Subgroups — C₁₉×#24450 #18030409

Order 4864.

1620 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2414	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#546	—	2	4	no	—
23	C₁₉×#546	—	2	4	no	—
24	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#123	—	2	1	no	—
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	—	2	1	no	—
28	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₉×#120	—	2	1	no	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
36	C₁₉×#468	—	2	4	no	—
37	C₁₉×#449	—	2	4	no	—
38	C₁₉×#447	—	2	4	no	—
39	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#418	—	2	4	no	—
41	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#394	—	2	1	no	—
55	C₁₉×#392	—	2	1	no	—
56	C₁₉×#390	—	2	1	no	—
57	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#388	—	2	1	no	—
60	C₁₉×#380	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₁₉	—	2	1	no	—
66	C₂×#41×C₁₉	—	2	2	no	—
67	C₂×#41×C₁₉	—	2	2	no	—
68	C₂×#41×C₁₉	—	2	2	no	—
69	C₂×#41×C₁₉	—	2	2	no	—
70	C₂×#41×C₁₉	—	4	1	no	—
71	C₂×#41×C₁₉	—	4	1	no	—
72	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₉	—	2	2	no	—
74	C₂²×D₄×C₁₉	—	2	2	no	—
75	C₂²×D₄×C₁₉	—	2	1	no	—
76	C₂²×D₄×C₁₉	—	2	1	no	—
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	—	2	1	no	—
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	—	2	2	no	—
81	C₂²×D₄×C₁₉	—	4	1	no	—
82	C₂²×D₄×C₁₉	—	4	1	no	—
83	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
85	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₉	—	2	1	no	—
89	C₂³×C₄×C₁₉	—	2	1	no	—
90	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×SD₁₆×C₁₉	—	2	2	no	—
93	C₂×SD₁₆×C₁₉	—	2	2	no	—
94	C₂×SD₁₆×C₁₉	—	4	1	no	—
95	C₂×D₈×C₁₉	—	2	2	no	—
96	C₂×D₈×C₁₉	—	2	2	no	—
97	C₂×D₈×C₁₉	—	2	2	no	—
98	C₂×D₈×C₁₉	—	2	2	no	—
99	C₂×D₈×C₁₉	—	4	1	no	—
100	C₂×D₈×C₁₉	—	4	1	no	—
101	C₂×M₁₆×C₁₉	—	2	2	no	—
102	C₂×M₁₆×C₁₉	—	2	2	no	—
103	C₂×M₁₆×C₁₉	—	4	1	no	—
104	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#124	—	2	2	no	—
109	C₁₉×#124	—	2	2	no	—
110	C₁₉×#123	—	2	8	no	—
111	C₁₉×C₂²⋊Q₈	—	2	2	no	—
112	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	complemented
113	C₁₉×#121	—	2	8	no	—
114	C₁₉×#121	—	2	2	no	—
115	C₁₉×#121	—	2	2	no	—
116	C₁₉×#121	—	2	2	no	—
117	C₁₉×#121	—	2	2	no	—
118	C₁₉×#121	—	2	2	no	—
119	C₁₉×#121	—	4	1	no	—
120	C₁₉×#120	—	2	8	no	—
121	C₄×D₄×C₁₉	—	2	2	no	—
122	C₄×D₄×C₁₉	—	2	2	no	—
123	C₄×D₄×C₁₉	—	2	2	no	—
124	C₄×D₄×C₁₉	—	2	2	no	—
125	C₁₉×#117	—	2	2	no	—
126	C₁₉×#117	—	4	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
135	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
148	C₂×C₄²×C₁₉	—	2	1	no	—
149	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
150	C₁₉×#107	—	2	2	no	—
151	C₁₉×#103	—	2	2	no	—
152	C₁₉×#103	—	2	2	no	—
153	C₁₉×#103	—	4	1	no	—
154	C₁₉×#102	—	2	2	no	—
155	C₁₉×#102	—	2	2	no	—
156	C₁₉×#102	—	2	2	no	—
157	C₁₉×#102	—	2	2	no	—
158	C₁₉×#102	—	2	2	no	—
159	C₁₉×#102	—	2	2	no	—
160	C₁₉×#102	D₄	1	4	yes	complemented
161	C₁₉×C₂²⋊C₈	—	2	2	no	—
162	C₁₉×C₂²⋊C₈	—	2	2	no	—
163	C₁₉×C₂²⋊C₈	—	4	1	no	—
164	C₁₉×#95	—	2	1	no	—
165	C₁₉×#95	—	2	1	no	—
166	C₂⁴×C₁₉	—	2	1	no	—
167	C₂⁴×C₁₉	—	2	1	no	—
168	C₂⁴×C₁₉	—	2	4	no	—
169	C₂⁴×C₁₉	—	2	1	no	—
170	C₂⁴×C₁₉	—	4	2	no	—
171	C₂⁴×C₁₉	—	4	2	no	—
172	C₂⁴×C₁₉	—	4	2	no	—
173	C₂⁴×C₁₉	—	4	2	no	—
174	C₂⁴×C₁₉	—	8	1	no	—
175	C₂⁴×C₁₉	—	8	1	no	—
176	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
178	#41×C₁₉	—	4	4	no	—
179	#41×C₁₉	—	4	4	no	—
180	#41×C₁₉	—	4	4	no	—
181	#41×C₁₉	—	4	4	no	—
182	C₂×Q₈×C₁₉	—	2	1	no	—
183	C₂×Q₈×C₁₉	—	2	1	no	—
184	C₂×Q₈×C₁₉	—	2	1	no	—
185	C₂×Q₈×C₁₉	—	2	1	no	—
186	C₂×Q₈×C₁₉	—	2	1	no	—
187	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₁₉	—	2	8	no	—
189	C₂×D₄×C₁₉	—	2	4	no	—
190	C₂×D₄×C₁₉	—	2	2	no	—
191	C₂×D₄×C₁₉	—	2	4	no	—
192	C₂×D₄×C₁₉	—	2	4	no	—
193	C₂×D₄×C₁₉	—	2	1	no	—
194	C₂×D₄×C₁₉	—	2	1	no	—
195	C₂×D₄×C₁₉	—	2	1	no	—
196	C₂×D₄×C₁₉	—	2	1	no	—
197	C₂×D₄×C₁₉	—	2	1	no	—
198	C₂×D₄×C₁₉	—	2	1	no	—
199	C₂×D₄×C₁₉	—	2	1	no	—
200	C₂×D₄×C₁₉	—	2	1	no	—
201	C₂×D₄×C₁₉	—	2	1	no	—
202	C₂×D₄×C₁₉	—	2	1	no	—
203	C₂×D₄×C₁₉	—	2	1	no	—
204	C₂×D₄×C₁₉	—	2	1	no	—
205	C₂×D₄×C₁₉	—	2	1	no	—
206	C₂×D₄×C₁₉	—	2	1	no	—
207	C₂×D₄×C₁₉	—	4	4	no	—
208	C₂×D₄×C₁₉	—	4	4	no	—
209	C₂×D₄×C₁₉	—	4	4	no	—
210	C₂×D₄×C₁₉	—	4	1	no	—
211	C₂×D₄×C₁₉	—	4	1	no	—
212	C₂×D₄×C₁₉	—	4	2	no	—
213	C₂×D₄×C₁₉	—	4	2	no	—
214	C₂×D₄×C₁₉	—	4	2	no	—
215	C₂×D₄×C₁₉	—	4	2	no	—
216	C₂×D₄×C₁₉	—	4	2	no	—
217	C₂×D₄×C₁₉	—	4	2	no	—
218	C₂×D₄×C₁₉	—	4	2	no	—
219	C₂×D₄×C₁₉	—	8	1	no	—
220	C₂×D₄×C₁₉	—	8	1	no	—
221	C₂×D₄×C₁₉	—	8	1	no	—
222	C₂×D₄×C₁₉	—	8	1	no	—
223	C₂×D₄×C₁₉	—	8	1	no	—
224	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₁₉	#41	1	2	yes	—
228	C₂²×C₄×C₁₉	—	2	1	no	—
229	C₂²×C₄×C₁₉	—	2	1	no	—
230	C₂²×C₄×C₁₉	—	2	1	no	—
231	C₂²×C₄×C₁₉	—	2	1	no	—
232	C₂²×C₄×C₁₉	—	2	4	no	—
233	C₂²×C₄×C₁₉	—	2	1	no	—
234	C₂²×C₄×C₁₉	—	2	1	no	—
235	C₂²×C₄×C₁₉	—	2	1	no	—
236	C₂²×C₄×C₁₉	—	2	4	no	—
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	2	1	no	—
239	C₂²×C₄×C₁₉	—	2	1	no	—
240	C₂²×C₄×C₁₉	—	2	1	no	—
241	C₂²×C₄×C₁₉	—	2	1	no	—
242	C₂²×C₄×C₁₉	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	1	no	—
245	C₂²×C₄×C₁₉	—	4	2	no	—
246	C₂²×C₄×C₁₉	—	4	2	no	—
247	C₂²×C₄×C₁₉	—	8	1	no	—
248	C₂²×C₄×C₁₉	—	8	1	no	—
249	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	SD₁₆×C₁₉	—	4	4	no	—
257	D₈×C₁₉	—	4	4	no	—
258	D₈×C₁₉	—	4	4	no	—
259	M₁₆×C₁₉	—	4	4	no	—
260	C₂×C₈×C₁₉	—	2	1	no	—
261	C₂×C₈×C₁₉	—	2	1	no	—
262	C₂×C₈×C₁₉	—	2	1	no	—
263	C₂×C₈×C₁₉	—	2	1	no	—
264	C₂×C₈×C₁₉	—	2	1	no	—
265	C₂×C₈×C₁₉	—	2	1	no	—
266	C₂×C₈×C₁₉	—	2	1	no	—
267	C₂×C₈×C₁₉	—	2	1	no	—
268	C₂×C₈×C₁₉	—	2	1	no	—
269	C₂×C₈×C₁₉	—	2	1	no	—
270	C₂×C₈×C₁₉	—	2	1	no	—
271	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₁₉	—	2	4	no	—
273	C₄⋊C₄×C₁₉	—	2	2	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	1	no	—
280	C₄⋊C₄×C₁₉	—	8	1	no	—
281	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₁₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₉	—	2	2	no	—
288	C₂²⋊C₄×C₁₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₉	—	2	2	no	—
290	C₂²⋊C₄×C₁₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₉	—	4	2	no	—
293	C₂²⋊C₄×C₁₉	—	4	2	no	—
294	C₂²⋊C₄×C₁₉	—	8	1	no	—
295	C₂²⋊C₄×C₁₉	—	8	1	no	—
296	C₄²×C₁₉	—	2	1	no	—
297	C₄²×C₁₉	—	2	1	no	—
298	C₄²×C₁₉	—	4	2	no	—
299	#24450	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂³×C₁₉	—	2	2	no	—
301	C₂³×C₁₉	—	2	1	no	—
302	C₂³×C₁₉	—	2	2	no	—
303	C₂³×C₁₉	—	2	1	no	—
304	C₂³×C₁₉	—	2	2	no	—
305	C₂³×C₁₉	—	2	1	no	—
306	C₂³×C₁₉	—	2	1	no	—
307	C₂³×C₁₉	—	2	1	no	—
308	C₂³×C₁₉	—	2	1	no	—
309	C₂³×C₁₉	—	2	2	no	—
310	C₂³×C₁₉	—	2	1	no	—
311	C₂³×C₁₉	—	2	1	no	—
312	C₂³×C₁₉	—	2	1	no	—
313	C₂³×C₁₉	—	2	1	no	—
314	C₂³×C₁₉	—	2	1	no	—
315	C₂³×C₁₉	—	2	1	no	—
316	C₂³×C₁₉	—	2	1	no	—
317	C₂³×C₁₉	—	4	8	no	—
318	C₂³×C₁₉	—	4	8	no	—
319	C₂³×C₁₉	—	4	1	no	—
320	C₂³×C₁₉	—	4	1	no	—
321	C₂³×C₁₉	—	4	1	no	—
322	C₂³×C₁₉	—	4	1	no	—
323	C₂³×C₁₉	—	4	1	no	—
324	C₂³×C₁₉	—	4	1	no	—
325	C₂³×C₁₉	—	4	1	no	—
326	C₂³×C₁₉	—	4	1	no	—
327	C₂³×C₁₉	—	4	1	no	—
328	C₂³×C₁₉	—	4	1	no	—
329	C₂³×C₁₉	—	4	1	no	—
330	C₂³×C₁₉	—	4	1	no	—
331	C₂³×C₁₉	—	4	1	no	—
332	C₂³×C₁₉	—	4	1	no	—
333	C₂³×C₁₉	—	4	1	no	—
334	C₂³×C₁₉	—	4	1	no	—
335	C₂³×C₁₉	—	4	1	no	—
336	C₂³×C₁₉	—	8	4	no	—
337	C₂³×C₁₉	—	8	4	no	—
338	C₂³×C₁₉	—	8	4	no	—
339	C₂³×C₁₉	—	8	4	no	—
340	C₂³×C₁₉	—	8	4	no	—
341	C₂³×C₁₉	#120	1	2	yes	—
342	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₁₉	—	2	2	no	—
344	Q₈×C₁₉	—	2	2	no	—
345	Q₈×C₁₉	—	4	1	no	—
346	Q₈×C₁₉	—	4	1	no	—
347	D₄×C₁₉	—	2	2	no	—
348	D₄×C₁₉	—	2	2	no	—
349	D₄×C₁₉	—	2	2	no	—
350	D₄×C₁₉	—	2	2	no	—
351	D₄×C₁₉	—	2	2	no	—
352	D₄×C₁₉	—	4	8	no	—
353	D₄×C₁₉	—	4	4	no	—
354	D₄×C₁₉	—	4	8	no	—
355	D₄×C₁₉	—	4	1	no	—
356	D₄×C₁₉	—	4	1	no	—
357	D₄×C₁₉	—	4	1	no	—
358	D₄×C₁₉	—	4	1	no	—
359	D₄×C₁₉	—	4	1	no	—
360	D₄×C₁₉	—	4	1	no	—
361	D₄×C₁₉	—	8	4	no	—
362	D₄×C₁₉	—	8	4	no	—
363	D₄×C₁₉	—	8	4	no	—
364	D₄×C₁₉	#121	1	4	yes	—
365	C₂×C₄×C₁₉	—	2	1	no	—
366	C₂×C₄×C₁₉	—	2	1	no	—
367	C₂×C₄×C₁₉	—	2	2	no	—
368	C₂×C₄×C₁₉	—	2	2	no	—
369	C₂×C₄×C₁₉	—	2	2	no	—
370	C₂×C₄×C₁₉	—	2	2	no	—
371	C₂×C₄×C₁₉	—	2	1	no	—
372	C₂×C₄×C₁₉	—	2	1	no	—
373	C₂×C₄×C₁₉	—	2	2	no	—
374	C₂×C₄×C₁₉	—	2	1	no	—
375	C₂×C₄×C₁₉	—	2	2	no	—
376	C₂×C₄×C₁₉	—	2	2	no	—
377	C₂×C₄×C₁₉	—	2	1	no	—
378	C₂×C₄×C₁₉	—	2	1	no	—
379	C₂×C₄×C₁₉	—	2	1	no	—
380	C₂×C₄×C₁₉	—	2	1	no	—
381	C₂×C₄×C₁₉	—	2	1	no	—
382	C₂×C₄×C₁₉	—	2	1	no	—
383	C₂×C₄×C₁₉	—	4	8	no	—
384	C₂×C₄×C₁₉	—	4	1	no	—
385	C₂×C₄×C₁₉	—	4	1	no	—
386	C₂×C₄×C₁₉	—	4	1	no	—
387	C₂×C₄×C₁₉	—	4	1	no	—
388	C₂×C₄×C₁₉	—	4	1	no	—
389	C₂×C₄×C₁₉	—	4	1	no	—
390	C₂×C₄×C₁₉	—	4	1	no	—
391	C₂×C₄×C₁₉	—	4	1	no	—
392	C₂×C₄×C₁₉	—	4	1	no	—
393	C₂×C₄×C₁₉	—	4	1	no	—
394	C₂×C₄×C₁₉	—	4	1	no	—
395	C₂×C₄×C₁₉	—	4	1	no	—
396	C₂×C₄×C₁₉	—	4	1	no	—
397	C₂×C₄×C₁₉	—	4	1	no	—
398	C₂×C₄×C₁₉	—	4	1	no	—
399	C₂×C₄×C₁₉	—	4	1	no	—
400	C₂×C₄×C₁₉	—	8	4	no	—
401	C₂×C₄×C₁₉	#120	1	2	yes	—
402	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
406	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
407	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
408	C₈×C₁₉	—	2	2	no	—
409	C₈×C₁₉	—	4	1	no	—
410	C₈×C₁₉	—	4	1	no	—
411	C₈×C₁₉	—	4	1	no	—
412	C₂×#546	C₂×C₁₉	1	1	yes	characteristic, complemented
413	C₂×#468	C₂×C₁₉	1	1	yes	characteristic, complemented
414	C₂×#449	C₂×C₁₉	1	1	yes	characteristic, complemented
415	C₂×#447	C₂×C₁₉	1	1	yes	characteristic, complemented
416	C₂×#418	C₂×C₁₉	1	1	yes	characteristic, complemented
417	#2414	C₂×C₁₉	1	1	yes	characteristic, complemented
418	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
419	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
420	#2012	C₂×C₁₉	1	1	yes	characteristic, complemented
421	#1999	C₂×C₁₉	1	1	yes	characteristic, complemented
422	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
423	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
424	#1870	C₂×C₁₉	1	1	yes	characteristic, complemented
425	#1862	C₂×C₁₉	1	1	yes	characteristic, complemented
426	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
427	C₂²×C₁₉	—	2	2	no	—
428	C₂²×C₁₉	—	2	4	no	—
429	C₂²×C₁₉	—	2	2	no	—
430	C₂²×C₁₉	—	2	2	no	—
431	C₂²×C₁₉	—	4	2	no	—
432	C₂²×C₁₉	—	4	2	no	—
433	C₂²×C₁₉	—	4	1	no	—
434	C₂²×C₁₉	—	4	2	no	—
435	C₂²×C₁₉	—	4	1	no	—
436	C₂²×C₁₉	—	4	2	no	—
437	C₂²×C₁₉	—	4	1	no	—
438	C₂²×C₁₉	—	4	2	no	—
439	C₂²×C₁₉	—	4	1	no	—
440	C₂²×C₁₉	—	4	2	no	—
441	C₂²×C₁₉	—	4	1	no	—
442	C₂²×C₁₉	—	4	2	no	—
443	C₂²×C₁₉	—	4	1	no	—
444	C₂²×C₁₉	—	4	2	no	—
445	C₂²×C₁₉	—	4	1	no	—
446	C₂²×C₁₉	—	4	2	no	—
447	C₂²×C₁₉	—	4	1	no	—
448	C₂²×C₁₉	—	4	1	no	—
449	C₂²×C₁₉	—	4	1	no	—
450	C₂²×C₁₉	—	4	1	no	—
451	C₂²×C₁₉	—	8	16	no	—
452	C₂²×C₁₉	—	8	1	no	—
453	C₂²×C₁₉	—	8	1	no	—
454	C₂²×C₁₉	—	8	1	no	—
455	C₂²×C₁₉	—	8	1	no	—
456	C₂²×C₁₉	—	8	1	no	—
457	C₂²×C₁₉	—	8	1	no	—
458	C₂²×C₁₉	—	8	1	no	—
459	C₂²×C₁₉	—	8	1	no	—
460	C₂²×C₁₉	—	8	1	no	—
461	C₂²×C₁₉	—	8	1	no	—
462	C₂²×C₁₉	—	8	1	no	—
463	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
464	C₂²×C₁₉	D₄²	1	1	yes	characteristic
465	C₂²×C₁₉	#546	1	1	yes	characteristic
466	C₂²×C₁₉	#575	1	1	yes	characteristic
467	C₂²×C₁₉	#575	1	1	yes	characteristic
468	C₂²×C₁₉	#576	1	1	yes	characteristic
469	C₂²×C₁₉	#576	1	1	yes	characteristic
470	C₄×C₁₉	—	2	2	no	—
471	C₄×C₁₉	—	4	1	no	—
472	C₄×C₁₉	—	4	2	no	—
473	C₄×C₁₉	—	4	1	no	—
474	C₄×C₁₉	—	4	1	no	—
475	C₄×C₁₉	—	4	2	no	—
476	C₄×C₁₉	—	4	2	no	—
477	C₄×C₁₉	—	8	1	no	—
478	C₄×C₁₉	—	8	1	no	—
479	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
480	C₄×C₁₉	#534	1	1	yes	characteristic
481	C₄×C₁₉	D₄²	1	1	yes	characteristic
482	C₄×C₁₉	#546	1	1	yes	characteristic
483	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
484	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
485	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
486	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
487	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
488	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
489	#546	—	2	4	no	—
490	#546	—	2	4	no	—
491	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
492	C₂×#123	—	2	1	no	—
493	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
494	C₂×#121	—	2	1	no	—
495	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
496	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
497	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
498	C₂×#120	—	2	1	no	—
499	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
501	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
502	C₂²×C₂²⋊C₄	—	2	1	no	—
503	#468	—	2	4	no	—
504	#449	—	2	4	no	—
505	#447	—	2	4	no	—
506	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
507	#418	—	2	4	no	—
508	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
509	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
510	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
511	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
512	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
513	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
514	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
515	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
516	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
517	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
518	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
520	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
521	#394	—	2	1	no	—
522	#392	—	2	1	no	—
523	#390	—	2	1	no	—
524	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
525	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
526	#388	—	2	1	no	—
527	#380	C₂²×C₁₉	1	1	yes	characteristic, complemented
528	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
529	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
530	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
531	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
532	C₂×C₁₉	—	4	2	no	—
533	C₂×C₁₉	—	4	4	no	—
534	C₂×C₁₉	—	8	1	no	—
535	C₂×C₁₉	—	8	2	no	—
536	C₂×C₁₉	—	16	1	no	—
537	C₂×C₁₉	#2410	1	1	yes	characteristic
538	C₂×C₁₉	#3005	1	1	yes	characteristic
539	C₂×C₁₉	#3008	1	1	yes	characteristic
540	C₂×C₁₉	#3268	1	1	yes	characteristic
541	C₂×C₁₉	#3273	1	1	yes	characteristic
542	C₂×C₁₉	#3319	1	1	yes	characteristic
543	C₂×C₁₉	#3322	1	1	yes	characteristic
544	C₂⁵	—	2	1	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	4	1	no	—
550	C₂×#41	—	4	1	no	—
551	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	2	2	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	2	no	—
560	C₂²×D₄	—	4	1	no	—
561	C₂²×D₄	—	4	1	no	—
562	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
563	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
564	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
565	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
567	C₂³×C₄	—	2	1	no	—
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
571	C₂×SD₁₆	—	2	2	no	—
572	C₂×SD₁₆	—	2	2	no	—
573	C₂×SD₁₆	—	4	1	no	—
574	C₂×D₈	—	2	2	no	—
575	C₂×D₈	—	2	2	no	—
576	C₂×D₈	—	2	2	no	—
577	C₂×D₈	—	2	2	no	—
578	C₂×D₈	—	4	1	no	—
579	C₂×D₈	—	4	1	no	—
580	C₂×M₁₆	—	2	2	no	—
581	C₂×M₁₆	—	2	2	no	—
582	C₂×M₁₆	—	4	1	no	—
583	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
584	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
585	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
586	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
587	#124	—	2	2	no	—
588	#124	—	2	2	no	—
589	#123	—	2	8	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	complemented
592	#121	—	2	8	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	4	1	no	—
599	#120	—	2	8	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	#117	—	2	2	no	—
605	#117	—	4	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	—	2	8	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
629	#107	—	2	2	no	—
630	#103	—	2	2	no	—
631	#103	—	2	2	no	—
632	#103	—	4	1	no	—
633	#102	—	2	2	no	—
634	#102	—	2	2	no	—
635	#102	—	2	2	no	—
636	#102	—	2	2	no	—
637	#102	—	2	2	no	—
638	#102	—	2	2	no	—
639	#102	D₄×C₁₉	1	4	yes	complemented
640	C₂²⋊C₈	—	2	2	no	—
641	C₂²⋊C₈	—	2	2	no	—
642	C₂²⋊C₈	—	4	1	no	—
643	#95	—	2	1	no	—
644	#95	—	2	1	no	—
645	C₁₉	#24450	1	1	yes	characteristic, direct product factor, Sylow
646	C₂⁴	—	2	1	no	—
647	C₂⁴	—	2	1	no	—
648	C₂⁴	—	2	4	no	—
649	C₂⁴	—	2	1	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	2	no	—
652	C₂⁴	—	4	2	no	—
653	C₂⁴	—	4	2	no	—
654	C₂⁴	—	8	1	no	—
655	C₂⁴	—	8	1	no	—
656	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
657	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
658	#41	—	4	4	no	—
659	#41	—	4	4	no	—
660	#41	—	4	4	no	—
661	#41	—	4	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	8	1	no	—
700	C₂×D₄	—	8	1	no	—
701	C₂×D₄	—	8	1	no	—
702	C₂×D₄	—	8	1	no	—
703	C₂×D₄	—	8	1	no	—
704	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
707	C₂×D₄	#41×C₁₉	1	2	yes	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	8	1	no	—
728	C₂²×C₄	—	8	1	no	—
729	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
734	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
736	SD₁₆	—	4	4	no	—
737	D₈	—	4	4	no	—
738	D₈	—	4	4	no	—
739	M₁₆	—	4	4	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	2	1	no	—
749	C₂×C₈	—	2	1	no	—
750	C₂×C₈	—	2	1	no	—
751	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	8	1	no	—
761	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
762	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	8	1	no	—
775	C₂²⋊C₄	—	8	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	4	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	4	8	no	—
797	C₂³	—	4	8	no	—
798	C₂³	—	4	1	no	—
799	C₂³	—	4	1	no	—
800	C₂³	—	4	1	no	—
801	C₂³	—	4	1	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	1	no	—
810	C₂³	—	4	1	no	—
811	C₂³	—	4	1	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	1	no	—
815	C₂³	—	8	4	no	—
816	C₂³	—	8	4	no	—
817	C₂³	—	8	4	no	—
818	C₂³	—	8	4	no	—
819	C₂³	—	8	4	no	—
820	C₂³	C₁₉×#120	1	2	yes	—
821	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	4	1	no	—
825	Q₈	—	4	1	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	4	8	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	8	4	no	—
841	D₄	—	8	4	no	—
842	D₄	—	8	4	no	—
843	D₄	C₁₉×#121	1	4	yes	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	8	4	no	—
880	C₂×C₄	C₁₉×#120	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
884	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
885	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
887	C₈	—	2	2	no	—
888	C₈	—	4	1	no	—
889	C₈	—	4	1	no	—
890	C₈	—	4	1	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	8	16	no	—
916	C₂²	—	8	1	no	—
917	C₂²	—	8	1	no	—
918	C₂²	—	8	1	no	—
919	C₂²	—	8	1	no	—
920	C₂²	—	8	1	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	—	8	1	no	—
924	C₂²	—	8	1	no	—
925	C₂²	—	8	1	no	—
926	C₂²	—	8	1	no	—
927	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
928	C₂²	D₄²×C₁₉	1	1	yes	characteristic
929	C₂²	C₁₉×#546	1	1	yes	characteristic
930	C₂²	C₁₉×#575	1	1	yes	characteristic
931	C₂²	C₁₉×#575	1	1	yes	characteristic
932	C₂²	C₁₉×#576	1	1	yes	characteristic
933	C₂²	C₁₉×#576	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	2	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	8	1	no	—
942	C₄	—	8	1	no	—
943	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
944	C₄	C₁₉×#534	1	1	yes	characteristic
945	C₄	D₄²×C₁₉	1	1	yes	characteristic
946	C₄	C₁₉×#546	1	1	yes	characteristic
947	C₂	—	4	2	no	—
948	C₂	—	4	4	no	—
949	C₂	—	8	1	no	—
950	C₂	—	8	2	no	—
951	C₂	—	16	1	no	—
952	C₂	C₁₉×#2410	1	1	yes	characteristic
953	C₂	C₁₉×#3005	1	1	yes	characteristic
954	C₂	C₁₉×#3008	1	1	yes	characteristic
955	C₂	C₁₉×#3268	1	1	yes	characteristic
956	C₂	C₁₉×#3273	1	1	yes	characteristic
957	C₂	C₁₉×#3319	1	1	yes	characteristic
958	C₂	C₁₉×#3322	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×#546	C₂	semidirect
2. C₂×C₁₉×#468	C₂	semidirect
3. C₂×C₁₉×#449	C₂	semidirect
4. C₂×C₁₉×#447	C₂	semidirect
5. C₂×C₁₉×#418	C₂	semidirect
6. C₁₉×#2414	C₂	semidirect
7. C₁₉×#2042	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#2012	C₂	semidirect
10. C₁₉×#1999	C₂	semidirect
11. C₁₉×#1879	C₂	semidirect
12. C₁₉×#1873	C₂	semidirect
13. C₁₉×#1870	C₂	semidirect
14. C₁₉×#1862	C₂	semidirect
15. C₁₉×#1788	C₂	semidirect
18. C₂²×SD₁₆×C₁₉	C₂²	semidirect
30. C₂×C₁₉×#121	C₂²	semidirect
39. C₂×C₁₉×#107	C₂²	semidirect
41. C₂×C₁₉×#103	C₂²	semidirect
42. C₂×C₁₉×#103	C₂²	semidirect
43. C₂×C₁₉×#103	C₂²	semidirect
50. C₂×C₁₉×#102	C₂²	semidirect
52. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
53. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
57. C₁₉×#390	C₂²	semidirect
58. C₁₉×#389	C₂²	semidirect
60. C₁₉×#380	C₂²	semidirect
61. C₁₉×#340	C₂²	semidirect
62. C₁₉×#340	C₂²	semidirect
63. C₁₉×#336	C₂²	semidirect
64. C₁₉×#336	C₂²	semidirect
84. C₂²×D₄×C₁₉	D₄	semidirect
112. C₁₉×C₂²⋊Q₈	D₄	semidirect
160. C₁₉×#102	D₄	semidirect
299. #24450	C₁₉	direct (N × H)
412. C₂×#546	C₂×C₁₉	semidirect
413. C₂×#468	C₂×C₁₉	semidirect
414. C₂×#449	C₂×C₁₉	semidirect
415. C₂×#447	C₂×C₁₉	semidirect
416. C₂×#418	C₂×C₁₉	semidirect
417. #2414	C₂×C₁₉	semidirect
418. #2042	C₂×C₁₉	semidirect
419. #2033	C₂×C₁₉	semidirect
420. #2012	C₂×C₁₉	semidirect
421. #1999	C₂×C₁₉	semidirect
422. #1879	C₂×C₁₉	semidirect
423. #1873	C₂×C₁₉	semidirect
424. #1870	C₂×C₁₉	semidirect
425. #1862	C₂×C₁₉	semidirect
426. #1788	C₂×C₁₉	semidirect
485. C₂²×SD₁₆	C₂²×C₁₉	semidirect
497. C₂×#121	C₂²×C₁₉	semidirect
506. C₂×#107	C₂²×C₁₉	semidirect
508. C₂×#103	C₂²×C₁₉	semidirect
509. C₂×#103	C₂²×C₁₉	semidirect
510. C₂×#103	C₂²×C₁₉	semidirect
517. C₂×#102	C₂²×C₁₉	semidirect
519. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
520. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
524. #390	C₂²×C₁₉	semidirect
525. #389	C₂²×C₁₉	semidirect
527. #380	C₂²×C₁₉	semidirect
528. #340	C₂²×C₁₉	semidirect
529. #340	C₂²×C₁₉	semidirect
530. #336	C₂²×C₁₉	semidirect
531. #336	C₂²×C₁₉	semidirect
563. C₂²×D₄	D₄×C₁₉	semidirect
591. C₂²⋊Q₈	D₄×C₁₉	semidirect
639. #102	D₄×C₁₉	semidirect
645. C₁₉	#24450	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×#546	2
C₂×C₁₉×#468	2
C₂×C₁₉×#449	2
C₂×C₁₉×#447	2
C₂×C₁₉×#418	2
C₁₉×#2414	2
C₁₉×#2042	2
C₁₉×#2033	2
C₁₉×#2012	2
C₁₉×#1999	2
C₁₉×#1879	2
C₁₉×#1873	2
C₁₉×#1870	2
C₁₉×#1862	2
C₁₉×#1788	2
#24450	19

Subgroups — C19×#24450 #18030409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24450 #18030409