Subgroups — C₁₉×#14083 #18020042

Order 4864.

1370 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
14	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#389	C₄	1	8	yes	complemented
30	C₁₉×#387	—	2	4	no	—
31	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
32	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
93	C₂×C₄²×C₁₉	—	2	2	no	—
94	C₂×C₄²×C₁₉	—	2	2	no	—
95	C₂×C₄²×C₁₉	—	2	2	no	—
96	C₂×C₄²×C₁₉	—	2	2	no	—
97	C₂×C₄²×C₁₉	—	2	2	no	—
98	C₂×C₄²×C₁₉	—	4	1	no	—
99	C₂×C₄²×C₁₉	—	4	1	no	—
100	C₂×C₄²×C₁₉	—	4	1	no	—
101	C₂×C₄²×C₁₉	—	4	1	no	—
102	C₂×C₄²×C₁₉	—	4	1	no	—
103	C₂×C₄²×C₁₉	—	4	1	no	—
104	C₂×C₄²×C₁₉	—	4	1	no	—
105	C₂×C₄²×C₁₉	—	4	1	no	—
106	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
107	C₂×C₄²×C₁₉	D₄	1	4	yes	—
108	C₁₉×#95	—	2	2	no	—
109	C₁₉×#95	—	2	2	no	—
110	C₁₉×#95	—	2	2	no	—
111	C₁₉×#95	—	2	2	no	—
112	C₁₉×#95	—	2	2	no	—
113	C₁₉×#95	—	2	2	no	—
114	C₁₉×#95	—	2	2	no	—
115	C₁₉×#95	—	2	2	no	—
116	C₁₉×#95	—	2	2	no	—
117	C₁₉×#95	—	2	2	no	—
118	C₁₉×#95	—	2	2	no	—
119	C₁₉×#95	—	2	2	no	—
120	C₁₉×#95	—	2	2	no	—
121	C₁₉×#95	—	2	2	no	—
122	C₁₉×#95	—	4	1	no	—
123	C₁₉×#95	—	4	1	no	—
124	C₁₉×#95	—	4	1	no	—
125	C₁₉×#95	—	4	1	no	—
126	C₁₉×#95	C₂×C₄	1	4	yes	—
127	C₁₉×#95	C₂×C₄	1	4	yes	—
128	C₁₉×#95	Q₈	1	4	yes	—
129	C₁₉×#95	Q₈	1	4	yes	—
130	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	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	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	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	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	1	no	—
210	C₂²×C₄×C₁₉	—	2	1	no	—
211	C₂²×C₄×C₁₉	—	2	1	no	—
212	C₂²×C₄×C₁₉	—	2	1	no	—
213	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
214	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
215	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
216	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
218	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
219	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
220	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
224	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
225	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
226	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
228	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
229	C₂²×C₄×C₁₉	#41	1	2	yes	—
230	C₂²×C₄×C₁₉	#41	1	2	yes	—
231	C₂²×C₄×C₁₉	#41	1	2	yes	—
232	C₂²×C₄×C₁₉	#41	1	2	yes	—
233	C₂²×C₄×C₁₉	#41	1	2	yes	—
234	C₂²×C₄×C₁₉	#41	1	2	yes	—
235	C₂²×C₄×C₁₉	#41	1	2	yes	—
236	C₄⋊C₄×C₁₉	—	2	8	no	—
237	C₄⋊C₄×C₁₉	—	2	8	no	—
238	C₄⋊C₄×C₁₉	—	2	8	no	—
239	C₄⋊C₄×C₁₉	—	2	8	no	—
240	C₄⋊C₄×C₁₉	—	4	4	no	—
241	C₄⋊C₄×C₁₉	—	4	4	no	—
242	C₄⋊C₄×C₁₉	—	4	4	no	—
243	C₄⋊C₄×C₁₉	—	4	4	no	—
244	C₄²×C₁₉	—	2	8	no	—
245	C₄²×C₁₉	—	4	4	no	—
246	C₄²×C₁₉	—	4	4	no	—
247	C₄²×C₁₉	—	4	4	no	—
248	C₄²×C₁₉	—	4	4	no	—
249	#14083	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
251	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
253	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
254	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
255	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
256	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
257	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
258	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
259	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
260	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
261	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	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	2	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	2	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	2	2	no	—
303	C₂×C₄×C₁₉	—	2	2	no	—
304	C₂×C₄×C₁₉	—	2	2	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	2	2	no	—
307	C₂×C₄×C₁₉	—	2	2	no	—
308	C₂×C₄×C₁₉	—	2	2	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	2	no	—
311	C₂×C₄×C₁₉	—	2	2	no	—
312	C₂×C₄×C₁₉	—	2	2	no	—
313	C₂×C₄×C₁₉	—	2	2	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	2	no	—
316	C₂×C₄×C₁₉	—	2	2	no	—
317	C₂×C₄×C₁₉	—	2	2	no	—
318	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
329	C₂×C₄×C₁₉	—	4	1	no	—
330	C₂×C₄×C₁₉	—	4	1	no	—
331	C₂×C₄×C₁₉	—	4	1	no	—
332	C₂×C₄×C₁₉	—	4	1	no	—
333	C₂×C₄×C₁₉	—	4	1	no	—
334	C₂×C₄×C₁₉	—	4	1	no	—
335	C₂×C₄×C₁₉	—	4	1	no	—
336	C₂×C₄×C₁₉	—	4	1	no	—
337	C₂×C₄×C₁₉	—	4	1	no	—
338	C₂×C₄×C₁₉	—	4	1	no	—
339	C₂×C₄×C₁₉	—	4	1	no	—
340	C₂×C₄×C₁₉	—	4	1	no	—
341	C₂×C₄×C₁₉	—	4	1	no	—
342	C₂×C₄×C₁₉	—	4	1	no	—
343	C₂×C₄×C₁₉	—	4	1	no	—
344	C₂×C₄×C₁₉	—	4	1	no	—
345	C₂×C₄×C₁₉	—	4	1	no	—
346	C₂×C₄×C₁₉	—	4	1	no	—
347	C₂×C₄×C₁₉	—	4	1	no	—
348	C₂×C₄×C₁₉	—	4	1	no	—
349	C₂×C₄×C₁₉	—	4	1	no	—
350	C₂×C₄×C₁₉	—	4	1	no	—
351	C₂×C₄×C₁₉	—	4	1	no	—
352	C₂×C₄×C₁₉	—	4	1	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	4	1	no	—
357	C₂×C₄×C₁₉	—	4	1	no	—
358	C₂×C₄×C₁₉	—	4	1	no	—
359	C₂×C₄×C₁₉	—	4	1	no	—
360	C₂×C₄×C₁₉	—	4	1	no	—
361	C₂×C₄×C₁₉	—	4	1	no	—
362	C₂×C₄×C₁₉	—	4	1	no	—
363	C₂×C₄×C₁₉	—	4	1	no	—
364	C₂×C₄×C₁₉	—	4	1	no	—
365	C₂×C₄×C₁₉	#117	1	4	yes	—
366	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
367	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
368	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
369	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
370	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
371	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
372	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
373	#1444	C₂×C₁₉	1	1	yes	characteristic
374	#1442	C₂×C₁₉	1	1	yes	characteristic
375	#1441	C₂×C₁₉	1	1	yes	characteristic
376	#1441	C₂×C₁₉	1	1	yes	characteristic
377	#1436	C₂×C₁₉	1	1	yes	characteristic
378	#1436	C₂×C₁₉	1	1	yes	characteristic
379	#1436	C₂×C₁₉	1	1	yes	characteristic
380	#1436	C₂×C₁₉	1	1	yes	characteristic
381	#1436	C₂×C₁₉	1	1	yes	characteristic
382	#1436	C₂×C₁₉	1	1	yes	characteristic
383	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
384	C₄×#95	C₂×C₁₉	1	1	yes	characteristic
385	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
386	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
387	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
388	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
389	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
390	C₂²×C₁₉	#518	1	1	yes	characteristic
391	C₂²×C₁₉	#520	1	1	yes	characteristic
392	C₂²×C₁₉	#525	1	1	yes	characteristic
393	C₂²×C₁₉	#525	1	1	yes	characteristic
394	C₂²×C₁₉	#529	1	1	yes	characteristic
395	C₂²×C₁₉	#529	1	1	yes	characteristic
396	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
397	C₂²×C₁₉	#532	1	1	yes	characteristic
398	C₂²×C₁₉	#533	1	1	yes	characteristic
399	C₂²×C₁₉	#533	1	1	yes	characteristic
400	C₂²×C₁₉	#534	1	1	yes	characteristic
401	C₂²×C₁₉	#537	1	1	yes	characteristic
402	C₂²×C₁₉	#538	1	1	yes	characteristic
403	C₂²×C₁₉	#539	1	1	yes	characteristic
404	C₂²×C₁₉	#551	1	1	yes	characteristic
405	C₂²×C₁₉	#551	1	1	yes	characteristic
406	C₂²×C₁₉	#552	1	1	yes	characteristic
407	C₂²×C₁₉	#553	1	1	yes	characteristic
408	C₂²×C₁₉	#553	1	1	yes	characteristic
409	C₂²×C₁₉	#553	1	1	yes	characteristic
410	C₂²×C₁₉	#554	1	1	yes	characteristic
411	C₂²×C₁₉	#554	1	1	yes	characteristic
412	C₂²×C₁₉	#554	1	1	yes	characteristic
413	C₂²×C₁₉	#554	1	1	yes	characteristic
414	C₂²×C₁₉	#554	1	1	yes	characteristic
415	C₂²×C₁₉	#554	1	1	yes	characteristic
416	C₂²×C₁₉	#556	1	1	yes	characteristic
417	C₂²×C₁₉	#557	1	1	yes	characteristic
418	C₂²×C₁₉	#557	1	1	yes	characteristic
419	C₂²×C₁₉	#559	1	1	yes	characteristic
420	C₄×C₁₉	—	2	4	no	—
421	C₄×C₁₉	—	2	4	no	—
422	C₄×C₁₉	—	2	4	no	—
423	C₄×C₁₉	—	2	4	no	—
424	C₄×C₁₉	—	2	4	no	—
425	C₄×C₁₉	—	4	2	no	—
426	C₄×C₁₉	—	4	2	no	—
427	C₄×C₁₉	—	4	2	no	—
428	C₄×C₁₉	—	4	2	no	—
429	C₄×C₁₉	—	4	2	no	—
430	C₄×C₁₉	—	4	2	no	—
431	C₄×C₁₉	—	4	2	no	—
432	C₄×C₁₉	—	4	2	no	—
433	C₄×C₁₉	—	8	1	no	—
434	C₄×C₁₉	—	8	1	no	—
435	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
440	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
441	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
442	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
443	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
444	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
445	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
446	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
447	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
448	#389	C₄×C₁₉	1	8	yes	complemented
449	#387	—	2	4	no	—
450	C₄×C₄⋊C₄	—	2	4	no	—
451	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
454	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
455	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
460	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
463	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
464	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
465	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
466	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
467	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
468	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
469	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
470	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
471	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
472	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
473	C₂×C₁₉	#2290	1	1	yes	characteristic
474	C₂×C₁₉	C₄×C₄⋊Q₈	1	1	yes	characteristic
475	C₂×C₁₉	#2325	1	1	yes	characteristic
476	C₂×C₁₉	#2345	1	1	yes	characteristic
477	C₂×C₁₉	#2355	1	1	yes	characteristic
478	C₂×C₁₉	#2368	1	1	yes	characteristic
479	C₂×C₁₉	#2370	1	1	yes	characteristic
480	C₂×C₁₉	#2583	1	1	yes	characteristic
481	C₂×C₁₉	#2584	1	1	yes	characteristic
482	C₂×C₁₉	#2587	1	1	yes	characteristic
483	C₂×C₁₉	#2588	1	1	yes	characteristic
484	C₂×C₁₉	#2589	1	1	yes	characteristic
485	C₂×C₁₉	#2590	1	1	yes	characteristic
486	C₂×C₁₉	#2601	1	1	yes	characteristic
487	C₂×C₁₉	#2602	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄⋊C₄	—	2	2	no	—
511	C₂×C₄⋊C₄	—	2	2	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	—	2	2	no	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	—	2	2	no	—
517	C₂×C₄⋊C₄	—	4	1	no	—
518	C₂×C₄⋊C₄	—	4	1	no	—
519	C₂×C₄⋊C₄	—	4	1	no	—
520	C₂×C₄⋊C₄	—	4	1	no	—
521	C₂×C₄⋊C₄	—	4	1	no	—
522	C₂×C₄⋊C₄	—	4	1	no	—
523	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
525	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
526	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
527	C₂×C₄²	—	2	2	no	—
528	C₂×C₄²	—	2	2	no	—
529	C₂×C₄²	—	2	2	no	—
530	C₂×C₄²	—	2	2	no	—
531	C₂×C₄²	—	2	2	no	—
532	C₂×C₄²	—	4	1	no	—
533	C₂×C₄²	—	4	1	no	—
534	C₂×C₄²	—	4	1	no	—
535	C₂×C₄²	—	4	1	no	—
536	C₂×C₄²	—	4	1	no	—
537	C₂×C₄²	—	4	1	no	—
538	C₂×C₄²	—	4	1	no	—
539	C₂×C₄²	—	4	1	no	—
540	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
541	C₂×C₄²	D₄×C₁₉	1	4	yes	—
542	#95	—	2	2	no	—
543	#95	—	2	2	no	—
544	#95	—	2	2	no	—
545	#95	—	2	2	no	—
546	#95	—	2	2	no	—
547	#95	—	2	2	no	—
548	#95	—	2	2	no	—
549	#95	—	2	2	no	—
550	#95	—	2	2	no	—
551	#95	—	2	2	no	—
552	#95	—	2	2	no	—
553	#95	—	2	2	no	—
554	#95	—	2	2	no	—
555	#95	—	2	2	no	—
556	#95	—	4	1	no	—
557	#95	—	4	1	no	—
558	#95	—	4	1	no	—
559	#95	—	4	1	no	—
560	#95	C₂×C₄×C₁₉	1	4	yes	—
561	#95	C₂×C₄×C₁₉	1	4	yes	—
562	#95	Q₈×C₁₉	1	4	yes	—
563	#95	Q₈×C₁₉	1	4	yes	—
564	C₁₉	#14083	1	1	yes	characteristic, direct product factor, Sylow
565	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	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	1	no	—
576	C₂²×C₄	—	2	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	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
649	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
650	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
651	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
652	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
653	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
654	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
655	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
656	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
657	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
658	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
659	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
660	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
661	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
662	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
663	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
664	C₂²×C₄	#41×C₁₉	1	2	yes	—
665	C₂²×C₄	#41×C₁₉	1	2	yes	—
666	C₂²×C₄	#41×C₁₉	1	2	yes	—
667	C₂²×C₄	#41×C₁₉	1	2	yes	—
668	C₂²×C₄	#41×C₁₉	1	2	yes	—
669	C₂²×C₄	#41×C₁₉	1	2	yes	—
670	C₂²×C₄	#41×C₁₉	1	2	yes	—
671	C₄⋊C₄	—	2	8	no	—
672	C₄⋊C₄	—	2	8	no	—
673	C₄⋊C₄	—	2	8	no	—
674	C₄⋊C₄	—	2	8	no	—
675	C₄⋊C₄	—	4	4	no	—
676	C₄⋊C₄	—	4	4	no	—
677	C₄⋊C₄	—	4	4	no	—
678	C₄⋊C₄	—	4	4	no	—
679	C₄²	—	2	8	no	—
680	C₄²	—	4	4	no	—
681	C₄²	—	4	4	no	—
682	C₄²	—	4	4	no	—
683	C₄²	—	4	4	no	—
684	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
685	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
686	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
687	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
688	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
689	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
690	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
691	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
692	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
693	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
694	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
695	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	C₁₉×#117	1	4	yes	—
800	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
801	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
802	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
803	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
804	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
805	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
806	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
807	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
808	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
809	C₂²	C₁₉×#518	1	1	yes	characteristic
810	C₂²	C₁₉×#520	1	1	yes	characteristic
811	C₂²	C₁₉×#525	1	1	yes	characteristic
812	C₂²	C₁₉×#525	1	1	yes	characteristic
813	C₂²	C₁₉×#529	1	1	yes	characteristic
814	C₂²	C₁₉×#529	1	1	yes	characteristic
815	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
816	C₂²	C₁₉×#532	1	1	yes	characteristic
817	C₂²	C₁₉×#533	1	1	yes	characteristic
818	C₂²	C₁₉×#533	1	1	yes	characteristic
819	C₂²	C₁₉×#534	1	1	yes	characteristic
820	C₂²	C₁₉×#537	1	1	yes	characteristic
821	C₂²	C₁₉×#538	1	1	yes	characteristic
822	C₂²	C₁₉×#539	1	1	yes	characteristic
823	C₂²	C₁₉×#551	1	1	yes	characteristic
824	C₂²	C₁₉×#551	1	1	yes	characteristic
825	C₂²	C₁₉×#552	1	1	yes	characteristic
826	C₂²	C₁₉×#553	1	1	yes	characteristic
827	C₂²	C₁₉×#553	1	1	yes	characteristic
828	C₂²	C₁₉×#553	1	1	yes	characteristic
829	C₂²	C₁₉×#554	1	1	yes	characteristic
830	C₂²	C₁₉×#554	1	1	yes	characteristic
831	C₂²	C₁₉×#554	1	1	yes	characteristic
832	C₂²	C₁₉×#554	1	1	yes	characteristic
833	C₂²	C₁₉×#554	1	1	yes	characteristic
834	C₂²	C₁₉×#554	1	1	yes	characteristic
835	C₂²	C₁₉×#556	1	1	yes	characteristic
836	C₂²	C₁₉×#557	1	1	yes	characteristic
837	C₂²	C₁₉×#557	1	1	yes	characteristic
838	C₂²	C₁₉×#559	1	1	yes	characteristic
839	C₄	—	2	4	no	—
840	C₄	—	2	4	no	—
841	C₄	—	2	4	no	—
842	C₄	—	2	4	no	—
843	C₄	—	2	4	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	8	1	no	—
853	C₄	—	8	1	no	—
854	C₂	C₁₉×#2290	1	1	yes	characteristic
855	C₂	C₄×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
856	C₂	C₁₉×#2325	1	1	yes	characteristic
857	C₂	C₁₉×#2345	1	1	yes	characteristic
858	C₂	C₁₉×#2355	1	1	yes	characteristic
859	C₂	C₁₉×#2368	1	1	yes	characteristic
860	C₂	C₁₉×#2370	1	1	yes	characteristic
861	C₂	C₁₉×#2583	1	1	yes	characteristic
862	C₂	C₁₉×#2584	1	1	yes	characteristic
863	C₂	C₁₉×#2587	1	1	yes	characteristic
864	C₂	C₁₉×#2588	1	1	yes	characteristic
865	C₂	C₁₉×#2589	1	1	yes	characteristic
866	C₂	C₁₉×#2590	1	1	yes	characteristic
867	C₂	C₁₉×#2601	1	1	yes	characteristic
868	C₂	C₁₉×#2602	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
29. C₁₉×#389	C₄	semidirect
249. #14083	C₁₉	direct (N × H)
448. #389	C₄×C₁₉	semidirect
564. C₁₉	#14083	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×#389	2
C₂×C₁₉×#387	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1444	2
C₁₉×#1442	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
C₄×C₁₉×#95	2
#14083	19

Subgroups — C19×#14083 #18020042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14083 #18020042