Subgroups — C₁₉×#32908 #18038867

Order 4864.

1894 conjugacy classes of subgroups.

The subgroup lattice has 672 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×#463	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1879	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1877	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1797	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×SD₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	—	2	8	no	—
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#463	—	2	8	no	—
28	C₁₉×#450	—	2	4	no	—
29	C₁₉×#447	—	2	4	no	—
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
32	C₂×C₁₉×#102	C₂²	1	2	yes	—
33	C₂×C₁₉×#102	C₂²	1	2	yes	—
34	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#388	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#386	—	2	1	no	—
43	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₁₉×#340	C₂²	1	2	yes	complemented
46	C₁₉×#336	C₂²	1	2	yes	complemented
47	C₂⁵×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	—	2	4	no	—
50	C₂²×D₄×C₁₉	—	2	4	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	D₄	1	4	yes	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	—	2	8	no	—
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	—	2	2	no	—
60	C₂³×C₄×C₁₉	—	2	2	no	—
61	C₂³×C₄×C₁₉	—	4	4	no	—
62	C₂³×C₄×C₁₉	—	4	4	no	—
63	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	2	4	no	—
67	C₂×SD₁₆×C₁₉	—	2	4	no	—
68	C₂×SD₁₆×C₁₉	—	2	4	no	—
69	C₂×D₈×C₁₉	—	2	4	no	—
70	C₂×D₈×C₁₉	—	2	4	no	—
71	C₂×D₈×C₁₉	—	2	4	no	—
72	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
74	C₁₉×#124	—	2	4	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₄×D₄×C₁₉	—	2	8	no	—
80	C₄×D₄×C₁₉	—	2	8	no	—
81	C₄×D₄×C₁₉	—	2	4	no	—
82	C₄×D₄×C₁₉	—	2	4	no	—
83	C₄×D₄×C₁₉	—	2	4	no	—
84	C₄×D₄×C₁₉	D₄	1	8	yes	complemented
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	—	2	4	no	—
101	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×C₄⋊C₈	—	2	4	no	—
106	C₁₉×#103	—	2	4	no	—
107	C₁₉×#102	—	2	4	no	—
108	C₁₉×#102	—	2	4	no	—
109	C₁₉×#102	—	2	4	no	—
110	C₁₉×C₂²⋊C₈	—	2	2	no	—
111	C₁₉×C₂²⋊C₈	—	2	2	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₂⁴×C₁₉	—	2	4	no	—
117	C₂⁴×C₁₉	—	2	4	no	—
118	C₂⁴×C₁₉	—	2	4	no	—
119	C₂⁴×C₁₉	—	2	2	no	—
120	C₂⁴×C₁₉	—	2	1	no	—
121	C₂⁴×C₁₉	—	4	2	no	—
122	C₂⁴×C₁₉	—	4	2	no	—
123	C₂⁴×C₁₉	—	4	2	no	—
124	C₂⁴×C₁₉	—	4	2	no	—
125	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	16	no	—
133	C₂×D₄×C₁₉	—	2	16	no	—
134	C₂×D₄×C₁₉	—	2	4	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	4	2	no	—
143	C₂×D₄×C₁₉	—	4	2	no	—
144	C₂×D₄×C₁₉	—	4	2	no	—
145	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
146	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
147	C₂×D₄×C₁₉	#41	1	4	yes	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	4	no	—
154	C₂²×C₄×C₁₉	—	2	8	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	8	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	4	1	no	—
163	C₂²×C₄×C₁₉	—	4	32	no	—
164	C₂²×C₄×C₁₉	—	4	4	no	—
165	C₂²×C₄×C₁₉	—	4	4	no	—
166	C₂²×C₄×C₁₉	—	4	4	no	—
167	C₂²×C₄×C₁₉	—	4	2	no	—
168	C₂²×C₄×C₁₉	—	4	2	no	—
169	C₂²×C₄×C₁₉	—	4	4	no	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	#41	1	2	yes	—
177	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	SD₁₆×C₁₉	—	4	8	no	—
179	D₈×C₁₉	—	4	8	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	2	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	4	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	4	2	no	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
194	C₂²⋊C₄×C₁₉	—	2	8	no	—
195	C₂²⋊C₄×C₁₉	—	2	8	no	—
196	C₂²⋊C₄×C₁₉	—	4	2	no	—
197	C₂²⋊C₄×C₁₉	—	4	2	no	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₂²⋊C₄×C₁₉	—	4	2	no	—
200	C₂²⋊C₄×C₁₉	—	4	2	no	—
201	C₂²⋊C₄×C₁₉	—	4	2	no	—
202	C₄²×C₁₉	—	2	2	no	—
203	C₄²×C₁₉	—	2	2	no	—
204	C₄²×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	C₂×D₄	1	4	yes	—
206	#32908	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	2	16	no	—
212	C₂³×C₁₉	—	2	4	no	—
213	C₂³×C₁₉	—	2	4	no	—
214	C₂³×C₁₉	—	2	4	no	—
215	C₂³×C₁₉	—	4	8	no	—
216	C₂³×C₁₉	—	4	8	no	—
217	C₂³×C₁₉	—	4	8	no	—
218	C₂³×C₁₉	—	4	8	no	—
219	C₂³×C₁₉	—	4	8	no	—
220	C₂³×C₁₉	—	4	2	no	—
221	C₂³×C₁₉	—	4	2	no	—
222	C₂³×C₁₉	—	4	2	no	—
223	C₂³×C₁₉	—	4	2	no	—
224	C₂³×C₁₉	—	4	8	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	#121	1	2	yes	—
233	C₂³×C₁₉	#135	1	2	yes	—
234	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
235	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₁₉	—	4	2	no	—
237	Q₈×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	2	16	no	—
239	D₄×C₁₉	—	2	4	no	—
240	D₄×C₁₉	—	2	4	no	—
241	D₄×C₁₉	—	2	4	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	8	4	no	—
245	D₄×C₁₉	#121	1	8	yes	—
246	C₂×C₄×C₁₉	—	2	8	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	4	no	—
256	C₂×C₄×C₁₉	—	2	4	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	4	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	4	4	no	—
262	C₂×C₄×C₁₉	—	4	16	no	—
263	C₂×C₄×C₁₉	—	4	16	no	—
264	C₂×C₄×C₁₉	—	4	8	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	#120	1	2	yes	—
277	C₂×C₄×C₁₉	#120	1	2	yes	—
278	C₂×C₄×C₁₉	#121	1	2	yes	—
279	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
280	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
283	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
284	C₈×C₁₉	—	4	2	no	—
285	C₈×C₁₉	—	4	2	no	—
286	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂×#463	C₂×C₁₉	1	2	yes	complemented
288	C₂×#450	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
290	#2850	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1879	C₂×C₁₉	1	2	yes	complemented
292	#1877	C₂×C₁₉	1	2	yes	complemented
293	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1804	C₂×C₁₉	1	2	yes	complemented
296	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	2	2	no	—
302	C₂²×C₁₉	—	2	2	no	—
303	C₂²×C₁₉	—	2	8	no	—
304	C₂²×C₁₉	—	4	32	no	—
305	C₂²×C₁₉	—	4	4	no	—
306	C₂²×C₁₉	—	4	4	no	—
307	C₂²×C₁₉	—	4	4	no	—
308	C₂²×C₁₉	—	4	4	no	—
309	C₂²×C₁₉	—	4	4	no	—
310	C₂²×C₁₉	—	4	4	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	8	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	—	8	1	no	—
318	C₂²×C₁₉	#463	1	4	yes	complemented
319	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
320	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
321	C₂²×C₁₉	#525	1	1	yes	characteristic
322	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
323	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
324	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₂²×C₁₉	#575	1	1	yes	characteristic
326	C₄×C₁₉	—	2	2	no	—
327	C₄×C₁₉	—	2	2	no	—
328	C₄×C₁₉	—	2	2	no	—
329	C₄×C₁₉	—	2	2	no	—
330	C₄×C₁₉	—	4	1	no	—
331	C₄×C₁₉	—	4	4	no	—
332	C₄×C₁₉	—	8	1	no	—
333	C₄×C₁₉	—	8	1	no	—
334	C₄×C₁₉	—	8	1	no	—
335	C₄×C₁₉	C₂×#121	1	2	yes	—
336	C₄×C₁₉	#525	1	2	yes	—
337	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
338	C₂⁴×C₄	—	2	1	no	—
339	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
340	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
341	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
342	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₄×D₄	—	2	8	no	—
345	C₂×C₄×D₄	—	2	1	no	—
346	C₂×C₄×D₄	—	2	1	no	—
347	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
348	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
349	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
350	C₂²×C₂²⋊C₄	—	2	1	no	—
351	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
352	#463	—	2	8	no	—
353	#450	—	2	4	no	—
354	#447	—	2	4	no	—
355	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
356	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
357	C₂×#102	C₂²×C₁₉	1	2	yes	—
358	C₂×#102	C₂²×C₁₉	1	2	yes	—
359	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
360	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
362	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#386	—	2	1	no	—
367	#386	—	2	1	no	—
368	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	#340	C₂²×C₁₉	1	2	yes	complemented
370	#340	C₂²×C₁₉	1	2	yes	complemented
371	#336	C₂²×C₁₉	1	2	yes	complemented
372	C₂×C₁₉	—	2	4	no	—
373	C₂×C₁₉	—	4	8	no	—
374	C₂×C₁₉	—	16	1	no	—
375	C₂×C₁₉	#2847	1	1	yes	characteristic
376	C₂×C₁₉	#3002	1	1	yes	characteristic
377	C₂×C₁₉	#3003	1	1	yes	characteristic
378	C₂×C₁₉	C₂×#463	1	1	yes	characteristic
379	C₂×C₁₉	#3036	1	1	yes	characteristic
380	C₂×C₁₉	#3105	1	1	yes	characteristic
381	C₂×C₁₉	#3114	1	1	yes	characteristic
382	C₂⁵	—	2	1	no	—
383	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×D₄	—	2	4	no	—
385	C₂²×D₄	—	2	4	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	2	no	—
389	C₂²×D₄	D₄×C₁₉	1	4	yes	—
390	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
391	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	—	2	2	no	—
395	C₂³×C₄	—	2	2	no	—
396	C₂³×C₄	—	4	4	no	—
397	C₂³×C₄	—	4	4	no	—
398	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
399	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×SD₁₆	—	2	4	no	—
402	C₂×SD₁₆	—	2	4	no	—
403	C₂×SD₁₆	—	2	4	no	—
404	C₂×D₈	—	2	4	no	—
405	C₂×D₈	—	2	4	no	—
406	C₂×D₈	—	2	4	no	—
407	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
408	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
409	#124	—	2	4	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	#121	—	2	2	no	—
413	#121	—	2	2	no	—
414	C₄×D₄	—	2	8	no	—
415	C₄×D₄	—	2	8	no	—
416	C₄×D₄	—	2	4	no	—
417	C₄×D₄	—	2	4	no	—
418	C₄×D₄	—	2	4	no	—
419	C₄×D₄	D₄×C₁₉	1	8	yes	complemented
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	4	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
426	C₂×C₂²⋊C₄	—	2	8	no	—
427	C₂×C₂²⋊C₄	—	2	2	no	—
428	C₂×C₂²⋊C₄	—	2	2	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₄²	—	2	4	no	—
436	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
437	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
440	C₄⋊C₈	—	2	4	no	—
441	#103	—	2	4	no	—
442	#102	—	2	4	no	—
443	#102	—	2	4	no	—
444	#102	—	2	4	no	—
445	C₂²⋊C₈	—	2	2	no	—
446	C₂²⋊C₈	—	2	2	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	C₁₉	#32908	1	1	yes	characteristic, direct product factor, Sylow
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	2	no	—
456	C₂⁴	—	2	1	no	—
457	C₂⁴	—	4	2	no	—
458	C₂⁴	—	4	2	no	—
459	C₂⁴	—	4	2	no	—
460	C₂⁴	—	4	2	no	—
461	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	2	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	16	no	—
469	C₂×D₄	—	2	16	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	4	2	no	—
480	C₂×D₄	—	4	2	no	—
481	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
482	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
483	C₂×D₄	#41×C₁₉	1	4	yes	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	8	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	8	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	32	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	—	4	4	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	4	no	—
506	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
511	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂²×C₄	#41×C₁₉	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
514	SD₁₆	—	4	8	no	—
515	D₈	—	4	8	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	2	no	—
540	C₄²	—	2	2	no	—
541	C₄²	C₂×D₄×C₁₉	1	4	yes	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	16	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	4	8	no	—
551	C₂³	—	4	8	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	4	8	no	—
555	C₂³	—	4	8	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	C₁₉×#121	1	2	yes	—
568	C₂³	C₁₉×#135	1	2	yes	—
569	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
570	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
571	Q₈	—	4	2	no	—
572	Q₈	—	4	2	no	—
573	D₄	—	2	16	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	4	no	—
576	D₄	—	2	4	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	8	4	no	—
580	D₄	C₁₉×#121	1	8	yes	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	16	no	—
598	C₂×C₄	—	4	16	no	—
599	C₂×C₄	—	4	8	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	C₁₉×#120	1	2	yes	—
612	C₂×C₄	C₁₉×#120	1	2	yes	—
613	C₂×C₄	C₁₉×#121	1	2	yes	—
614	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
616	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
617	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
618	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
619	C₈	—	4	2	no	—
620	C₈	—	4	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	8	no	—
628	C₂²	—	4	32	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	—	8	1	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	C₁₉×#463	1	4	yes	complemented
643	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
644	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
645	C₂²	C₁₉×#525	1	1	yes	characteristic
646	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
647	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
648	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
649	C₂²	C₁₉×#575	1	1	yes	characteristic
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	4	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	—	8	1	no	—
659	C₄	C₂×C₁₉×#121	1	2	yes	—
660	C₄	C₁₉×#525	1	2	yes	—
661	C₂	—	2	4	no	—
662	C₂	—	4	8	no	—
663	C₂	—	16	1	no	—
664	C₂	C₁₉×#2847	1	1	yes	characteristic
665	C₂	C₁₉×#3002	1	1	yes	characteristic
666	C₂	C₁₉×#3003	1	1	yes	characteristic
667	C₂	C₂×C₁₉×#463	1	1	yes	characteristic
668	C₂	C₁₉×#3036	1	1	yes	characteristic
669	C₂	C₁₉×#3105	1	1	yes	characteristic
670	C₂	C₁₉×#3114	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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
2. C₂×C₁₉×#463	C₂	semidirect
3. C₂×C₁₉×#450	C₂	semidirect
5. C₁₉×#2850	C₂	semidirect
6. C₁₉×#1879	C₂	semidirect
7. C₁₉×#1877	C₂	semidirect
8. C₁₉×#1874	C₂	semidirect
9. C₁₉×#1872	C₂	semidirect
10. C₁₉×#1804	C₂	semidirect
11. C₁₉×#1797	C₂	semidirect
16. C₂×C₁₉×#124	C₂²	semidirect
30. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
31. C₂×C₁₉×#103	C₂²	semidirect
34. C₂×C₁₉×#102	C₂²	semidirect
37. C₁₉×#391	C₂²	semidirect
38. C₁₉×#390	C₂²	semidirect
43. C₁₉×#382	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
45. C₁₉×#340	C₂²	semidirect
46. C₁₉×#336	C₂²	semidirect
84. C₄×D₄×C₁₉	D₄	semidirect
206. #32908	C₁₉	direct (N × H)
286. C₂²×C₄×D₄	C₂×C₁₉	semidirect
287. C₂×#463	C₂×C₁₉	semidirect
288. C₂×#450	C₂×C₁₉	semidirect
290. #2850	C₂×C₁₉	semidirect
291. #1879	C₂×C₁₉	semidirect
292. #1877	C₂×C₁₉	semidirect
293. #1874	C₂×C₁₉	semidirect
294. #1872	C₂×C₁₉	semidirect
295. #1804	C₂×C₁₉	semidirect
296. #1797	C₂×C₁₉	semidirect
318. C₂²×C₁₉	#463	semidirect
341. C₂×#124	C₂²×C₁₉	semidirect
355. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
356. C₂×#103	C₂²×C₁₉	semidirect
359. C₂×#102	C₂²×C₁₉	semidirect
362. #391	C₂²×C₁₉	semidirect
363. #390	C₂²×C₁₉	semidirect
368. #382	C₂²×C₁₉	semidirect
369. #340	C₂²×C₁₉	semidirect
370. #340	C₂²×C₁₉	semidirect
371. #336	C₂²×C₁₉	semidirect
419. C₄×D₄	D₄×C₁₉	semidirect
451. C₁₉	#32908	direct (N × H)
642. C₂²	C₁₉×#463	semidirect

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×#463	2
C₂×C₁₉×#450	2
C₂×C₁₉×#447	2
C₁₉×#2850	2
C₁₉×#1879	2
C₁₉×#1877	2
C₁₉×#1874	2
C₁₉×#1872	2
C₁₉×#1804	2
C₁₉×#1797	2
#32908	19

Subgroups — C19×#32908 #18038867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32908 #18038867