Subgroups — C₁₉×#24792 #18030751

Order 4864.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2414	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2065	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1809	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	—	2	1	no	—
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#469	—	2	4	no	—
28	C₁₉×#469	—	2	4	no	—
29	C₁₉×#436	—	2	4	no	—
30	C₁₉×#428	—	2	4	no	—
31	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
46	C₁₉×#396	—	2	1	no	—
47	C₁₉×#394	—	2	1	no	—
48	C₁₉×#394	—	2	1	no	—
49	C₁₉×#392	—	2	1	no	—
50	C₁₉×#390	—	2	1	no	—
51	C₁₉×#390	C₂²	1	1	yes	characteristic
52	C₁₉×#390	C₂²	1	1	yes	characteristic
53	C₁₉×#389	C₂²	1	1	yes	characteristic
54	C₁₉×#389	C₂²	1	1	yes	characteristic
55	C₁₉×#388	—	2	1	no	—
56	C₁₉×#386	—	2	1	no	—
57	C₁₉×#380	C₂²	1	1	yes	characteristic
58	C₁₉×#380	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#340	C₂²	1	1	yes	characteristic
62	C₁₉×#340	C₂²	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	—	2	1	no	—
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×D₈×C₁₉	—	2	2	no	—
74	C₂×D₈×C₁₉	—	2	2	no	—
75	C₂×D₈×C₁₉	—	2	2	no	—
76	C₂×M₁₆×C₁₉	—	2	2	no	—
77	C₂×M₁₆×C₁₉	—	2	2	no	—
78	C₂×M₁₆×C₁₉	—	2	2	no	—
79	C₂×M₁₆×C₁₉	—	2	2	no	—
80	C₂×M₁₆×C₁₉	—	2	2	no	—
81	C₂×M₁₆×C₁₉	D₄	1	4	yes	complemented
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	4	1	no	—
93	C₁₉×#121	—	4	1	no	—
94	C₁₉×#121	—	4	4	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	4	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₁₉	—	2	1	no	—
125	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₁₉×#107	—	2	2	no	—
127	C₁₉×#107	—	2	2	no	—
128	C₁₉×#106	—	2	2	no	—
129	C₁₉×#106	—	2	2	no	—
130	C₁₉×#106	D₄	1	4	yes	complemented
131	C₁₉×C₄⋊C₈	—	2	2	no	—
132	C₁₉×#102	—	2	2	no	—
133	C₁₉×#102	—	2	2	no	—
134	C₁₉×#102	—	2	2	no	—
135	C₁₉×#102	—	2	2	no	—
136	C₁₉×#102	—	4	1	no	—
137	C₁₉×#102	—	4	1	no	—
138	C₁₉×C₂²⋊C₈	—	2	2	no	—
139	C₁₉×C₂²⋊C₈	—	2	2	no	—
140	C₄×C₈×C₁₉	—	2	2	no	—
141	C₁₉×#95	—	2	1	no	—
142	C₁₉×#95	—	2	1	no	—
143	C₁₉×#95	—	2	1	no	—
144	C₁₉×#95	—	2	1	no	—
145	C₂⁴×C₁₉	—	2	1	no	—
146	C₂⁴×C₁₉	—	2	1	no	—
147	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	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	—	4	1	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	4	2	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	4	2	no	—
170	C₂×D₄×C₁₉	—	4	2	no	—
171	C₂×D₄×C₁₉	—	4	2	no	—
172	C₂×D₄×C₁₉	—	8	1	no	—
173	C₂×D₄×C₁₉	—	8	1	no	—
174	C₂×D₄×C₁₉	—	8	1	no	—
175	C₂×D₄×C₁₉	—	8	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	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	—	4	2	no	—
193	C₂²×C₄×C₁₉	—	4	2	no	—
194	C₂²×C₄×C₁₉	—	8	1	no	—
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	#41	1	2	yes	—
201	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
202	D₈×C₁₉	—	4	4	no	—
203	M₁₆×C₁₉	—	2	8	no	—
204	M₁₆×C₁₉	—	4	4	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	2	1	no	—
207	C₂×C₈×C₁₉	—	2	1	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	C₂×D₄	1	2	yes	—
214	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
215	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
216	C₂×C₈×C₁₉	#41	1	2	yes	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	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	—	4	2	no	—
229	C₄⋊C₄×C₁₉	—	4	2	no	—
230	C₄⋊C₄×C₁₉	—	8	1	no	—
231	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
232	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
233	C₂²⋊C₄×C₁₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₉	—	2	2	no	—
235	C₂²⋊C₄×C₁₉	—	4	2	no	—
236	C₂²⋊C₄×C₁₉	—	4	2	no	—
237	C₂²⋊C₄×C₁₉	—	4	2	no	—
238	C₂²⋊C₄×C₁₉	—	4	2	no	—
239	C₂²⋊C₄×C₁₉	—	4	2	no	—
240	C₂²⋊C₄×C₁₉	—	4	2	no	—
241	C₂²⋊C₄×C₁₉	—	4	2	no	—
242	C₂²⋊C₄×C₁₉	—	4	2	no	—
243	C₂²⋊C₄×C₁₉	—	8	1	no	—
244	C₂²⋊C₄×C₁₉	—	8	1	no	—
245	C₂²⋊C₄×C₁₉	—	8	1	no	—
246	C₄²×C₁₉	—	2	1	no	—
247	C₄²×C₁₉	—	2	1	no	—
248	C₄²×C₁₉	—	4	2	no	—
249	#24792	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₉	—	2	1	no	—
251	C₂³×C₁₉	—	2	1	no	—
252	C₂³×C₁₉	—	2	1	no	—
253	C₂³×C₁₉	—	2	1	no	—
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	1	no	—
261	C₂³×C₁₉	—	2	1	no	—
262	C₂³×C₁₉	—	2	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	—	4	1	no	—
275	C₂³×C₁₉	—	4	1	no	—
276	C₂³×C₁₉	—	4	1	no	—
277	C₂³×C₁₉	#121	1	2	yes	—
278	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	D₄×C₁₉	—	4	4	no	—
280	D₄×C₁₉	—	4	1	no	—
281	D₄×C₁₉	—	4	1	no	—
282	D₄×C₁₉	—	4	1	no	—
283	D₄×C₁₉	—	4	1	no	—
284	D₄×C₁₉	—	4	1	no	—
285	D₄×C₁₉	—	4	1	no	—
286	D₄×C₁₉	—	4	1	no	—
287	D₄×C₁₉	—	4	1	no	—
288	D₄×C₁₉	—	8	4	no	—
289	D₄×C₁₉	—	8	4	no	—
290	D₄×C₁₉	—	8	4	no	—
291	D₄×C₁₉	—	8	4	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	1	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	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	2	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	2	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	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	1	no	—
319	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
327	C₂×C₄×C₁₉	—	4	1	no	—
328	C₂×C₄×C₁₉	—	8	4	no	—
329	C₂×C₄×C₁₉	#121	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	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
337	C₈×C₁₉	—	2	2	no	—
338	C₈×C₁₉	—	4	1	no	—
339	C₈×C₁₉	—	4	1	no	—
340	C₈×C₁₉	#121	1	4	yes	complemented
341	C₂×#469	C₂×C₁₉	1	1	yes	characteristic, complemented
342	C₂×#469	C₂×C₁₉	1	1	yes	characteristic, complemented
343	C₂×#436	C₂×C₁₉	1	1	yes	characteristic, complemented
344	C₂×#428	C₂×C₁₉	1	1	yes	characteristic, complemented
345	#2416	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#2414	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#2067	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2065	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#2034	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
351	#1970	C₂×C₁₉	1	1	yes	characteristic, complemented
352	#1941	C₂×C₁₉	1	1	yes	characteristic, complemented
353	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
355	#1809	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	1	no	—
364	C₂²×C₁₉	—	4	1	no	—
365	C₂²×C₁₉	—	4	1	no	—
366	C₂²×C₁₉	—	4	1	no	—
367	C₂²×C₁₉	—	4	1	no	—
368	C₂²×C₁₉	—	4	1	no	—
369	C₂²×C₁₉	—	4	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	—	8	1	no	—
378	C₂²×C₁₉	—	8	1	no	—
379	C₂²×C₁₉	—	8	1	no	—
380	C₂²×C₁₉	—	8	1	no	—
381	C₂²×C₁₉	—	8	1	no	—
382	C₂²×C₁₉	—	8	1	no	—
383	C₂²×C₁₉	—	8	1	no	—
384	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
385	C₂²×C₁₉	D₄²	1	1	yes	characteristic
386	C₂²×C₁₉	#547	1	1	yes	characteristic
387	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂²×C₁₉	#575	1	1	yes	characteristic
389	C₂²×C₁₉	#576	1	1	yes	characteristic
390	C₂²×C₁₉	#577	1	1	yes	characteristic
391	C₄×C₁₉	—	2	2	no	—
392	C₄×C₁₉	—	2	2	no	—
393	C₄×C₁₉	—	4	1	no	—
394	C₄×C₁₉	—	4	2	no	—
395	C₄×C₁₉	—	4	2	no	—
396	C₄×C₁₉	—	4	1	no	—
397	C₄×C₁₉	—	8	1	no	—
398	C₄×C₁₉	—	8	1	no	—
399	C₄×C₁₉	—	8	1	no	—
400	C₄×C₁₉	—	8	1	no	—
401	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
402	C₄×C₁₉	#537	1	1	yes	characteristic
403	C₄×C₁₉	#548	1	1	yes	characteristic
404	C₄×C₁₉	#553	1	1	yes	characteristic
405	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
406	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
407	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
408	C₂×#121	—	2	1	no	—
409	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
411	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
412	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
414	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
416	#469	—	2	4	no	—
417	#469	—	2	4	no	—
418	#436	—	2	4	no	—
419	#428	—	2	4	no	—
420	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
423	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
424	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
425	C₂×C₄⋊C₈	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×#102	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
431	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
432	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
435	#396	—	2	1	no	—
436	#394	—	2	1	no	—
437	#394	—	2	1	no	—
438	#392	—	2	1	no	—
439	#390	—	2	1	no	—
440	#390	C₂²×C₁₉	1	1	yes	characteristic
441	#390	C₂²×C₁₉	1	1	yes	characteristic
442	#389	C₂²×C₁₉	1	1	yes	characteristic
443	#389	C₂²×C₁₉	1	1	yes	characteristic
444	#388	—	2	1	no	—
445	#386	—	2	1	no	—
446	#380	C₂²×C₁₉	1	1	yes	characteristic
447	#380	C₂²×C₁₉	1	1	yes	characteristic
448	#340	C₂²×C₁₉	1	1	yes	characteristic
449	#340	C₂²×C₁₉	1	1	yes	characteristic
450	#340	C₂²×C₁₉	1	1	yes	characteristic
451	#340	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×C₁₉	—	4	2	no	—
453	C₂×C₁₉	—	8	1	no	—
454	C₂×C₁₉	—	16	1	no	—
455	C₂×C₁₉	—	16	1	no	—
456	C₂×C₁₉	#2416	1	1	yes	characteristic
457	C₂×C₁₉	#3055	1	1	yes	characteristic
458	C₂×C₁₉	#3062	1	1	yes	characteristic
459	C₂×C₁₉	#3274	1	1	yes	characteristic
460	C₂×C₁₉	#3275	1	1	yes	characteristic
461	C₂×C₁₉	#3354	1	1	yes	characteristic
462	C₂×C₁₉	#3355	1	1	yes	characteristic
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	—	2	2	no	—
476	C₂×M₁₆	—	2	2	no	—
477	C₂×M₁₆	—	2	2	no	—
478	C₂×M₁₆	—	2	2	no	—
479	C₂×M₁₆	—	2	2	no	—
480	C₂×M₁₆	—	2	2	no	—
481	C₂×M₁₆	D₄×C₁₉	1	4	yes	complemented
482	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	4	1	no	—
493	#121	—	4	1	no	—
494	#121	—	4	4	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	#117	—	2	2	no	—
498	#117	—	4	1	no	—
499	C₂×C₄⋊C₄	—	2	2	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	4	1	no	—
504	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
526	#107	—	2	2	no	—
527	#107	—	2	2	no	—
528	#106	—	2	2	no	—
529	#106	—	2	2	no	—
530	#106	D₄×C₁₉	1	4	yes	complemented
531	C₄⋊C₈	—	2	2	no	—
532	#102	—	2	2	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	4	1	no	—
537	#102	—	4	1	no	—
538	C₂²⋊C₈	—	2	2	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₄×C₈	—	2	2	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	C₁₉	#24792	1	1	yes	characteristic, direct product factor, Sylow
546	C₂⁴	—	2	1	no	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	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	1	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	8	1	no	—
574	C₂×D₄	—	8	1	no	—
575	C₂×D₄	—	8	1	no	—
576	C₂×D₄	—	8	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	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	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	8	1	no	—
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	C₂×D₄×C₁₉	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
601	C₂²×C₄	#41×C₁₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
603	D₈	—	4	4	no	—
604	M₁₆	—	2	8	no	—
605	M₁₆	—	4	4	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	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
615	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
616	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
617	C₂×C₈	#41×C₁₉	1	2	yes	—
618	C₄⋊C₄	—	2	2	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	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	8	1	no	—
632	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	8	1	no	—
645	C₂²⋊C₄	—	8	1	no	—
646	C₂²⋊C₄	—	8	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	1	no	—
649	C₄²	—	4	2	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	C₁₉×#121	1	2	yes	—
678	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
679	D₄	—	4	4	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	4	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	4	1	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	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	8	4	no	—
729	C₂×C₄	C₁₉×#121	1	2	yes	—
730	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
733	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
734	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
735	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
736	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
737	C₈	—	2	2	no	—
738	C₈	—	4	1	no	—
739	C₈	—	4	1	no	—
740	C₈	C₁₉×#121	1	4	yes	complemented
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
770	C₂²	D₄²×C₁₉	1	1	yes	characteristic
771	C₂²	C₁₉×#547	1	1	yes	characteristic
772	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
773	C₂²	C₁₉×#575	1	1	yes	characteristic
774	C₂²	C₁₉×#576	1	1	yes	characteristic
775	C₂²	C₁₉×#577	1	1	yes	characteristic
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	—	8	1	no	—
785	C₄	—	8	1	no	—
786	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
787	C₄	C₁₉×#537	1	1	yes	characteristic
788	C₄	C₁₉×#548	1	1	yes	characteristic
789	C₄	C₁₉×#553	1	1	yes	characteristic
790	C₂	—	4	2	no	—
791	C₂	—	8	1	no	—
792	C₂	—	16	1	no	—
793	C₂	—	16	1	no	—
794	C₂	C₁₉×#2416	1	1	yes	characteristic
795	C₂	C₁₉×#3055	1	1	yes	characteristic
796	C₂	C₁₉×#3062	1	1	yes	characteristic
797	C₂	C₁₉×#3274	1	1	yes	characteristic
798	C₂	C₁₉×#3275	1	1	yes	characteristic
799	C₂	C₁₉×#3354	1	1	yes	characteristic
800	C₂	C₁₉×#3355	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#469	C₂	semidirect
2. C₂×C₁₉×#469	C₂	semidirect
3. C₂×C₁₉×#436	C₂	semidirect
4. C₂×C₁₉×#428	C₂	semidirect
5. C₁₉×#2416	C₂	semidirect
6. C₁₉×#2414	C₂	semidirect
7. C₁₉×#2067	C₂	semidirect
8. C₁₉×#2065	C₂	semidirect
9. C₁₉×#2034	C₂	semidirect
10. C₁₉×#2033	C₂	semidirect
11. C₁₉×#1970	C₂	semidirect
12. C₁₉×#1941	C₂	semidirect
13. C₁₉×#1875	C₂	semidirect
14. C₁₉×#1874	C₂	semidirect
15. C₁₉×#1809	C₂	semidirect
81. C₂×M₁₆×C₁₉	D₄	semidirect
130. C₁₉×#106	D₄	semidirect
249. #24792	C₁₉	direct (N × H)
340. C₈×C₁₉	#121	semidirect
341. C₂×#469	C₂×C₁₉	semidirect
342. C₂×#469	C₂×C₁₉	semidirect
343. C₂×#436	C₂×C₁₉	semidirect
344. C₂×#428	C₂×C₁₉	semidirect
345. #2416	C₂×C₁₉	semidirect
346. #2414	C₂×C₁₉	semidirect
347. #2067	C₂×C₁₉	semidirect
348. #2065	C₂×C₁₉	semidirect
349. #2034	C₂×C₁₉	semidirect
350. #2033	C₂×C₁₉	semidirect
351. #1970	C₂×C₁₉	semidirect
352. #1941	C₂×C₁₉	semidirect
353. #1875	C₂×C₁₉	semidirect
354. #1874	C₂×C₁₉	semidirect
355. #1809	C₂×C₁₉	semidirect
481. C₂×M₁₆	D₄×C₁₉	semidirect
530. #106	D₄×C₁₉	semidirect
545. C₁₉	#24792	direct (N × H)
740. C₈	C₁₉×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#469	2
C₂×C₁₉×#436	2
C₂×C₁₉×#428	2
C₁₉×#2416	2
C₁₉×#2414	2
C₁₉×#2067	2
C₁₉×#2065	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#1970	2
C₁₉×#1941	2
C₁₉×#1875	2
C₁₉×#1874	2
C₁₉×#1809	2
#24792	19

Subgroups — C19×#24792 #18030751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24792 #18030751