Subgroups — C₁₉×#60368 #18066327

Order 4864.

4726 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3013	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3011	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3010	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3005	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3004	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₉×2₋¹⁺⁴	—	2	2	no	—
14	C₂×C₁₉×2₋¹⁺⁴	—	2	2	no	—
15	C₂×C₁₉×2₋¹⁺⁴	—	2	8	no	—
16	C₂×C₁₉×2₋¹⁺⁴	—	2	8	no	—
17	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	—
18	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	complemented
19	C₂²×#41×C₁₉	—	2	2	no	—
20	C₂²×#41×C₁₉	—	2	1	no	—
21	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×#41×C₁₉	C₂²	1	2	yes	complemented
25	C₂³×Q₈×C₁₉	—	2	1	no	—
26	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂³×Q₈×C₁₉	C₂²	1	2	yes	complemented
28	C₁₉×#575	—	2	8	no	—
29	C₂×C₁₉×#137	—	2	8	no	—
30	C₂×C₁₉×#137	C₂²	1	2	yes	—
31	C₂×C₁₉×#137	C₂²	1	4	yes	—
32	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
33	C₂×C₁₉×#137	C₂²	1	4	yes	complemented
34	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
35	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
36	C₂×C₁₉×#135	C₂²	1	4	yes	complemented
37	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
38	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
39	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#537	C₂²	1	4	yes	complemented
42	C₁₉×#536	—	2	1	no	—
43	C₁₉×#536	C₂²	1	2	yes	complemented
44	C₁₉×#535	—	2	1	no	—
45	C₁₉×#535	C₂²	1	2	yes	complemented
46	C₁₉×#534	—	2	2	no	—
47	C₁₉×#532	—	2	2	no	—
48	C₁₉×#525	—	2	2	no	—
49	C₁₉×#525	C₂²	1	4	yes	—
50	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
51	C₁₉×#452	C₂²	1	16	yes	complemented
52	C₁₉×#451	C₂²	1	16	yes	complemented
53	C₁₉×#449	C₂²	1	16	yes	complemented
54	C₁₉×#448	C₂²	1	16	yes	complemented
55	C₁₉×#419	C₂²	1	2	yes	complemented
56	C₁₉×#419	C₂²	1	4	yes	complemented
57	C₁₉×#419	C₂²	1	4	yes	complemented
58	C₁₉×#418	C₂²	1	2	yes	complemented
59	C₁₉×#417	C₂²	1	4	yes	complemented
60	C₁₉×#416	C₂²	1	4	yes	complemented
61	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
62	C₁₉×#408	C₂²	1	4	yes	complemented
63	C₁₉×#408	C₂²	1	4	yes	complemented
64	C₁₉×#407	C₂²	1	4	yes	complemented
65	C₁₉×2₋¹⁺⁴	—	2	32	no	—
66	C₁₉×2₋¹⁺⁴	—	2	32	no	—
67	C₁₉×2₋¹⁺⁴	—	2	16	no	—
68	C₁₉×2₋¹⁺⁴	—	2	16	no	—
69	C₁₉×2₋¹⁺⁴	—	2	16	no	—
70	C₁₉×2₋¹⁺⁴	—	2	16	no	—
71	C₂×#41×C₁₉	—	2	32	no	—
72	C₂×#41×C₁₉	—	2	16	no	—
73	C₂×#41×C₁₉	—	2	8	no	—
74	C₂×#41×C₁₉	—	2	8	no	—
75	C₂×#41×C₁₉	—	2	4	no	—
76	C₂×#41×C₁₉	—	2	4	no	—
77	C₂×#41×C₁₉	—	2	8	no	—
78	C₂×#41×C₁₉	—	2	8	no	—
79	C₂×#41×C₁₉	—	2	4	no	—
80	C₂×#41×C₁₉	—	2	1	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	—	2	4	no	—
83	C₂×#41×C₁₉	—	2	4	no	—
84	C₂×#41×C₁₉	—	2	4	no	—
85	C₂×#41×C₁₉	—	2	1	no	—
86	C₂×#41×C₁₉	—	2	1	no	—
87	C₂×#41×C₁₉	—	2	4	no	—
88	C₂×#41×C₁₉	—	2	4	no	—
89	C₂×#41×C₁₉	D₄	1	2	yes	—
90	C₂×#41×C₁₉	D₄	1	2	yes	—
91	C₂×#41×C₁₉	D₄	1	8	yes	complemented
92	C₂×#41×C₁₉	C₂³	1	8	yes	—
93	C₂×#41×C₁₉	C₂³	1	2	yes	—
94	C₂×#41×C₁₉	C₂³	1	2	yes	—
95	C₂×#41×C₁₉	C₂³	1	2	yes	—
96	C₂×#41×C₁₉	C₂³	1	2	yes	—
97	C₂×#41×C₁₉	C₂³	1	2	yes	—
98	C₂×#41×C₁₉	C₂³	1	2	yes	—
99	C₂²×Q₈×C₁₉	—	2	16	no	—
100	C₂²×Q₈×C₁₉	—	2	4	no	—
101	C₂²×Q₈×C₁₉	—	2	4	no	—
102	C₂²×Q₈×C₁₉	—	2	8	no	—
103	C₂²×Q₈×C₁₉	—	2	8	no	—
104	C₂²×Q₈×C₁₉	—	2	1	no	—
105	C₂²×Q₈×C₁₉	—	2	2	no	—
106	C₂²×Q₈×C₁₉	—	2	4	no	—
107	C₂²×Q₈×C₁₉	—	2	1	no	—
108	C₂²×Q₈×C₁₉	—	2	1	no	—
109	C₂²×Q₈×C₁₉	—	2	4	no	—
110	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
111	C₂²×Q₈×C₁₉	D₄	1	8	yes	complemented
112	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
113	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
115	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
116	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
117	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₁₉	—	2	1	no	—
119	C₂²×D₄×C₁₉	—	2	2	no	—
120	C₂²×D₄×C₁₉	—	2	1	no	—
121	C₂²×D₄×C₁₉	D₄	1	2	yes	—
122	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
123	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₉	—	2	1	no	—
126	C₂³×C₄×C₁₉	—	2	2	no	—
127	C₂³×C₄×C₁₉	—	2	1	no	—
128	C₂³×C₄×C₁₉	—	2	2	no	—
129	C₂³×C₄×C₁₉	—	2	1	no	—
130	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#137	—	2	8	no	—
133	C₁₉×#137	—	2	16	no	—
134	C₁₉×#137	—	2	16	no	—
135	C₁₉×#137	—	2	8	no	—
136	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
137	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
138	C₁₉×#135	—	2	16	no	—
139	C₂×Q₁₆×C₁₉	—	2	8	no	—
140	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
141	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	—
142	C₂×SD₁₆×C₁₉	—	2	8	no	—
143	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
144	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
145	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
146	C₂×D₈×C₁₉	C₂³	1	4	yes	—
147	C₂×M₁₆×C₁₉	—	2	4	no	—
148	C₂×M₁₆×C₁₉	—	2	4	no	—
149	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
150	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
151	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
152	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
153	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
154	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
155	C₁₉×C₄⋊Q₈	—	2	2	no	—
156	C₁₉×#127	—	2	2	no	—
157	C₁₉×#124	—	2	2	no	—
158	C₁₉×#124	—	2	2	no	—
159	C₁₉×#123	—	2	4	no	—
160	C₁₉×#123	—	2	4	no	—
161	C₁₉×C₂²⋊Q₈	—	2	4	no	—
162	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
163	C₁₉×#121	—	2	4	no	—
164	C₁₉×#121	—	2	8	no	—
165	C₁₉×#121	C₂³	1	8	yes	—
166	C₁₉×#120	—	2	4	no	—
167	C₁₉×#120	—	2	4	no	—
168	C₄×D₄×C₁₉	—	2	8	no	—
169	C₁₉×#117	—	2	1	no	—
170	C₁₉×#117	—	2	1	no	—
171	C₁₉×#117	C₂³	1	2	yes	—
172	C₁₉×#117	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂×C₄²×C₁₉	—	2	1	no	—
176	C₁₉×#103	C₂³	1	16	yes	—
177	C₁₉×#103	C₂³	1	8	yes	—
178	C₁₉×#102	C₂³	1	8	yes	—
179	C₁₉×C₂²⋊C₈	C₂³	1	16	yes	—
180	C₂⁴×C₁₉	—	2	1	no	—
181	C₂⁴×C₁₉	—	2	1	no	—
182	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
183	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
184	#41×C₁₉	—	2	64	no	—
185	#41×C₁₉	—	2	64	no	—
186	#41×C₁₉	—	2	32	no	—
187	#41×C₁₉	—	2	32	no	—
188	#41×C₁₉	—	2	32	no	—
189	#41×C₁₉	—	2	16	no	—
190	#41×C₁₉	—	2	16	no	—
191	#41×C₁₉	—	2	8	no	—
192	#41×C₁₉	—	2	8	no	—
193	#41×C₁₉	—	2	8	no	—
194	#41×C₁₉	—	2	8	no	—
195	#41×C₁₉	—	2	4	no	—
196	#41×C₁₉	—	2	4	no	—
197	#41×C₁₉	—	2	4	no	—
198	#41×C₁₉	—	2	4	no	—
199	#41×C₁₉	—	2	4	no	—
200	#41×C₁₉	—	2	4	no	—
201	#41×C₁₉	—	2	4	no	—
202	#41×C₁₉	—	2	4	no	—
203	#41×C₁₉	—	2	4	no	—
204	#41×C₁₉	—	2	4	no	—
205	#41×C₁₉	—	4	4	no	—
206	#41×C₁₉	—	4	4	no	—
207	#41×C₁₉	C₂×D₄	1	8	yes	—
208	#41×C₁₉	C₂×D₄	1	8	yes	—
209	C₂×Q₈×C₁₉	—	2	16	no	—
210	C₂×Q₈×C₁₉	—	2	32	no	—
211	C₂×Q₈×C₁₉	—	2	32	no	—
212	C₂×Q₈×C₁₉	—	2	32	no	—
213	C₂×Q₈×C₁₉	—	2	16	no	—
214	C₂×Q₈×C₁₉	—	2	16	no	—
215	C₂×Q₈×C₁₉	—	2	4	no	—
216	C₂×Q₈×C₁₉	—	2	8	no	—
217	C₂×Q₈×C₁₉	—	2	8	no	—
218	C₂×Q₈×C₁₉	—	2	8	no	—
219	C₂×Q₈×C₁₉	—	2	2	no	—
220	C₂×Q₈×C₁₉	—	2	4	no	—
221	C₂×Q₈×C₁₉	—	2	8	no	—
222	C₂×Q₈×C₁₉	—	2	2	no	—
223	C₂×Q₈×C₁₉	—	2	1	no	—
224	C₂×Q₈×C₁₉	—	2	2	no	—
225	C₂×Q₈×C₁₉	—	2	2	no	—
226	C₂×Q₈×C₁₉	—	2	4	no	—
227	C₂×Q₈×C₁₉	—	2	4	no	—
228	C₂×Q₈×C₁₉	—	2	1	no	—
229	C₂×Q₈×C₁₉	—	2	2	no	—
230	C₂×Q₈×C₁₉	—	2	2	no	—
231	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
232	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
233	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
234	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
235	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
236	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
237	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
240	C₂×D₄×C₁₉	—	2	16	no	—
241	C₂×D₄×C₁₉	—	2	8	no	—
242	C₂×D₄×C₁₉	—	2	8	no	—
243	C₂×D₄×C₁₉	—	2	8	no	—
244	C₂×D₄×C₁₉	—	2	2	no	—
245	C₂×D₄×C₁₉	—	2	2	no	—
246	C₂×D₄×C₁₉	—	2	2	no	—
247	C₂×D₄×C₁₉	—	2	2	no	—
248	C₂×D₄×C₁₉	—	2	8	no	—
249	C₂×D₄×C₁₉	—	2	4	no	—
250	C₂×D₄×C₁₉	—	2	1	no	—
251	C₂×D₄×C₁₉	—	2	2	no	—
252	C₂×D₄×C₁₉	—	2	2	no	—
253	C₂×D₄×C₁₉	—	2	2	no	—
254	C₂×D₄×C₁₉	—	2	1	no	—
255	C₂×D₄×C₁₉	—	4	4	no	—
256	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
257	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
258	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
261	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
262	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₉	—	2	16	no	—
264	C₂²×C₄×C₁₉	—	2	16	no	—
265	C₂²×C₄×C₁₉	—	2	8	no	—
266	C₂²×C₄×C₁₉	—	2	2	no	—
267	C₂²×C₄×C₁₉	—	2	1	no	—
268	C₂²×C₄×C₁₉	—	2	8	no	—
269	C₂²×C₄×C₁₉	—	2	2	no	—
270	C₂²×C₄×C₁₉	—	2	2	no	—
271	C₂²×C₄×C₁₉	—	2	8	no	—
272	C₂²×C₄×C₁₉	—	2	8	no	—
273	C₂²×C₄×C₁₉	—	2	2	no	—
274	C₂²×C₄×C₁₉	—	2	2	no	—
275	C₂²×C₄×C₁₉	—	2	4	no	—
276	C₂²×C₄×C₁₉	—	2	4	no	—
277	C₂²×C₄×C₁₉	—	2	1	no	—
278	C₂²×C₄×C₁₉	—	2	2	no	—
279	C₂²×C₄×C₁₉	—	2	2	no	—
280	C₂²×C₄×C₁₉	—	2	2	no	—
281	C₂²×C₄×C₁₉	—	4	4	no	—
282	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
283	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
288	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
289	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
293	Q₁₆×C₁₉	—	2	16	no	—
294	Q₁₆×C₁₉	—	2	8	no	—
295	SD₁₆×C₁₉	—	2	16	no	—
296	SD₁₆×C₁₉	—	2	8	no	—
297	SD₁₆×C₁₉	—	2	8	no	—
298	D₈×C₁₉	—	2	8	no	—
299	M₁₆×C₁₉	—	2	4	no	—
300	M₁₆×C₁₉	—	2	4	no	—
301	M₁₆×C₁₉	—	2	4	no	—
302	M₁₆×C₁₉	—	2	4	no	—
303	C₂×C₈×C₁₉	—	2	4	no	—
304	C₂×C₈×C₁₉	—	2	4	no	—
305	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
306	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₁₉	—	2	2	no	—
308	C₄⋊C₄×C₁₉	—	2	8	no	—
309	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
310	C₂²⋊C₄×C₁₉	—	2	2	no	—
311	C₂²⋊C₄×C₁₉	—	2	2	no	—
312	C₂²⋊C₄×C₁₉	—	2	8	no	—
313	C₂²⋊C₄×C₁₉	—	2	8	no	—
314	C₄²×C₁₉	—	2	2	no	—
315	C₄²×C₁₉	—	2	2	no	—
316	#60368	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂³×C₁₉	—	2	4	no	—
318	C₂³×C₁₉	—	2	4	no	—
319	C₂³×C₁₉	—	2	2	no	—
320	C₂³×C₁₉	—	2	2	no	—
321	C₂³×C₁₉	—	4	2	no	—
322	C₂³×C₁₉	—	4	4	no	—
323	C₂³×C₁₉	—	4	4	no	—
324	C₂³×C₁₉	—	4	2	no	—
325	C₂³×C₁₉	—	8	2	no	—
326	C₂³×C₁₉	#120	1	4	yes	—
327	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
328	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
329	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
330	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₁₉	—	2	32	no	—
332	Q₈×C₁₉	—	2	4	no	—
333	Q₈×C₁₉	—	2	8	no	—
334	Q₈×C₁₉	—	2	8	no	—
335	Q₈×C₁₉	—	2	8	no	—
336	Q₈×C₁₉	—	2	4	no	—
337	Q₈×C₁₉	—	2	4	no	—
338	Q₈×C₁₉	—	2	2	no	—
339	Q₈×C₁₉	—	2	4	no	—
340	Q₈×C₁₉	—	2	2	no	—
341	Q₈×C₁₉	—	2	2	no	—
342	Q₈×C₁₉	—	4	2	no	—
343	Q₈×C₁₉	C₂²×D₄	1	4	yes	—
344	Q₈×C₁₉	C₂²×D₄	1	8	yes	—
345	D₄×C₁₉	—	2	32	no	—
346	D₄×C₁₉	—	2	8	no	—
347	D₄×C₁₉	—	2	8	no	—
348	D₄×C₁₉	—	2	8	no	—
349	D₄×C₁₉	—	2	8	no	—
350	D₄×C₁₉	—	2	4	no	—
351	D₄×C₁₉	—	2	4	no	—
352	D₄×C₁₉	—	2	4	no	—
353	D₄×C₁₉	—	2	2	no	—
354	D₄×C₁₉	—	2	2	no	—
355	D₄×C₁₉	—	2	2	no	—
356	D₄×C₁₉	—	4	4	no	—
357	D₄×C₁₉	—	4	4	no	—
358	D₄×C₁₉	—	4	2	no	—
359	D₄×C₁₉	—	8	8	no	—
360	D₄×C₁₉	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₁₉	—	2	32	no	—
362	C₂×C₄×C₁₉	—	2	32	no	—
363	C₂×C₄×C₁₉	—	2	8	no	—
364	C₂×C₄×C₁₉	—	2	4	no	—
365	C₂×C₄×C₁₉	—	2	4	no	—
366	C₂×C₄×C₁₉	—	2	8	no	—
367	C₂×C₄×C₁₉	—	2	8	no	—
368	C₂×C₄×C₁₉	—	2	4	no	—
369	C₂×C₄×C₁₉	—	2	2	no	—
370	C₂×C₄×C₁₉	—	2	8	no	—
371	C₂×C₄×C₁₉	—	2	8	no	—
372	C₂×C₄×C₁₉	—	2	8	no	—
373	C₂×C₄×C₁₉	—	2	4	no	—
374	C₂×C₄×C₁₉	—	2	4	no	—
375	C₂×C₄×C₁₉	—	2	4	no	—
376	C₂×C₄×C₁₉	—	2	2	no	—
377	C₂×C₄×C₁₉	—	4	2	no	—
378	C₂×C₄×C₁₉	—	4	4	no	—
379	C₂×C₄×C₁₉	—	4	4	no	—
380	C₂×C₄×C₁₉	—	8	2	no	—
381	C₂×C₄×C₁₉	#120	1	4	yes	—
382	C₂×C₄×C₁₉	#120	1	4	yes	—
383	C₂×C₄×C₁₉	#120	1	4	yes	—
384	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
395	C₈×C₁₉	—	2	4	no	—
396	C₈×C₁₉	—	2	4	no	—
397	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic, complemented
398	C₂×#575	C₂×C₁₉	1	1	yes	characteristic, complemented
399	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
400	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
401	#3013	C₂×C₁₉	1	8	yes	complemented
402	#3011	C₂×C₁₉	1	4	yes	complemented
403	#3010	C₂×C₁₉	1	4	yes	complemented
404	#3005	C₂×C₁₉	1	4	yes	complemented
405	#3004	C₂×C₁₉	1	4	yes	complemented
406	#2896	C₂×C₁₉	1	1	yes	characteristic, complemented
407	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
408	#2879	C₂×C₁₉	1	1	yes	characteristic, complemented
409	C₂²×C₁₉	—	2	2	no	—
410	C₂²×C₁₉	—	2	2	no	—
411	C₂²×C₁₉	—	2	2	no	—
412	C₂²×C₁₉	—	2	8	no	—
413	C₂²×C₁₉	—	2	4	no	—
414	C₂²×C₁₉	—	2	4	no	—
415	C₂²×C₁₉	—	4	4	no	—
416	C₂²×C₁₉	—	4	8	no	—
417	C₂²×C₁₉	—	4	8	no	—
418	C₂²×C₁₉	—	4	4	no	—
419	C₂²×C₁₉	—	4	4	no	—
420	C₂²×C₁₉	—	4	2	no	—
421	C₂²×C₁₉	—	8	4	no	—
422	C₂²×C₁₉	C₂×#120	1	2	yes	—
423	C₂²×C₁₉	C₂×#120	1	2	yes	—
424	C₂²×C₁₉	C₂×#120	1	2	yes	—
425	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₁₉	—	2	8	no	—
427	C₄×C₁₉	—	2	4	no	—
428	C₄×C₁₉	—	2	4	no	—
429	C₄×C₁₉	—	4	4	no	—
430	C₄×C₁₉	—	4	2	no	—
431	C₄×C₁₉	C₂×#120	1	2	yes	—
432	C₄×C₁₉	C₂×#120	1	2	yes	—
433	C₄×C₁₉	C₂×#120	1	2	yes	—
434	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
436	C₂×2₋¹⁺⁴	—	2	2	no	—
437	C₂×2₋¹⁺⁴	—	2	2	no	—
438	C₂×2₋¹⁺⁴	—	2	8	no	—
439	C₂×2₋¹⁺⁴	—	2	8	no	—
440	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	—
441	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	complemented
442	C₂²×#41	—	2	2	no	—
443	C₂²×#41	—	2	1	no	—
444	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
445	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
446	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
447	C₂²×#41	C₂²×C₁₉	1	2	yes	complemented
448	C₂³×Q₈	—	2	1	no	—
449	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
450	C₂³×Q₈	C₂²×C₁₉	1	2	yes	complemented
451	#575	—	2	8	no	—
452	C₂×#137	—	2	8	no	—
453	C₂×#137	C₂²×C₁₉	1	2	yes	—
454	C₂×#137	C₂²×C₁₉	1	4	yes	—
455	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
456	C₂×#137	C₂²×C₁₉	1	4	yes	complemented
457	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
458	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
459	C₂×#135	C₂²×C₁₉	1	4	yes	complemented
460	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
461	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
462	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
463	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
464	#537	C₂²×C₁₉	1	4	yes	complemented
465	#536	—	2	1	no	—
466	#536	C₂²×C₁₉	1	2	yes	complemented
467	#535	—	2	1	no	—
468	#535	C₂²×C₁₉	1	2	yes	complemented
469	#534	—	2	2	no	—
470	#532	—	2	2	no	—
471	#525	—	2	2	no	—
472	#525	C₂²×C₁₉	1	4	yes	—
473	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
474	#452	C₂²×C₁₉	1	16	yes	complemented
475	#451	C₂²×C₁₉	1	16	yes	complemented
476	#449	C₂²×C₁₉	1	16	yes	complemented
477	#448	C₂²×C₁₉	1	16	yes	complemented
478	#419	C₂²×C₁₉	1	4	yes	complemented
479	#419	C₂²×C₁₉	1	4	yes	complemented
480	#419	C₂²×C₁₉	1	2	yes	complemented
481	#418	C₂²×C₁₉	1	2	yes	complemented
482	#417	C₂²×C₁₉	1	4	yes	complemented
483	#416	C₂²×C₁₉	1	4	yes	complemented
484	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
485	#408	C₂²×C₁₉	1	4	yes	complemented
486	#408	C₂²×C₁₉	1	4	yes	complemented
487	#407	C₂²×C₁₉	1	4	yes	complemented
488	C₂×C₁₉	—	2	2	no	—
489	C₂×C₁₉	—	2	2	no	—
490	C₂×C₁₉	—	2	2	no	—
491	C₂×C₁₉	—	4	4	no	—
492	C₂×C₁₉	—	4	4	no	—
493	C₂×C₁₉	—	8	2	no	—
494	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
495	C₂×C₁₉	#3586	1	2	yes	—
496	2₋¹⁺⁴	—	2	32	no	—
497	2₋¹⁺⁴	—	2	32	no	—
498	2₋¹⁺⁴	—	2	16	no	—
499	2₋¹⁺⁴	—	2	16	no	—
500	2₋¹⁺⁴	—	2	16	no	—
501	2₋¹⁺⁴	—	2	16	no	—
502	C₂×#41	—	2	32	no	—
503	C₂×#41	—	2	16	no	—
504	C₂×#41	—	2	8	no	—
505	C₂×#41	—	2	8	no	—
506	C₂×#41	—	2	4	no	—
507	C₂×#41	—	2	4	no	—
508	C₂×#41	—	2	8	no	—
509	C₂×#41	—	2	8	no	—
510	C₂×#41	—	2	4	no	—
511	C₂×#41	—	2	1	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	—	2	4	no	—
514	C₂×#41	—	2	4	no	—
515	C₂×#41	—	2	4	no	—
516	C₂×#41	—	2	1	no	—
517	C₂×#41	—	2	1	no	—
518	C₂×#41	—	2	4	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	D₄×C₁₉	1	2	yes	—
521	C₂×#41	D₄×C₁₉	1	2	yes	—
522	C₂×#41	D₄×C₁₉	1	8	yes	complemented
523	C₂×#41	C₂³×C₁₉	1	2	yes	—
524	C₂×#41	C₂³×C₁₉	1	2	yes	—
525	C₂×#41	C₂³×C₁₉	1	8	yes	—
526	C₂×#41	C₂³×C₁₉	1	2	yes	—
527	C₂×#41	C₂³×C₁₉	1	2	yes	—
528	C₂×#41	C₂³×C₁₉	1	2	yes	—
529	C₂×#41	C₂³×C₁₉	1	2	yes	—
530	C₂²×Q₈	—	2	16	no	—
531	C₂²×Q₈	—	2	4	no	—
532	C₂²×Q₈	—	2	4	no	—
533	C₂²×Q₈	—	2	8	no	—
534	C₂²×Q₈	—	2	8	no	—
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	—	2	2	no	—
537	C₂²×Q₈	—	2	4	no	—
538	C₂²×Q₈	—	2	1	no	—
539	C₂²×Q₈	—	2	1	no	—
540	C₂²×Q₈	—	2	4	no	—
541	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
542	C₂²×Q₈	D₄×C₁₉	1	8	yes	complemented
543	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
545	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
546	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
547	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
548	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	2	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	D₄×C₁₉	1	2	yes	—
553	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
556	C₂³×C₄	—	2	1	no	—
557	C₂³×C₄	—	2	2	no	—
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	—	2	2	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
562	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
563	#137	—	2	8	no	—
564	#137	—	2	16	no	—
565	#137	—	2	16	no	—
566	#137	—	2	8	no	—
567	AGL(1,ℤ/8)	—	2	8	no	—
568	AGL(1,ℤ/8)	—	2	8	no	—
569	#135	—	2	16	no	—
570	C₂×Q₁₆	—	2	8	no	—
571	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	—
572	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
573	C₂×SD₁₆	—	2	8	no	—
574	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
575	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
576	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
577	C₂×D₈	C₂³×C₁₉	1	4	yes	—
578	C₂×M₁₆	—	2	4	no	—
579	C₂×M₁₆	—	2	4	no	—
580	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
581	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
582	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
583	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
584	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
585	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
586	C₄⋊Q₈	—	2	2	no	—
587	#127	—	2	2	no	—
588	#124	—	2	2	no	—
589	#124	—	2	2	no	—
590	#123	—	2	4	no	—
591	#123	—	2	4	no	—
592	C₂²⋊Q₈	—	2	4	no	—
593	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
594	#121	—	2	4	no	—
595	#121	—	2	8	no	—
596	#121	C₂³×C₁₉	1	8	yes	—
597	#120	—	2	4	no	—
598	#120	—	2	4	no	—
599	C₄×D₄	—	2	8	no	—
600	#117	—	2	1	no	—
601	#117	—	2	1	no	—
602	#117	C₂³×C₁₉	1	2	yes	—
603	#117	C₂³×C₁₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₄²	—	2	1	no	—
607	#103	C₂³×C₁₉	1	16	yes	—
608	#103	C₂³×C₁₉	1	8	yes	—
609	#102	C₂³×C₁₉	1	8	yes	—
610	C₂²⋊C₈	C₂³×C₁₉	1	16	yes	—
611	C₁₉	#60368	1	1	yes	characteristic, direct product factor, Sylow
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	1	no	—
614	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
615	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
616	#41	—	2	64	no	—
617	#41	—	2	64	no	—
618	#41	—	2	32	no	—
619	#41	—	2	32	no	—
620	#41	—	2	32	no	—
621	#41	—	2	16	no	—
622	#41	—	2	16	no	—
623	#41	—	2	8	no	—
624	#41	—	2	8	no	—
625	#41	—	2	8	no	—
626	#41	—	2	8	no	—
627	#41	—	2	4	no	—
628	#41	—	2	4	no	—
629	#41	—	2	4	no	—
630	#41	—	2	4	no	—
631	#41	—	2	4	no	—
632	#41	—	2	4	no	—
633	#41	—	2	4	no	—
634	#41	—	2	4	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	4	4	no	—
638	#41	—	4	4	no	—
639	#41	C₂×D₄×C₁₉	1	8	yes	—
640	#41	C₂×D₄×C₁₉	1	8	yes	—
641	C₂×Q₈	—	2	16	no	—
642	C₂×Q₈	—	2	32	no	—
643	C₂×Q₈	—	2	32	no	—
644	C₂×Q₈	—	2	32	no	—
645	C₂×Q₈	—	2	16	no	—
646	C₂×Q₈	—	2	16	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	2	8	no	—
649	C₂×Q₈	—	2	8	no	—
650	C₂×Q₈	—	2	8	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	8	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	4	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
664	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
665	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
666	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
667	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
668	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
669	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
670	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
672	C₂×D₄	—	2	16	no	—
673	C₂×D₄	—	2	8	no	—
674	C₂×D₄	—	2	8	no	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
689	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
690	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
692	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
693	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
694	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
695	C₂²×C₄	—	2	16	no	—
696	C₂²×C₄	—	2	16	no	—
697	C₂²×C₄	—	2	8	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	8	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	8	no	—
704	C₂²×C₄	—	2	8	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	4	4	no	—
714	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
715	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
716	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
720	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
721	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
722	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
725	Q₁₆	—	2	16	no	—
726	Q₁₆	—	2	8	no	—
727	SD₁₆	—	2	16	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	2	8	no	—
730	D₈	—	2	8	no	—
731	M₁₆	—	2	4	no	—
732	M₁₆	—	2	4	no	—
733	M₁₆	—	2	4	no	—
734	M₁₆	—	2	4	no	—
735	C₂×C₈	—	2	4	no	—
736	C₂×C₈	—	2	4	no	—
737	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
738	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	8	no	—
741	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	8	no	—
745	C₂²⋊C₄	—	2	8	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₂³	—	2	4	no	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	4	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	8	2	no	—
757	C₂³	C₁₉×#120	1	4	yes	—
758	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
759	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
760	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
761	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
762	Q₈	—	2	32	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	2	8	no	—
765	Q₈	—	2	8	no	—
766	Q₈	—	2	8	no	—
767	Q₈	—	2	4	no	—
768	Q₈	—	2	4	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	4	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	C₂²×D₄×C₁₉	1	4	yes	—
775	Q₈	C₂²×D₄×C₁₉	1	8	yes	—
776	D₄	—	2	32	no	—
777	D₄	—	2	8	no	—
778	D₄	—	2	8	no	—
779	D₄	—	2	8	no	—
780	D₄	—	2	8	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	2	no	—
790	D₄	—	8	8	no	—
791	D₄	C₂²×D₄×C₁₉	1	4	yes	—
792	C₂×C₄	—	2	32	no	—
793	C₂×C₄	—	2	32	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	2	8	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	8	2	no	—
812	C₂×C₄	C₁₉×#120	1	4	yes	—
813	C₂×C₄	C₁₉×#120	1	4	yes	—
814	C₂×C₄	C₁₉×#120	1	4	yes	—
815	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
816	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
825	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
826	C₈	—	2	4	no	—
827	C₈	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	8	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	8	no	—
836	C₂²	—	4	8	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	8	4	no	—
841	C₂²	C₂×C₁₉×#120	1	2	yes	—
842	C₂²	C₂×C₁₉×#120	1	2	yes	—
843	C₂²	C₂×C₁₉×#120	1	2	yes	—
844	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
845	C₄	—	2	8	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	4	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	4	no	—
850	C₄	C₂×C₁₉×#120	1	2	yes	—
851	C₄	C₂×C₁₉×#120	1	2	yes	—
852	C₄	C₂×C₁₉×#120	1	2	yes	—
853	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
854	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
855	C₂	—	2	2	no	—
856	C₂	—	2	2	no	—
857	C₂	—	2	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	4	4	no	—
860	C₂	—	8	2	no	—
861	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic
862	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×2₋¹⁺⁴	C₂	semidirect
2. C₂×C₁₉×#575	C₂	semidirect
3. C₂²×C₁₉×#137	C₂	semidirect
4. C₁₉×#3449	C₂	semidirect
5. C₁₉×#3013	C₂	semidirect
6. C₁₉×#3011	C₂	semidirect
7. C₁₉×#3010	C₂	semidirect
8. C₁₉×#3005	C₂	semidirect
9. C₁₉×#3004	C₂	semidirect
10. C₁₉×#2896	C₂	semidirect
11. C₂×C₁₉×#419	C₂	semidirect
12. C₁₉×#2879	C₂	semidirect
18. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
24. C₂²×#41×C₁₉	C₂²	semidirect
27. C₂³×Q₈×C₁₉	C₂²	semidirect
32. C₂×C₁₉×#137	C₂²	semidirect
33. C₂×C₁₉×#137	C₂²	semidirect
35. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×C₁₉×#135	C₂²	semidirect
37. C₂²×Q₁₆×C₁₉	C₂²	semidirect
38. C₂²×SD₁₆×C₁₉	C₂²	semidirect
41. C₁₉×#537	C₂²	semidirect
43. C₁₉×#536	C₂²	semidirect
45. C₁₉×#535	C₂²	semidirect
51. C₁₉×#452	C₂²	semidirect
52. C₁₉×#451	C₂²	semidirect
53. C₁₉×#449	C₂²	semidirect
54. C₁₉×#448	C₂²	semidirect
55. C₁₉×#419	C₂²	semidirect
56. C₁₉×#419	C₂²	semidirect
57. C₁₉×#419	C₂²	semidirect
58. C₁₉×#418	C₂²	semidirect
59. C₁₉×#417	C₂²	semidirect
60. C₁₉×#416	C₂²	semidirect
61. C₂×C₁₉×#103	C₂²	semidirect
62. C₁₉×#408	C₂²	semidirect
63. C₁₉×#408	C₂²	semidirect
64. C₁₉×#407	C₂²	semidirect
91. C₂×#41×C₁₉	D₄	semidirect
111. C₂²×Q₈×C₁₉	D₄	semidirect
316. #60368	C₁₉	direct (N × H)
397. C₂²×2₋¹⁺⁴	C₂×C₁₉	semidirect
398. C₂×#575	C₂×C₁₉	semidirect
399. C₂²×#137	C₂×C₁₉	semidirect
400. #3449	C₂×C₁₉	semidirect
401. #3013	C₂×C₁₉	semidirect
402. #3011	C₂×C₁₉	semidirect
403. #3010	C₂×C₁₉	semidirect
404. #3005	C₂×C₁₉	semidirect
405. #3004	C₂×C₁₉	semidirect
406. #2896	C₂×C₁₉	semidirect
407. C₂×#419	C₂×C₁₉	semidirect
408. #2879	C₂×C₁₉	semidirect
441. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
447. C₂²×#41	C₂²×C₁₉	semidirect
450. C₂³×Q₈	C₂²×C₁₉	semidirect
455. C₂×#137	C₂²×C₁₉	semidirect
456. C₂×#137	C₂²×C₁₉	semidirect
458. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
459. C₂×#135	C₂²×C₁₉	semidirect
460. C₂²×Q₁₆	C₂²×C₁₉	semidirect
461. C₂²×SD₁₆	C₂²×C₁₉	semidirect
464. #537	C₂²×C₁₉	semidirect
466. #536	C₂²×C₁₉	semidirect
468. #535	C₂²×C₁₉	semidirect
474. #452	C₂²×C₁₉	semidirect
475. #451	C₂²×C₁₉	semidirect
476. #449	C₂²×C₁₉	semidirect
477. #448	C₂²×C₁₉	semidirect
478. #419	C₂²×C₁₉	semidirect
479. #419	C₂²×C₁₉	semidirect
480. #419	C₂²×C₁₉	semidirect
481. #418	C₂²×C₁₉	semidirect
482. #417	C₂²×C₁₉	semidirect
483. #416	C₂²×C₁₉	semidirect
484. C₂×#103	C₂²×C₁₉	semidirect
485. #408	C₂²×C₁₉	semidirect
486. #408	C₂²×C₁₉	semidirect
487. #407	C₂²×C₁₉	semidirect
522. C₂×#41	D₄×C₁₉	semidirect
542. C₂²×Q₈	D₄×C₁₉	semidirect
611. C₁₉	#60368	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×2₋¹⁺⁴	2
C₂×C₁₉×#575	2
C₂²×C₁₉×#137	2
C₁₉×#3449	2
C₁₉×#3013	2
C₁₉×#3011	2
C₁₉×#3010	2
C₁₉×#3005	2
C₁₉×#3004	2
C₁₉×#2896	2
C₂×C₁₉×#419	2
C₁₉×#2879	2
#60368	19

Subgroups — C19×#60368 #18066327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60368 #18066327