Subgroups — C₁₉×#23569 #18029528

Order 4864.

1272 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic
13	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#529	—	2	4	no	—
19	C₁₉×#529	—	2	4	no	—
20	C₂×C₁₉×#126	—	2	1	no	—
21	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#123	—	2	1	no	—
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₉	—	2	1	no	—
29	C₂×C₄×D₄×C₁₉	—	2	1	no	—
30	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#117	—	2	1	no	—
33	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₁₉	—	2	4	no	—
35	C₄×D₈×C₁₉	—	2	4	no	—
36	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#390	C₂²	1	1	yes	characteristic
51	C₁₉×#389	C₂²	1	1	yes	characteristic
52	C₁₉×#388	—	2	1	no	—
53	C₁₉×#386	—	2	1	no	—
54	C₁₉×#380	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#336	C₂²	1	1	yes	characteristic
62	C₁₉×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×SD₁₆×C₁₉	—	2	2	no	—
74	C₂×SD₁₆×C₁₉	—	2	2	no	—
75	C₂×SD₁₆×C₁₉	—	2	2	no	—
76	C₂×D₈×C₁₉	—	2	2	no	—
77	C₂×D₈×C₁₉	—	2	2	no	—
78	C₂×D₈×C₁₉	—	2	2	no	—
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×#126	—	2	8	no	—
84	C₁₉×#125	—	2	2	no	—
85	C₁₉×#125	—	2	2	no	—
86	C₁₉×#124	—	2	2	no	—
87	C₁₉×#124	—	2	2	no	—
88	C₁₉×#123	—	2	8	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₄×Q₈×C₁₉	—	2	2	no	—
96	C₄×Q₈×C₁₉	D₄	1	4	yes	complemented
97	C₄×D₄×C₁₉	—	2	8	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	4	4	no	—
102	C₄×D₄×C₁₉	D₄	1	4	yes	complemented
103	C₁₉×#117	—	2	8	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₄²×C₁₉	—	2	1	no	—
125	C₂×C₄²×C₁₉	—	2	2	no	—
126	C₂×C₄²×C₁₉	—	2	2	no	—
127	C₂×C₄²×C₁₉	—	2	1	no	—
128	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#107	—	2	2	no	—
133	C₁₉×#106	—	2	2	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×#102	—	2	2	no	—
142	C₁₉×C₂²⋊C₈	—	2	2	no	—
143	C₁₉×C₂²⋊C₈	—	2	2	no	—
144	C₄×C₈×C₁₉	—	2	2	no	—
145	C₄×C₈×C₁₉	—	2	2	no	—
146	C₁₉×#95	—	2	1	no	—
147	C₁₉×#95	—	2	1	no	—
148	C₁₉×#95	—	2	1	no	—
149	C₂⁴×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	—	2	1	no	—
151	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₉	—	2	4	no	—
159	C₂×D₄×C₁₉	—	2	4	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	2	1	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	4	2	no	—
171	C₂×D₄×C₁₉	—	4	2	no	—
172	C₂×D₄×C₁₉	—	4	2	no	—
173	C₂×D₄×C₁₉	—	4	2	no	—
174	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₁₉	#41	1	2	yes	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	2	4	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	4	2	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	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
206	SD₁₆×C₁₉	—	2	8	no	—
207	D₈×C₁₉	—	2	8	no	—
208	C₂×C₈×C₁₉	—	2	1	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	—	2	1	no	—
211	C₂×C₈×C₁₉	—	2	1	no	—
212	C₂×C₈×C₁₉	—	2	1	no	—
213	C₂×C₈×C₁₉	—	2	1	no	—
214	C₂×C₈×C₁₉	—	2	1	no	—
215	C₂×C₈×C₁₉	—	2	1	no	—
216	C₂×C₈×C₁₉	—	2	1	no	—
217	C₂×C₈×C₁₉	—	2	1	no	—
218	C₂×C₈×C₁₉	#41	1	2	yes	—
219	C₂×C₈×C₁₉	#41	1	2	yes	—
220	C₄⋊C₄×C₁₉	—	2	4	no	—
221	C₄⋊C₄×C₁₉	—	2	4	no	—
222	C₄⋊C₄×C₁₉	—	2	4	no	—
223	C₄⋊C₄×C₁₉	—	2	4	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	4	2	no	—
232	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
233	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₁₉	#41	1	2	yes	—
235	C₂²⋊C₄×C₁₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₉	—	4	2	no	—
242	C₂²⋊C₄×C₁₉	—	4	2	no	—
243	C₂²⋊C₄×C₁₉	—	4	2	no	—
244	C₂²⋊C₄×C₁₉	—	4	2	no	—
245	C₄²×C₁₉	—	2	2	no	—
246	C₄²×C₁₉	—	2	2	no	—
247	C₄²×C₁₉	—	2	4	no	—
248	C₄²×C₁₉	—	2	1	no	—
249	C₄²×C₁₉	—	2	1	no	—
250	C₄²×C₁₉	—	4	2	no	—
251	C₄²×C₁₉	C₂×D₄	1	2	yes	—
252	C₄²×C₁₉	C₂×D₄	1	2	yes	—
253	#23569	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂³×C₁₉	—	2	1	no	—
255	C₂³×C₁₉	—	2	1	no	—
256	C₂³×C₁₉	—	2	1	no	—
257	C₂³×C₁₉	—	2	1	no	—
258	C₂³×C₁₉	—	2	1	no	—
259	C₂³×C₁₉	—	2	1	no	—
260	C₂³×C₁₉	—	2	2	no	—
261	C₂³×C₁₉	—	2	2	no	—
262	C₂³×C₁₉	—	4	1	no	—
263	C₂³×C₁₉	—	4	1	no	—
264	C₂³×C₁₉	—	4	1	no	—
265	C₂³×C₁₉	—	4	1	no	—
266	C₂³×C₁₉	—	4	1	no	—
267	C₂³×C₁₉	—	4	1	no	—
268	C₂³×C₁₉	—	4	1	no	—
269	C₂³×C₁₉	—	4	1	no	—
270	C₂³×C₁₉	—	4	1	no	—
271	C₂³×C₁₉	—	4	1	no	—
272	C₂³×C₁₉	—	4	1	no	—
273	C₂³×C₁₉	—	4	1	no	—
274	C₂³×C₁₉	#135	1	2	yes	—
275	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₁₉	—	2	2	no	—
277	Q₈×C₁₉	—	2	2	no	—
278	Q₈×C₁₉	—	4	1	no	—
279	Q₈×C₁₉	—	4	1	no	—
280	D₄×C₁₉	—	2	2	no	—
281	D₄×C₁₉	—	2	2	no	—
282	D₄×C₁₉	—	2	2	no	—
283	D₄×C₁₉	—	2	2	no	—
284	D₄×C₁₉	—	4	8	no	—
285	D₄×C₁₉	—	4	8	no	—
286	D₄×C₁₉	—	4	1	no	—
287	D₄×C₁₉	—	4	1	no	—
288	D₄×C₁₉	—	4	1	no	—
289	D₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	2	1	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	2	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	1	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	4	4	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	4	no	—
319	C₂×C₄×C₁₉	—	4	8	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	1	no	—
325	C₂×C₄×C₁₉	—	4	1	no	—
326	C₂×C₄×C₁₉	—	8	4	no	—
327	C₂×C₄×C₁₉	#120	1	2	yes	—
328	C₂×C₄×C₁₉	#120	1	2	yes	—
329	C₂×C₄×C₁₉	#135	1	2	yes	—
330	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
331	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
337	C₈×C₁₉	—	2	2	no	—
338	C₈×C₁₉	—	2	2	no	—
339	C₈×C₁₉	—	4	1	no	—
340	C₈×C₁₉	—	4	1	no	—
341	C₂×#529	C₂×C₁₉	1	1	yes	characteristic, complemented
342	C₂×C₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
343	C₂×C₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
344	C₄×#121	C₂×C₁₉	1	1	yes	characteristic, complemented
345	#2059	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2034	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#2025	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#2012	C₂×C₁₉	1	1	yes	characteristic, complemented
351	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
352	#1999	C₂×C₁₉	1	1	yes	characteristic
353	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
354	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
355	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
356	C₂²×C₁₉	—	2	2	no	—
357	C₂²×C₁₉	—	2	2	no	—
358	C₂²×C₁₉	—	2	2	no	—
359	C₂²×C₁₉	—	4	1	no	—
360	C₂²×C₁₉	—	4	1	no	—
361	C₂²×C₁₉	—	4	1	no	—
362	C₂²×C₁₉	—	4	1	no	—
363	C₂²×C₁₉	—	4	2	no	—
364	C₂²×C₁₉	—	4	2	no	—
365	C₂²×C₁₉	—	4	2	no	—
366	C₂²×C₁₉	—	4	2	no	—
367	C₂²×C₁₉	—	4	2	no	—
368	C₂²×C₁₉	—	4	2	no	—
369	C₂²×C₁₉	—	8	1	no	—
370	C₂²×C₁₉	—	8	1	no	—
371	C₂²×C₁₉	—	8	1	no	—
372	C₂²×C₁₉	—	8	1	no	—
373	C₂²×C₁₉	—	8	1	no	—
374	C₂²×C₁₉	—	8	1	no	—
375	C₂²×C₁₉	—	8	1	no	—
376	C₂²×C₁₉	—	8	1	no	—
377	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
378	C₂²×C₁₉	#525	1	1	yes	characteristic
379	C₂²×C₁₉	#532	1	1	yes	characteristic
380	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
381	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
382	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₂²×C₁₉	#575	1	1	yes	characteristic
384	C₄×C₁₉	—	2	2	no	—
385	C₄×C₁₉	—	4	2	no	—
386	C₄×C₁₉	—	4	1	no	—
387	C₄×C₁₉	—	4	2	no	—
388	C₄×C₁₉	—	4	1	no	—
389	C₄×C₁₉	—	4	2	no	—
390	C₄×C₁₉	—	4	1	no	—
391	C₄×C₁₉	—	4	2	no	—
392	C₄×C₁₉	—	8	1	no	—
393	C₄×C₁₉	—	8	1	no	—
394	C₄×C₁₉	#449	1	4	yes	—
395	C₄×C₁₉	#525	1	1	yes	characteristic
396	C₄×C₁₉	#525	1	1	yes	characteristic
397	C₄×C₁₉	#532	1	1	yes	characteristic
398	C₄×C₁₉	#532	1	1	yes	characteristic
399	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
400	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
401	#529	—	2	4	no	—
402	#529	—	2	4	no	—
403	C₂×#126	—	2	1	no	—
404	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×#123	—	2	1	no	—
407	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
408	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
409	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
411	C₂×C₄×D₄	—	2	1	no	—
412	C₂×C₄×D₄	—	2	1	no	—
413	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
415	C₂×#117	—	2	1	no	—
416	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
417	C₄×SD₁₆	—	2	4	no	—
418	C₄×D₈	—	2	4	no	—
419	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
420	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
423	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
424	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
425	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
426	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
428	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
429	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
431	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
432	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
433	#390	C₂²×C₁₉	1	1	yes	characteristic
434	#389	C₂²×C₁₉	1	1	yes	characteristic
435	#388	—	2	1	no	—
436	#386	—	2	1	no	—
437	#380	C₂²×C₁₉	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
439	C₄×C₂²⋊C₄	—	2	1	no	—
440	#340	C₂²×C₁₉	1	1	yes	characteristic
441	#340	C₂²×C₁₉	1	1	yes	characteristic
442	#340	C₂²×C₁₉	1	1	yes	characteristic
443	#340	C₂²×C₁₉	1	1	yes	characteristic
444	#336	C₂²×C₁₉	1	1	yes	characteristic
445	#336	C₂²×C₁₉	1	1	yes	characteristic
446	C₂×C₁₉	—	4	2	no	—
447	C₂×C₁₉	—	8	2	no	—
448	C₂×C₁₉	—	8	2	no	—
449	C₂×C₁₉	#2388	1	1	yes	characteristic
450	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
451	C₂×C₁₉	#3002	1	1	yes	characteristic
452	C₂×C₁₉	#3102	1	1	yes	characteristic
453	C₂×C₁₉	#3105	1	1	yes	characteristic
454	C₂×C₁₉	#3168	1	1	yes	characteristic
455	C₂×C₁₉	#3171	1	1	yes	characteristic
456	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
464	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	—	2	2	no	—
469	C₂×D₈	—	2	2	no	—
470	C₂×D₈	—	2	2	no	—
471	C₂×D₈	—	2	2	no	—
472	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
476	#126	—	2	8	no	—
477	#125	—	2	2	no	—
478	#125	—	2	2	no	—
479	#124	—	2	2	no	—
480	#124	—	2	2	no	—
481	#123	—	2	8	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	D₄×C₁₉	1	4	yes	complemented
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	4	4	no	—
495	C₄×D₄	D₄×C₁₉	1	4	yes	complemented
496	#117	—	2	8	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	2	no	—
519	C₂×C₄²	—	2	2	no	—
520	C₂×C₄²	—	2	1	no	—
521	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
522	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
525	#107	—	2	2	no	—
526	#106	—	2	2	no	—
527	#103	—	2	2	no	—
528	#103	—	2	2	no	—
529	#103	—	2	2	no	—
530	#102	—	2	2	no	—
531	#102	—	2	2	no	—
532	#102	—	2	2	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	C₂²⋊C₈	—	2	2	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₄×C₈	—	2	2	no	—
538	C₄×C₈	—	2	2	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	C₁₉	#23569	1	1	yes	characteristic, direct product factor, Sylow
543	C₂⁴	—	2	1	no	—
544	C₂⁴	—	2	1	no	—
545	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
569	C₂×D₄	#41×C₁₉	1	2	yes	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
600	SD₁₆	—	2	8	no	—
601	D₈	—	2	8	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	#41×C₁₉	1	2	yes	—
613	C₂×C₈	#41×C₁₉	1	2	yes	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
628	C₄⋊C₄	#41×C₁₉	1	2	yes	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	4	2	no	—
645	C₄²	C₂×D₄×C₁₉	1	2	yes	—
646	C₄²	C₂×D₄×C₁₉	1	2	yes	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	C₁₉×#135	1	2	yes	—
668	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
669	Q₈	—	2	2	no	—
670	Q₈	—	2	2	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	2	no	—
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	4	8	no	—
678	D₄	—	4	8	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	C₁₉×#120	1	2	yes	—
721	C₂×C₄	C₁₉×#120	1	2	yes	—
722	C₂×C₄	C₁₉×#135	1	2	yes	—
723	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
726	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
727	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
729	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
730	C₈	—	2	2	no	—
731	C₈	—	2	2	no	—
732	C₈	—	4	1	no	—
733	C₈	—	4	1	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	8	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
756	C₂²	C₁₉×#525	1	1	yes	characteristic
757	C₂²	C₁₉×#532	1	1	yes	characteristic
758	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
759	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
760	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
761	C₂²	C₁₉×#575	1	1	yes	characteristic
762	C₄	—	2	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	2	no	—
770	C₄	—	8	1	no	—
771	C₄	—	8	1	no	—
772	C₄	C₁₉×#449	1	4	yes	—
773	C₄	C₁₉×#525	1	1	yes	characteristic
774	C₄	C₁₉×#525	1	1	yes	characteristic
775	C₄	C₁₉×#532	1	1	yes	characteristic
776	C₄	C₁₉×#532	1	1	yes	characteristic
777	C₂	—	4	2	no	—
778	C₂	—	8	2	no	—
779	C₂	—	8	2	no	—
780	C₂	C₁₉×#2388	1	1	yes	characteristic
781	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
782	C₂	C₁₉×#3002	1	1	yes	characteristic
783	C₂	C₁₉×#3102	1	1	yes	characteristic
784	C₂	C₁₉×#3105	1	1	yes	characteristic
785	C₂	C₁₉×#3168	1	1	yes	characteristic
786	C₂	C₁₉×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
prime radical	C₁₉×#1999	C₂
LCS	G ▷ C₂²×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. C₂×C₁₉×#529	C₂	semidirect
2. C₂×C₄×SD₁₆×C₁₉	C₂	semidirect
3. C₂×C₄×D₈×C₁₉	C₂	semidirect
4. C₄×C₁₉×#121	C₂	semidirect
5. C₁₉×#2059	C₂	semidirect
6. C₁₉×#2042	C₂	semidirect
7. C₁₉×#2036	C₂	semidirect
8. C₁₉×#2034	C₂	semidirect
9. C₁₉×#2025	C₂	semidirect
10. C₁₉×#2012	C₂	semidirect
11. C₁₉×#2000	C₂	semidirect
13. C₄×C₁₉×#103	C₂	semidirect
14. C₄×C₁₉×#102	C₂	semidirect
15. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
96. C₄×Q₈×C₁₉	D₄	semidirect
102. C₄×D₄×C₁₉	D₄	semidirect
253. #23569	C₁₉	direct (N × H)
341. C₂×#529	C₂×C₁₉	semidirect
342. C₂×C₄×SD₁₆	C₂×C₁₉	semidirect
343. C₂×C₄×D₈	C₂×C₁₉	semidirect
344. C₄×#121	C₂×C₁₉	semidirect
345. #2059	C₂×C₁₉	semidirect
346. #2042	C₂×C₁₉	semidirect
347. #2036	C₂×C₁₉	semidirect
348. #2034	C₂×C₁₉	semidirect
349. #2025	C₂×C₁₉	semidirect
350. #2012	C₂×C₁₉	semidirect
351. #2000	C₂×C₁₉	semidirect
353. C₄×#103	C₂×C₁₉	semidirect
354. C₄×#102	C₂×C₁₉	semidirect
355. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
489. C₄×Q₈	D₄×C₁₉	semidirect
495. C₄×D₄	D₄×C₁₉	semidirect
542. C₁₉	#23569	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#529	2
C₂×C₄×SD₁₆×C₁₉	2
C₂×C₄×D₈×C₁₉	2
C₄×C₁₉×#121	2
C₁₉×#2059	2
C₁₉×#2042	2
C₁₉×#2036	2
C₁₉×#2034	2
C₁₉×#2025	2
C₁₉×#2012	2
C₁₉×#2000	2
C₁₉×#1999	2
C₄×C₁₉×#103	2
C₄×C₁₉×#102	2
C₄×C₁₉×C₂²⋊C₈	2
#23569	19

Subgroups — C19×#23569 #18029528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23569 #18029528