	C₂×D₈	1	2	yes	—
228	C₂³×C₁₉	#135	1	2	yes	—
229	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	D₄×C₁₉	—	2	16	no	—
231	D₄×C₁₉	—	2	4	no	—
232	D₄×C₁₉	—	2	4	no	—
233	D₄×C₁₉	—	2	4	no	—
234	D₄×C₁₉	—	2	4	no	—
235	D₄×C₁₉	—	4	8	no	—
236	D₄×C₁₉	—	4	2	no	—
237	D₄×C₁₉	C₄×D₄	1	8	yes	complemented
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	8	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	4	4	no	—
253	C₂×C₄×C₁₉	—	4	16	no	—
254	C₂×C₄×C₁₉	—	4	8	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	16	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	8	4	no	—
267	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
268	C₂×C₄×C₁₉	#120	1	2	yes	—
269	C₂×C₄×C₁₉	#120	1	2	yes	—
270	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
271	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
272	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
273	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
276	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
277	C₈×C₁₉	—	2	4	no	—
278	C₈×C₁₉	—	4	2	no	—
279	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
280	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
281	C₂×C₄×D₈	C₂×C₁₉	1	2	yes	complemented
282	C₄×#121	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1879	C₂×C₁₉	1	2	yes	complemented
284	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1862	C₂×C₁₉	1	2	yes	complemented
286	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₄×#102	C₂×C₁₉	1	2	yes	complemented
289	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	8	no	—
297	C₂²×C₁₉	—	4	32	no	—
298	C₂²×C₁₉	—	4	4	no	—
299	C₂²×C₁₉	—	4	4	no	—
300	C₂²×C₁₉	—	4	4	no	—
301	C₂²×C₁₉	—	4	4	no	—
302	C₂²×C₁₉	—	4	4	no	—
303	C₂²×C₁₉	—	4	4	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	C₄×D₈	1	4	yes	complemented
312	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
314	C₂²×C₁₉	#525	1	1	yes	characteristic
315	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
316	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
317	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂²×C₁₉	#575	1	1	yes	characteristic
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	—	2	2	no	—
321	C₄×C₁₉	—	2	2	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	4	4	no	—
324	C₄×C₁₉	—	4	1	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	—	8	1	no	—
327	C₄×C₁₉	#447	1	4	yes	direct product factor
328	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
329	C₄×C₁₉	#525	1	2	yes	—
330	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₂⁴×C₄	—	2	1	no	—
332	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
333	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₄×D₄	—	2	8	no	—
335	C₂×C₄×D₄	—	2	1	no	—
336	C₂×C₄×D₄	—	2	1	no	—
337	C₂×C₄×D₄	—	2	1	no	—
338	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
339	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
340	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	—	2	1	no	—
343	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
344	#447	C₄×C₁₉	1	8	yes	direct product factor
345	C₄×D₈	—	2	8	no	—
346	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
347	C₂×#102	C₂²×C₁₉	1	2	yes	—
348	C₂×#102	C₂²×C₁₉	1	2	yes	—
349	C₂×#102	C₂²×C₁₉	1	2	yes	—
350	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
351	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	complemented
354	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#388	—	2	1	no	—
357	#386	—	2	1	no	—
358	#380	C₂²×C₁₉	1	1	yes	characteristic
359	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	C₄×C₂²⋊C₄	—	2	1	no	—
361	#340	C₂²×C₁₉	1	2	yes	complemented
362	#340	C₂²×C₁₉	1	2	yes	complemented
363	#336	C₂²×C₁₉	1	2	yes	complemented
364	C₂×C₁₉	—	2	4	no	—
365	C₂×C₁₉	—	4	8	no	—
366	C₂×C₁₉	—	8	2	no	—
367	C₂×C₁₉	C₄×#120	1	1	yes	characteristic
368	C₂×C₁₉	C₂×C₄×D₈	1	1	yes	characteristic
369	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
371	C₂×C₁₉	#3002	1	1	yes	characteristic
372	C₂×C₁₉	#3100	1	1	yes	characteristic
373	C₂×C₁₉	#3105	1	1	yes	characteristic
374	C₂⁵	—	2	1	no	—
375	C₂²×D₄	—	2	4	no	—
376	C₂²×D₄	—	2	4	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
381	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
383	C₂³×C₄	—	2	8	no	—
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	—	2	2	no	—
386	C₂³×C₄	—	2	2	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	4	4	no	—
389	C₂³×C₄	—	4	4	no	—
390	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
391	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×D₈	—	2	4	no	—
394	C₂×D₈	—	2	4	no	—
395	C₂×D₈	C₂×C₄×C₁₉	1	8	yes	complemented
396	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
397	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
398	#121	—	2	2	no	—
399	#121	C₂×C₄×C₁₉	1	4	yes	complemented
400	C₄×D₄	—	2	8	no	—
401	C₄×D₄	—	2	8	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	4	no	—
406	C₄×D₄	—	4	4	no	—
407	C₄×D₄	D₄×C₁₉	1	8	yes	complemented
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	4	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
415	C₂×C₂²⋊C₄	—	2	8	no	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₄²	—	2	4	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
429	#107	—	2	4	no	—
430	#102	—	2	4	no	—
431	#102	—	2	4	no	—
432	#102	—	2	4	no	—
433	#102	C₂×C₄×C₁₉	1	8	yes	complemented
434	C₂²⋊C₈	—	2	2	no	—
435	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	complemented
436	C₄×C₈	—	2	4	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	C₁₉	C₄×#447	1	1	yes	characteristic, direct product factor, Sylow
441	C₂⁴	—	2	4	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	4	no	—
444	C₂⁴	—	2	2	no	—
445	C₂⁴	—	2	1	no	—
446	C₂⁴	—	4	2	no	—
447	C₂⁴	—	4	2	no	—
448	C₂⁴	—	4	2	no	—
449	C₂⁴	—	4	2	no	—
450	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	16	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
466	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	complemented
467	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
468	C₂×D₄	#41×C₁₉	1	4	yes	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	8	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	—	4	4	no	—
484	C₂²×C₄	—	4	32	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	4	no	—
488	C₂²×C₄	—	4	4	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
494	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
495	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂²×C₄	#41×C₁₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
502	D₈	—	2	16	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	complemented
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	complemented
516	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	4	2	no	—
528	C₄²	C₂×D₄×C₁₉	1	4	yes	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	16	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	4	8	no	—
539	C₂³	—	4	8	no	—
540	C₂³	—	4	8	no	—
541	C₂³	—	4	8	no	—
542	C₂³	—	4	8	no	—
543	C₂³	—	4	8	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	C₄×D₄×C₁₉	1	2	yes	—
555	C₂³	C₂×D₈×C₁₉	1	2	yes	—
556	C₂³	C₁₉×#135	1	2	yes	—
557	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
558	D₄	—	2	16	no	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	4	8	no	—
564	D₄	—	4	2	no	—
565	D₄	C₄×D₄×C₁₉	1	8	yes	complemented
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	16	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	16	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	8	4	no	—
595	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
596	C₂×C₄	C₁₉×#120	1	2	yes	—
597	C₂×C₄	C₁₉×#120	1	2	yes	—
598	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
599	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
600	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
601	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
603	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
604	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
605	C₈	—	2	4	no	—
606	C₈	—	4	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	8	no	—
614	C₂²	—	4	32	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	4	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	C₄×D₈×C₁₉	1	4	yes	complemented
629	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
630	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
631	C₂²	C₁₉×#525	1	1	yes	characteristic
632	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
633	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
634	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
635	C₂²	C₁₉×#575	1	1	yes	characteristic
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	4	no	—
641	C₄	—	4	1	no	—
642	C₄	—	8	1	no	—
643	C₄	—	8	1	no	—
644	C₄	C₁₉×#447	1	4	yes	direct product factor
645	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
646	C₄	C₁₉×#525	1	2	yes	—
647	C₂	—	2	4	no	—
648	C₂	—	4	8	no	—
649	C₂	—	8	2	no	—
650	C₂	C₄×C₁₉×#120	1	1	yes	characteristic
651	C₂	C₂×C₄×D₈×C₁₉	1	1	yes	characteristic
652	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
653	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
654	C₂	C₁₉×#3002	1	1	yes	characteristic
655	C₂	C₁₉×#3100	1	1	yes	characteristic
656	C₂	C₁₉×#3105	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
prime radical	C₂×C₁₉×#447	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×D₄×C₁₉	C₂	semidirect
3. C₂×C₄×D₈×C₁₉	C₂	semidirect
4. C₄×C₁₉×#121	C₂	semidirect
5. C₁₉×#1879	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1862	C₂	semidirect
8. C₁₉×#1852	C₂	semidirect
9. C₁₉×#1786	C₂	semidirect
10. C₄×C₁₉×#102	C₂	semidirect
11. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
22. C₂×C₄×D₄×C₁₉	C₂²	semidirect
26. C₁₉×#447	C₄	direct (N × H)
28. C₂×C₁₉×#107	C₂²	semidirect
32. C₂×C₁₉×#102	C₂²	semidirect
35. C₂×C₄×C₈×C₁₉	C₂²	semidirect
36. C₁₉×#390	C₂²	semidirect
37. C₁₉×#389	C₂²	semidirect
41. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
45. C₁₉×#336	C₂²	semidirect
52. C₂²×D₄×C₁₉	C₂×C₄	semidirect
67. C₂×D₈×C₁₉	C₂×C₄	semidirect
71. C₁₉×#121	C₂×C₄	semidirect
79. C₄×D₄×C₁₉	D₄	semidirect
105. C₁₉×#102	C₂×C₄	semidirect
107. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
137. C₂×D₄×C₁₉	C₂²×C₄	semidirect
164. C₂²×C₄×C₁₉	D₈	semidirect
179. C₂×C₈×C₁₉	C₂²×C₄	semidirect
186. C₄⋊C₄×C₁₉	C₂²×C₄	semidirect
200. C₄×#447	C₁₉	direct (N × H)
237. D₄×C₁₉	C₄×D₄	semidirect
279. C₂²×C₄×D₄	C₂×C₁₉	semidirect
281. C₂×C₄×D₈	C₂×C₁₉	semidirect
282. C₄×#121	C₂×C₁₉	semidirect
283. #1879	C₂×C₁₉	semidirect
284. #1874	C₂×C₁₉	semidirect
285. #1862	C₂×C₁₉	semidirect
286. #1852	C₂×C₁₉	semidirect
287. #1786	C₂×C₁₉	semidirect
288. C₄×#102	C₂×C₁₉	semidirect
289. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
311. C₂²×C₁₉	C₄×D₈	semidirect
327. C₄×C₁₉	#447	direct (N × H)
340. C₂×C₄×D₄	C₂²×C₁₉	semidirect
344. #447	C₄×C₁₉	direct (N × H)
346. C₂×#107	C₂²×C₁₉	semidirect
350. C₂×#102	C₂²×C₁₉	semidirect
353. C₂×C₄×C₈	C₂²×C₁₉	semidirect
354. #390	C₂²×C₁₉	semidirect
355. #389	C₂²×C₁₉	semidirect
359. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
361. #340	C₂²×C₁₉	semidirect
362. #340	C₂²×C₁₉	semidirect
363. #336	C₂²×C₁₉	semidirect
380. C₂²×D₄	C₂×C₄×C₁₉	semidirect
395. C₂×D₈	C₂×C₄×C₁₉	semidirect
399. #121	C₂×C₄×C₁₉	semidirect
407. C₄×D₄	D₄×C₁₉	semidirect
433. #102	C₂×C₄×C₁₉	semidirect
435. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
440. C₁₉	C₄×#447	direct (N × H)
466. C₂×D₄	C₂²×C₄×C₁₉	semidirect
493. C₂²×C₄	D₈×C₁₉	semidirect
508. C₂×C₈	C₂²×C₄×C₁₉	semidirect
515. C₄⋊C₄	C₂²×C₄×C₁₉	semidirect
565. D₄	C₄×D₄×C₁₉	semidirect
628. C₂²	C₄×D₈×C₁₉	semidirect
644. C₄	C₁₉×#447	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×C₄×D₄×C₁₉	2
C₂×C₁₉×#447	2
C₂×C₄×D₈×C₁₉	2
C₄×C₁₉×#121	2
C₁₉×#1879	2
C₁₉×#1874	2
C₁₉×#1862	2
C₁₉×#1852	2
C₁₉×#1786	2
C₄×C₁₉×#102	2
C₄×C₁₉×C₂²⋊C₈	2
C₄×#447	19

Subgroups — C4×C19×#447 #18027405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#447 #18027405