Subgroups — C₁₉×#32905 #18038864

Order 4864.

1868 conjugacy classes of subgroups.

The subgroup lattice has 542 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
2	C₂×C₁₉×#461	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#450	C₂	1	2	yes	maximal
4	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1877	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1872	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1802	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	—	2	1	no	—
11	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	—
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	—	2	8	no	—
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#461	—	2	8	no	—
23	C₁₉×#450	—	2	8	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
26	C₂×C₁₉×#102	C₂²	1	4	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₁₉×#391	C₂²	1	2	yes	complemented
29	C₁₉×#389	—	2	1	no	—
30	C₁₉×#389	—	2	1	no	—
31	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#380	—	2	1	no	—
33	C₁₉×#380	—	2	1	no	—
34	C₁₉×#340	C₂²	1	4	yes	complemented
35	C₁₉×#336	C₂²	1	2	yes	complemented
36	C₂⁵×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	D₄	1	4	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	8	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	—	4	4	no	—
49	C₂³×C₄×C₁₉	—	4	4	no	—
50	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₉	—	2	8	no	—
54	C₂×SD₁₆×C₁₉	—	2	8	no	—
55	C₂×SD₁₆×C₁₉	—	2	8	no	—
56	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
57	C₁₉×C₄⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	4	no	—
60	C₄×D₄×C₁₉	—	2	8	no	—
61	C₄×D₄×C₁₉	—	2	8	no	—
62	C₄×D₄×C₁₉	—	2	4	no	—
63	C₄×D₄×C₁₉	—	2	4	no	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	D₄	1	8	yes	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	—	2	4	no	—
80	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊C₈	—	2	4	no	—
85	C₁₉×#103	—	2	8	no	—
86	C₁₉×#102	—	2	8	no	—
87	C₁₉×C₂²⋊C₈	—	2	4	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₂⁴×C₁₉	—	2	4	no	—
91	C₂⁴×C₁₉	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	4	2	no	—
95	C₂⁴×C₁₉	—	4	2	no	—
96	C₂⁴×C₁₉	—	4	2	no	—
97	C₂⁴×C₁₉	—	4	2	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	4	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	16	no	—
106	C₂×D₄×C₁₉	—	2	16	no	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
112	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
113	C₂×D₄×C₁₉	#41	1	4	yes	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	8	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	32	no	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	—	4	2	no	—
131	C₂²×C₄×C₁₉	—	4	4	no	—
132	C₂²×C₄×C₁₉	—	4	4	no	—
133	C₂²×C₄×C₁₉	—	4	4	no	—
134	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	#41	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	SD₁₆×C₁₉	—	4	16	no	—
144	C₂×C₈×C₁₉	—	2	4	no	—
145	C₂×C₈×C₁₉	—	2	4	no	—
146	C₂×C₈×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	4	2	no	—
153	C₄⋊C₄×C₁₉	—	4	2	no	—
154	C₄⋊C₄×C₁₉	—	4	4	no	—
155	C₄⋊C₄×C₁₉	—	4	2	no	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
157	C₂²⋊C₄×C₁₉	—	2	8	no	—
158	C₂²⋊C₄×C₁₉	—	2	8	no	—
159	C₂²⋊C₄×C₁₉	—	4	4	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	C₂×D₄	1	4	yes	—
164	#32905	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	2	16	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	4	no	—
173	C₂³×C₁₉	—	4	8	no	—
174	C₂³×C₁₉	—	4	8	no	—
175	C₂³×C₁₉	—	4	8	no	—
176	C₂³×C₁₉	—	4	8	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	8	no	—
183	C₂³×C₁₉	#121	1	2	yes	—
184	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
185	C₂³×C₁₉	#137	1	2	yes	—
186	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₉	—	4	4	no	—
188	Q₈×C₁₉	—	4	4	no	—
189	D₄×C₁₉	—	2	16	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	4	no	—
193	D₄×C₁₉	#121	1	8	yes	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	8	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	4	4	no	—
208	C₂×C₄×C₁₉	—	4	16	no	—
209	C₂×C₄×C₁₉	—	4	8	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	16	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	#120	1	2	yes	—
220	C₂×C₄×C₁₉	#120	1	2	yes	—
221	C₂×C₄×C₁₉	#121	1	2	yes	—
222	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
225	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
228	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
229	C₈×C₁₉	—	4	4	no	—
230	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
231	C₂×#461	C₂×C₁₉	1	2	yes	complemented
232	C₂×#450	C₂×C₁₉	1	2	yes	—
233	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1877	C₂×C₁₉	1	4	yes	complemented
235	#1872	C₂×C₁₉	1	2	yes	complemented
236	#1802	C₂×C₁₉	1	2	yes	complemented
237	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	8	no	—
245	C₂²×C₁₉	—	4	32	no	—
246	C₂²×C₁₉	—	4	4	no	—
247	C₂²×C₁₉	—	4	4	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	#461	1	4	yes	complemented
253	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
254	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
255	C₂²×C₁₉	#525	1	1	yes	characteristic
256	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
259	C₂²×C₁₉	#575	1	1	yes	characteristic
260	C₄×C₁₉	—	2	2	no	—
261	C₄×C₁₉	—	2	2	no	—
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	4	4	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₄×C₁₉	—	8	2	no	—
267	C₄×C₁₉	#450	1	4	yes	complemented
268	C₄×C₁₉	C₂×#121	1	2	yes	—
269	C₄×C₁₉	#525	1	2	yes	—
270	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
271	C₂⁴×C₄	—	2	1	no	—
272	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	—
273	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
274	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
275	C₂×C₄×D₄	—	2	8	no	—
276	C₂×C₄×D₄	—	2	1	no	—
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	—	2	1	no	—
282	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
283	#461	—	2	8	no	—
284	#450	—	2	8	no	—
285	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
286	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
287	C₂×#102	C₂²×C₁₉	1	4	yes	—
288	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
289	#391	C₂²×C₁₉	1	2	yes	complemented
290	#389	—	2	1	no	—
291	#389	—	2	1	no	—
292	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
293	#380	—	2	1	no	—
294	#380	—	2	1	no	—
295	#340	C₂²×C₁₉	1	4	yes	complemented
296	#336	C₂²×C₁₉	1	2	yes	complemented
297	C₂×C₁₉	—	2	4	no	—
298	C₂×C₁₉	—	4	8	no	—
299	C₂×C₁₉	#2847	1	1	yes	characteristic
300	C₂×C₁₉	C₂×#450	1	1	yes	characteristic
301	C₂×C₁₉	#3007	1	1	yes	characteristic
302	C₂×C₁₉	C₂×#461	1	1	yes	characteristic
303	C₂×C₁₉	#3036	1	1	yes	characteristic
304	C₂×C₁₉	#3101	1	1	yes	characteristic
305	C₂×C₁₉	#3110	1	1	yes	characteristic
306	C₂⁵	—	2	1	no	—
307	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	2	4	no	—
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	D₄×C₁₉	1	4	yes	—
313	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
314	C₂³×C₄	—	2	8	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	2	2	no	—
317	C₂³×C₄	—	2	2	no	—
318	C₂³×C₄	—	4	4	no	—
319	C₂³×C₄	—	4	4	no	—
320	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
321	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×SD₁₆	—	2	8	no	—
324	C₂×SD₁₆	—	2	8	no	—
325	C₂×SD₁₆	—	2	8	no	—
326	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
327	C₄⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	4	no	—
330	C₄×D₄	—	2	8	no	—
331	C₄×D₄	—	2	8	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	D₄×C₁₉	1	8	yes	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
345	C₂×C₂²⋊C₄	—	2	8	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₄²	—	2	4	no	—
350	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
354	C₄⋊C₈	—	2	4	no	—
355	#103	—	2	8	no	—
356	#102	—	2	8	no	—
357	C₂²⋊C₈	—	2	4	no	—
358	#95	—	2	2	no	—
359	#95	—	2	2	no	—
360	C₁₉	#32905	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	4	no	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	4	2	no	—
366	C₂⁴	—	4	2	no	—
367	C₂⁴	—	4	2	no	—
368	C₂⁴	—	4	2	no	—
369	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	16	no	—
377	C₂×D₄	—	2	16	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
383	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
384	C₂×D₄	#41×C₁₉	1	4	yes	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	32	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	—	4	4	no	—
405	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	#41×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
414	SD₁₆	—	4	16	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	4	no	—
417	C₂×C₈	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂×D₄×C₁₉	1	4	yes	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	16	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	8	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	4	8	no	—
446	C₂³	—	4	8	no	—
447	C₂³	—	4	8	no	—
448	C₂³	—	4	8	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	C₁₉×#121	1	2	yes	—
454	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
455	C₂³	C₁₉×#137	1	2	yes	—
456	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
457	Q₈	—	4	4	no	—
458	Q₈	—	4	4	no	—
459	D₄	—	2	16	no	—
460	D₄	—	2	4	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	4	no	—
463	D₄	C₁₉×#121	1	8	yes	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	16	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	16	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	C₁₉×#120	1	2	yes	—
490	C₂×C₄	C₁₉×#120	1	2	yes	—
491	C₂×C₄	C₁₉×#121	1	2	yes	—
492	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
493	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
494	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
497	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
498	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
499	C₈	—	4	4	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	4	32	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	C₁₉×#461	1	4	yes	complemented
515	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
516	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
517	C₂²	C₁₉×#525	1	1	yes	characteristic
518	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
519	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
520	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
521	C₂²	C₁₉×#575	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	1	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	2	no	—
529	C₄	C₁₉×#450	1	4	yes	complemented
530	C₄	C₂×C₁₉×#121	1	2	yes	—
531	C₄	C₁₉×#525	1	2	yes	—
532	C₂	—	2	4	no	—
533	C₂	—	4	8	no	—
534	C₂	C₁₉×#2847	1	1	yes	characteristic
535	C₂	C₂×C₁₉×#450	1	1	yes	characteristic
536	C₂	C₁₉×#3007	1	1	yes	characteristic
537	C₂	C₂×C₁₉×#461	1	1	yes	characteristic
538	C₂	C₁₉×#3036	1	1	yes	characteristic
539	C₂	C₁₉×#3101	1	1	yes	characteristic
540	C₂	C₁₉×#3110	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
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
2. C₂×C₁₉×#461	C₂	semidirect
4. C₁₉×#2857	C₂	semidirect
5. C₁₉×#1877	C₂	semidirect
6. C₁₉×#1872	C₂	semidirect
7. C₁₉×#1802	C₂	semidirect
8. C₁₉×#1797	C₂	semidirect
12. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
25. C₂×C₁₉×#103	C₂²	semidirect
28. C₁₉×#391	C₂²	semidirect
31. C₁₉×#384	C₂²	semidirect
34. C₁₉×#340	C₂²	semidirect
35. C₁₉×#336	C₂²	semidirect
134. C₂²×C₄×C₁₉	SD₁₆	semidirect
164. #32905	C₁₉	direct (N × H)
231. C₂×#461	C₂×C₁₉	semidirect
233. #2857	C₂×C₁₉	semidirect
234. #1877	C₂×C₁₉	semidirect
235. #1872	C₂×C₁₉	semidirect
236. #1802	C₂×C₁₉	semidirect
237. #1797	C₂×C₁₉	semidirect
252. C₂²×C₁₉	#461	semidirect
267. C₄×C₁₉	#450	semidirect
273. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
285. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
286. C₂×#103	C₂²×C₁₉	semidirect
289. #391	C₂²×C₁₉	semidirect
292. #384	C₂²×C₁₉	semidirect
295. #340	C₂²×C₁₉	semidirect
296. #336	C₂²×C₁₉	semidirect
360. C₁₉	#32905	direct (N × H)
405. C₂²×C₄	SD₁₆×C₁₉	semidirect
514. C₂²	C₁₉×#461	semidirect
529. C₄	C₁₉×#450	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×#461	2
C₂×C₁₉×#450	2
C₁₉×#2857	2
C₁₉×#1877	2
C₁₉×#1872	2
C₁₉×#1802	2
C₁₉×#1797	2
#32905	19

Subgroups — C19×#32905 #18038864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32905 #18038864