Subgroups — C₁₉×#24008 #18029967

Order 4864.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#525	—	2	4	no	—
19	C₁₉×#525	—	2	4	no	—
20	C₂×C₁₉×#123	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#120	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	—	2	1	no	—
27	C₂×C₄×D₄×C₁₉	—	2	1	no	—
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₁₉×#485	—	2	4	no	—
32	C₁₉×#482	—	2	4	no	—
33	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₉×C₂²⋊C₈	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×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₁₉×#381	—	2	1	no	—
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₁₉×#380	C₂²	1	1	yes	characteristic
54	C₁₉×#380	C₂²	1	1	yes	characteristic
55	C₁₉×#380	C₂²	1	1	yes	characteristic
56	C₁₉×#379	—	2	1	no	—
57	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#340	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	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
64	C₂×#41×C₁₉	—	2	2	no	—
65	C₂×#41×C₁₉	—	2	2	no	—
66	C₂×#41×C₁₉	—	2	2	no	—
67	C₂×#41×C₁₉	—	2	2	no	—
68	C₂×#41×C₁₉	—	4	1	no	—
69	C₂×#41×C₁₉	—	4	1	no	—
70	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂²×D₄×C₁₉	—	2	1	no	—
73	C₂²×D₄×C₁₉	—	2	1	no	—
74	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	—	2	1	no	—
76	C₂³×C₄×C₁₉	—	2	2	no	—
77	C₂³×C₄×C₁₉	—	2	2	no	—
78	C₂³×C₄×C₁₉	—	2	2	no	—
79	C₂³×C₄×C₁₉	—	2	2	no	—
80	C₂³×C₄×C₁₉	—	4	1	no	—
81	C₂³×C₄×C₁₉	—	4	1	no	—
82	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#123	—	2	8	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	D₄	1	4	yes	—
101	C₁₉×#120	—	2	8	no	—
102	C₄×D₄×C₁₉	—	2	8	no	—
103	C₄×D₄×C₁₉	—	2	8	no	—
104	C₁₉×#117	—	2	2	no	—
105	C₁₉×#117	—	2	2	no	—
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	2	no	—
108	C₁₉×#117	—	4	1	no	—
109	C₁₉×#117	—	4	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄²×C₁₉	—	2	1	no	—
130	C₂×C₄²×C₁₉	—	2	1	no	—
131	C₂×C₄²×C₁₉	—	2	1	no	—
132	C₁₉×#107	—	2	2	no	—
133	C₁₉×#107	—	2	2	no	—
134	C₁₉×#106	—	2	2	no	—
135	C₁₉×#106	—	2	2	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#103	—	4	1	no	—
139	C₁₉×#103	—	4	1	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×#102	—	2	2	no	—
142	C₁₉×#102	—	4	1	no	—
143	C₁₉×#102	—	4	1	no	—
144	C₁₉×C₂²⋊C₈	—	2	2	no	—
145	C₁₉×C₂²⋊C₈	—	2	2	no	—
146	C₁₉×C₂²⋊C₈	—	2	2	no	—
147	C₁₉×C₂²⋊C₈	—	2	2	no	—
148	C₁₉×C₂²⋊C₈	—	4	1	no	—
149	C₁₉×C₂²⋊C₈	—	4	1	no	—
150	C₁₉×#95	—	2	1	no	—
151	C₁₉×#95	—	2	1	no	—
152	C₁₉×#95	—	2	1	no	—
153	C₁₉×#95	—	2	1	no	—
154	C₂⁴×C₁₉	—	2	2	no	—
155	C₂⁴×C₁₉	—	2	2	no	—
156	C₂⁴×C₁₉	—	2	2	no	—
157	C₂⁴×C₁₉	—	2	1	no	—
158	C₂⁴×C₁₉	—	4	1	no	—
159	C₂⁴×C₁₉	—	4	1	no	—
160	C₂⁴×C₁₉	—	4	1	no	—
161	C₂⁴×C₁₉	—	4	1	no	—
162	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
165	#41×C₁₉	—	4	4	no	—
166	#41×C₁₉	—	4	4	no	—
167	#41×C₁₉	—	4	4	no	—
168	#41×C₁₉	—	4	4	no	—
169	C₂×Q₈×C₁₉	—	2	1	no	—
170	C₂×Q₈×C₁₉	—	2	1	no	—
171	C₂×Q₈×C₁₉	—	2	1	no	—
172	C₂×Q₈×C₁₉	—	2	1	no	—
173	C₂×Q₈×C₁₉	—	2	1	no	—
174	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₁₉	—	2	4	no	—
176	C₂×D₄×C₁₉	—	2	4	no	—
177	C₂×D₄×C₁₉	—	2	4	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	1	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	4	2	no	—
184	C₂×D₄×C₁₉	—	4	2	no	—
185	C₂×D₄×C₁₉	—	4	2	no	—
186	C₂×D₄×C₁₉	—	4	2	no	—
187	C₂×D₄×C₁₉	—	4	2	no	—
188	C₂×D₄×C₁₉	—	4	2	no	—
189	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	4	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
205	C₂²×C₄×C₁₉	—	2	2	no	—
206	C₂²×C₄×C₁₉	—	2	2	no	—
207	C₂²×C₄×C₁₉	—	2	2	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	—	2	1	no	—
214	C₂²×C₄×C₁₉	—	2	1	no	—
215	C₂²×C₄×C₁₉	—	2	1	no	—
216	C₂²×C₄×C₁₉	—	2	1	no	—
217	C₂²×C₄×C₁₉	—	2	1	no	—
218	C₂²×C₄×C₁₉	—	4	1	no	—
219	C₂²×C₄×C₁₉	—	4	1	no	—
220	C₂²×C₄×C₁₉	—	4	1	no	—
221	C₂²×C₄×C₁₉	—	4	4	no	—
222	C₂²×C₄×C₁₉	—	4	4	no	—
223	C₂²×C₄×C₁₉	—	4	4	no	—
224	C₂²×C₄×C₁₉	—	4	4	no	—
225	C₂²×C₄×C₁₉	—	4	2	no	—
226	C₂²×C₄×C₁₉	—	4	2	no	—
227	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₉	#41	1	2	yes	—
233	C₂²×C₄×C₁₉	#41	1	2	yes	—
234	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₁₉	—	2	1	no	—
236	C₂×C₈×C₁₉	—	2	1	no	—
237	C₂×C₈×C₁₉	—	2	1	no	—
238	C₂×C₈×C₁₉	—	2	1	no	—
239	C₂×C₈×C₁₉	—	2	1	no	—
240	C₂×C₈×C₁₉	—	2	1	no	—
241	C₂×C₈×C₁₉	—	2	1	no	—
242	C₂×C₈×C₁₉	—	2	1	no	—
243	C₂×C₈×C₁₉	—	2	1	no	—
244	C₂×C₈×C₁₉	—	2	1	no	—
245	C₂×C₈×C₁₉	—	2	1	no	—
246	C₂×C₈×C₁₉	—	2	1	no	—
247	C₄⋊C₄×C₁₉	—	2	4	no	—
248	C₄⋊C₄×C₁₉	—	2	4	no	—
249	C₄⋊C₄×C₁₉	—	2	1	no	—
250	C₄⋊C₄×C₁₉	—	2	1	no	—
251	C₄⋊C₄×C₁₉	—	2	1	no	—
252	C₄⋊C₄×C₁₉	—	2	1	no	—
253	C₄⋊C₄×C₁₉	—	2	1	no	—
254	C₄⋊C₄×C₁₉	—	2	1	no	—
255	C₄⋊C₄×C₁₉	—	2	1	no	—
256	C₄⋊C₄×C₁₉	—	2	1	no	—
257	C₄⋊C₄×C₁₉	—	2	1	no	—
258	C₄⋊C₄×C₁₉	—	2	1	no	—
259	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
261	C₂²⋊C₄×C₁₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₉	—	4	2	no	—
267	C₂²⋊C₄×C₁₉	—	4	2	no	—
268	C₂²⋊C₄×C₁₉	—	4	2	no	—
269	C₂²⋊C₄×C₁₉	—	4	2	no	—
270	C₂²⋊C₄×C₁₉	—	4	2	no	—
271	C₂²⋊C₄×C₁₉	—	4	2	no	—
272	C₄²×C₁₉	—	2	4	no	—
273	C₄²×C₁₉	—	4	2	no	—
274	C₄²×C₁₉	—	4	2	no	—
275	#24008	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₁₉	—	2	1	no	—
277	C₂³×C₁₉	—	2	1	no	—
278	C₂³×C₁₉	—	2	1	no	—
279	C₂³×C₁₉	—	2	1	no	—
280	C₂³×C₁₉	—	2	1	no	—
281	C₂³×C₁₉	—	2	1	no	—
282	C₂³×C₁₉	—	2	1	no	—
283	C₂³×C₁₉	—	2	1	no	—
284	C₂³×C₁₉	—	2	1	no	—
285	C₂³×C₁₉	—	2	1	no	—
286	C₂³×C₁₉	—	2	1	no	—
287	C₂³×C₁₉	—	2	1	no	—
288	C₂³×C₁₉	—	2	1	no	—
289	C₂³×C₁₉	—	2	1	no	—
290	C₂³×C₁₉	—	2	1	no	—
291	C₂³×C₁₉	—	2	1	no	—
292	C₂³×C₁₉	—	2	1	no	—
293	C₂³×C₁₉	—	2	1	no	—
294	C₂³×C₁₉	—	2	2	no	—
295	C₂³×C₁₉	—	4	4	no	—
296	C₂³×C₁₉	—	4	4	no	—
297	C₂³×C₁₉	—	4	4	no	—
298	C₂³×C₁₉	—	4	4	no	—
299	C₂³×C₁₉	—	4	4	no	—
300	C₂³×C₁₉	—	4	4	no	—
301	C₂³×C₁₉	—	4	4	no	—
302	C₂³×C₁₉	—	4	1	no	—
303	C₂³×C₁₉	—	4	1	no	—
304	C₂³×C₁₉	—	4	1	no	—
305	C₂³×C₁₉	—	4	1	no	—
306	C₂³×C₁₉	—	4	1	no	—
307	C₂³×C₁₉	—	4	1	no	—
308	C₂³×C₁₉	#120	1	2	yes	—
309	C₂³×C₁₉	#123	1	2	yes	—
310	C₂³×C₁₉	#135	1	2	yes	—
311	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₁₉	—	2	2	no	—
313	Q₈×C₁₉	—	2	2	no	—
314	Q₈×C₁₉	—	4	1	no	—
315	Q₈×C₁₉	—	4	1	no	—
316	D₄×C₁₉	—	2	2	no	—
317	D₄×C₁₉	—	2	2	no	—
318	D₄×C₁₉	—	4	8	no	—
319	D₄×C₁₉	—	4	8	no	—
320	D₄×C₁₉	—	4	8	no	—
321	D₄×C₁₉	—	4	1	no	—
322	D₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	2	1	no	—
324	C₂×C₄×C₁₉	—	2	1	no	—
325	C₂×C₄×C₁₉	—	2	1	no	—
326	C₂×C₄×C₁₉	—	2	1	no	—
327	C₂×C₄×C₁₉	—	2	2	no	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	2	no	—
330	C₂×C₄×C₁₉	—	2	2	no	—
331	C₂×C₄×C₁₉	—	2	2	no	—
332	C₂×C₄×C₁₉	—	2	2	no	—
333	C₂×C₄×C₁₉	—	2	2	no	—
334	C₂×C₄×C₁₉	—	2	2	no	—
335	C₂×C₄×C₁₉	—	2	2	no	—
336	C₂×C₄×C₁₉	—	2	2	no	—
337	C₂×C₄×C₁₉	—	2	1	no	—
338	C₂×C₄×C₁₉	—	2	2	no	—
339	C₂×C₄×C₁₉	—	2	1	no	—
340	C₂×C₄×C₁₉	—	2	1	no	—
341	C₂×C₄×C₁₉	—	4	4	no	—
342	C₂×C₄×C₁₉	—	4	4	no	—
343	C₂×C₄×C₁₉	—	4	4	no	—
344	C₂×C₄×C₁₉	—	4	8	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	—	4	1	no	—
366	C₂×C₄×C₁₉	—	4	1	no	—
367	C₂×C₄×C₁₉	#120	1	2	yes	—
368	C₂×C₄×C₁₉	#123	1	2	yes	—
369	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
373	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
375	C₈×C₁₉	—	4	1	no	—
376	C₈×C₁₉	—	4	1	no	—
377	C₈×C₁₉	—	4	1	no	—
378	C₈×C₁₉	—	4	1	no	—
379	C₂×#525	C₂×C₁₉	1	1	yes	characteristic
380	C₂×#485	C₂×C₁₉	1	1	yes	characteristic, complemented
381	C₂×#482	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
383	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
384	#2035	C₂×C₁₉	1	1	yes	characteristic, complemented
385	#2034	C₂×C₁₉	1	1	yes	characteristic, complemented
386	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
387	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
388	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#1854	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#1854	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
392	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#1779	C₂×C₁₉	1	1	yes	characteristic, complemented
394	C₂²×C₁₉	—	2	2	no	—
395	C₂²×C₁₉	—	2	2	no	—
396	C₂²×C₁₉	—	2	2	no	—
397	C₂²×C₁₉	—	2	2	no	—
398	C₂²×C₁₉	—	2	2	no	—
399	C₂²×C₁₉	—	2	2	no	—
400	C₂²×C₁₉	—	2	2	no	—
401	C₂²×C₁₉	—	2	2	no	—
402	C₂²×C₁₉	—	2	2	no	—
403	C₂²×C₁₉	—	4	16	no	—
404	C₂²×C₁₉	—	4	1	no	—
405	C₂²×C₁₉	—	4	1	no	—
406	C₂²×C₁₉	—	4	1	no	—
407	C₂²×C₁₉	—	4	1	no	—
408	C₂²×C₁₉	—	4	1	no	—
409	C₂²×C₁₉	—	4	1	no	—
410	C₂²×C₁₉	—	4	1	no	—
411	C₂²×C₁₉	—	4	1	no	—
412	C₂²×C₁₉	—	4	1	no	—
413	C₂²×C₁₉	—	4	1	no	—
414	C₂²×C₁₉	—	4	1	no	—
415	C₂²×C₁₉	—	4	1	no	—
416	C₂²×C₁₉	—	4	2	no	—
417	C₂²×C₁₉	—	4	2	no	—
418	C₂²×C₁₉	—	4	2	no	—
419	C₂²×C₁₉	—	8	1	no	—
420	C₂²×C₁₉	—	8	1	no	—
421	C₂²×C₁₉	—	8	1	no	—
422	C₂²×C₁₉	—	8	1	no	—
423	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
424	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
425	C₂²×C₁₉	#534	1	1	yes	characteristic
426	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
427	C₂²×C₁₉	#575	1	1	yes	characteristic
428	C₂²×C₁₉	#575	1	1	yes	characteristic
429	C₂²×C₁₉	#575	1	1	yes	characteristic
430	C₄×C₁₉	—	2	2	no	—
431	C₄×C₁₉	—	2	2	no	—
432	C₄×C₁₉	—	4	1	no	—
433	C₄×C₁₉	—	4	2	no	—
434	C₄×C₁₉	—	4	2	no	—
435	C₄×C₁₉	—	4	2	no	—
436	C₄×C₁₉	—	8	1	no	—
437	C₄×C₁₉	—	8	1	no	—
438	C₄×C₁₉	—	8	1	no	—
439	C₄×C₁₉	—	8	1	no	—
440	C₄×C₁₉	#546	1	1	yes	characteristic
441	C₄×C₁₉	#546	1	1	yes	characteristic
442	C₄×C₁₉	#546	1	1	yes	characteristic
443	C₄×C₁₉	#546	1	1	yes	characteristic
444	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
445	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
446	#525	—	2	4	no	—
447	#525	—	2	4	no	—
448	C₂×#123	—	2	1	no	—
449	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
450	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
451	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#120	—	2	1	no	—
454	C₂×C₄×D₄	—	2	1	no	—
455	C₂×C₄×D₄	—	2	1	no	—
456	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
459	#485	—	2	4	no	—
460	#482	—	2	4	no	—
461	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
462	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
463	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
464	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
465	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
466	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
467	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
468	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
469	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
470	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
471	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
472	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
473	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
475	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
476	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
478	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
479	#381	—	2	1	no	—
480	#380	C₂²×C₁₉	1	1	yes	characteristic
481	#380	C₂²×C₁₉	1	1	yes	characteristic
482	#380	C₂²×C₁₉	1	1	yes	characteristic
483	#380	C₂²×C₁₉	1	1	yes	characteristic
484	#379	—	2	1	no	—
485	C₄×C₂²⋊C₄	—	2	1	no	—
486	C₄×C₂²⋊C₄	—	2	1	no	—
487	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
488	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
489	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
490	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
491	C₂×C₁₉	—	4	2	no	—
492	C₂×C₁₉	—	4	2	no	—
493	C₂×C₁₉	—	4	2	no	—
494	C₂×C₁₉	—	8	2	no	—
495	C₂×C₁₉	#2405	1	1	yes	characteristic
496	C₂×C₁₉	#3002	1	1	yes	characteristic
497	C₂×C₁₉	#3005	1	1	yes	characteristic
498	C₂×C₁₉	#3091	1	1	yes	characteristic
499	C₂×C₁₉	#3093	1	1	yes	characteristic
500	C₂×C₁₉	#3191	1	1	yes	characteristic
501	C₂×C₁₉	#3197	1	1	yes	characteristic
502	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
503	C₂×#41	—	2	2	no	—
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	4	1	no	—
508	C₂×#41	—	4	1	no	—
509	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	2	no	—
516	C₂³×C₄	—	2	2	no	—
517	C₂³×C₄	—	2	2	no	—
518	C₂³×C₄	—	2	2	no	—
519	C₂³×C₄	—	4	1	no	—
520	C₂³×C₄	—	4	1	no	—
521	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
522	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
523	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
531	#123	—	2	8	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	D₄×C₁₉	1	4	yes	—
540	#120	—	2	8	no	—
541	C₄×D₄	—	2	8	no	—
542	C₄×D₄	—	2	8	no	—
543	#117	—	2	2	no	—
544	#117	—	2	2	no	—
545	#117	—	2	2	no	—
546	#117	—	2	2	no	—
547	#117	—	4	1	no	—
548	#117	—	4	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	2	1	no	—
571	#107	—	2	2	no	—
572	#107	—	2	2	no	—
573	#106	—	2	2	no	—
574	#106	—	2	2	no	—
575	#103	—	2	2	no	—
576	#103	—	2	2	no	—
577	#103	—	4	1	no	—
578	#103	—	4	1	no	—
579	#102	—	2	2	no	—
580	#102	—	2	2	no	—
581	#102	—	4	1	no	—
582	#102	—	4	1	no	—
583	C₂²⋊C₈	—	2	2	no	—
584	C₂²⋊C₈	—	2	2	no	—
585	C₂²⋊C₈	—	2	2	no	—
586	C₂²⋊C₈	—	2	2	no	—
587	C₂²⋊C₈	—	4	1	no	—
588	C₂²⋊C₈	—	4	1	no	—
589	#95	—	2	1	no	—
590	#95	—	2	1	no	—
591	#95	—	2	1	no	—
592	#95	—	2	1	no	—
593	C₁₉	#24008	1	1	yes	characteristic, direct product factor, Sylow
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	4	1	no	—
599	C₂⁴	—	4	1	no	—
600	C₂⁴	—	4	1	no	—
601	C₂⁴	—	4	1	no	—
602	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
604	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
605	#41	—	4	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
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	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	4	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	—	4	4	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
671	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
672	C₂²×C₄	#41×C₁₉	1	2	yes	—
673	C₂²×C₄	#41×C₁₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₄²	—	2	4	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	2	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	4	4	no	—
736	C₂³	—	4	4	no	—
737	C₂³	—	4	4	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	C₁₉×#120	1	2	yes	—
748	C₂³	C₁₉×#123	1	2	yes	—
749	C₂³	C₁₉×#135	1	2	yes	—
750	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	4	1	no	—
754	Q₈	—	4	1	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	8	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	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	C₁₉×#120	1	2	yes	—
807	C₂×C₄	C₁₉×#123	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
810	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
811	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
812	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
813	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
814	C₈	—	4	1	no	—
815	C₈	—	4	1	no	—
816	C₈	—	4	1	no	—
817	C₈	—	4	1	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	4	16	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
848	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
849	C₂²	C₁₉×#534	1	1	yes	characteristic
850	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
851	C₂²	C₁₉×#575	1	1	yes	characteristic
852	C₂²	C₁₉×#575	1	1	yes	characteristic
853	C₂²	C₁₉×#575	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	8	1	no	—
861	C₄	—	8	1	no	—
862	C₄	—	8	1	no	—
863	C₄	—	8	1	no	—
864	C₄	C₁₉×#546	1	1	yes	characteristic
865	C₄	C₁₉×#546	1	1	yes	characteristic
866	C₄	C₁₉×#546	1	1	yes	characteristic
867	C₄	C₁₉×#546	1	1	yes	characteristic
868	C₂	—	4	2	no	—
869	C₂	—	4	2	no	—
870	C₂	—	4	2	no	—
871	C₂	—	8	2	no	—
872	C₂	C₁₉×#2405	1	1	yes	characteristic
873	C₂	C₁₉×#3002	1	1	yes	characteristic
874	C₂	C₁₉×#3005	1	1	yes	characteristic
875	C₂	C₁₉×#3091	1	1	yes	characteristic
876	C₂	C₁₉×#3093	1	1	yes	characteristic
877	C₂	C₁₉×#3191	1	1	yes	characteristic
878	C₂	C₁₉×#3197	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#525	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#485	C₂	semidirect
3. C₂×C₁₉×#482	C₂	semidirect
4. C₁₉×#2280	C₂	semidirect
5. C₁₉×#2036	C₂	semidirect
6. C₁₉×#2035	C₂	semidirect
7. C₁₉×#2034	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#1875	C₂	semidirect
10. C₁₉×#1873	C₂	semidirect
11. C₁₉×#1854	C₂	semidirect
12. C₁₉×#1854	C₂	semidirect
13. C₁₉×#1788	C₂	semidirect
14. C₁₉×#1788	C₂	semidirect
15. C₁₉×#1779	C₂	semidirect
33. C₂×C₁₉×#107	C₂²	semidirect
34. C₂×C₁₉×#107	C₂²	semidirect
35. C₂×C₁₉×#106	C₂²	semidirect
36. C₂×C₁₉×#106	C₂²	semidirect
37. C₂×C₁₉×#103	C₂²	semidirect
38. C₂×C₁₉×#103	C₂²	semidirect
39. C₂×C₁₉×#103	C₂²	semidirect
40. C₂×C₁₉×#103	C₂²	semidirect
41. C₂×C₁₉×#102	C₂²	semidirect
42. C₂×C₁₉×#102	C₂²	semidirect
43. C₂×C₁₉×#102	C₂²	semidirect
44. C₂×C₁₉×#102	C₂²	semidirect
59. C₁₉×#340	C₂²	semidirect
60. C₁₉×#340	C₂²	semidirect
61. C₁₉×#340	C₂²	semidirect
62. C₁₉×#340	C₂²	semidirect
275. #24008	C₁₉	direct (N × H)
380. C₂×#485	C₂×C₁₉	semidirect
381. C₂×#482	C₂×C₁₉	semidirect
382. #2280	C₂×C₁₉	semidirect
383. #2036	C₂×C₁₉	semidirect
384. #2035	C₂×C₁₉	semidirect
385. #2034	C₂×C₁₉	semidirect
386. #2033	C₂×C₁₉	semidirect
387. #1875	C₂×C₁₉	semidirect
388. #1873	C₂×C₁₉	semidirect
389. #1854	C₂×C₁₉	semidirect
390. #1854	C₂×C₁₉	semidirect
391. #1788	C₂×C₁₉	semidirect
392. #1788	C₂×C₁₉	semidirect
393. #1779	C₂×C₁₉	semidirect
461. C₂×#107	C₂²×C₁₉	semidirect
462. C₂×#107	C₂²×C₁₉	semidirect
463. C₂×#106	C₂²×C₁₉	semidirect
464. C₂×#106	C₂²×C₁₉	semidirect
465. C₂×#103	C₂²×C₁₉	semidirect
466. C₂×#103	C₂²×C₁₉	semidirect
467. C₂×#103	C₂²×C₁₉	semidirect
468. C₂×#103	C₂²×C₁₉	semidirect
469. C₂×#102	C₂²×C₁₉	semidirect
470. C₂×#102	C₂²×C₁₉	semidirect
471. C₂×#102	C₂²×C₁₉	semidirect
472. C₂×#102	C₂²×C₁₉	semidirect
487. #340	C₂²×C₁₉	semidirect
488. #340	C₂²×C₁₉	semidirect
489. #340	C₂²×C₁₉	semidirect
490. #340	C₂²×C₁₉	semidirect
593. C₁₉	#24008	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×#525	2
C₂×C₁₉×#485	2
C₂×C₁₉×#482	2
C₁₉×#2280	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#1875	2
C₁₉×#1873	2
C₁₉×#1854	2
C₁₉×#1788	2
C₁₉×#1779	2
#24008	19

Subgroups — C19×#24008 #18029967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24008 #18029967