Subgroups — C₁₉×#60422 #18066381

Order 4864.

2714 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3046	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3045	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3044	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3043	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3042	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3041	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3035	C₂	1	8	yes	maximal, complemented
12	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#575	—	2	8	no	—
19	C₂×C₁₉×#137	C₂²	1	2	yes	—
20	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#135	—	2	8	no	—
24	C₂×C₁₉×#135	C₂²	1	4	yes	—
25	C₂×C₁₉×#135	C₂²	1	4	yes	complemented
26	C₂×C₁₉×#135	C₂²	1	4	yes	complemented
27	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#537	—	2	2	no	—
34	C₁₉×#536	C₂²	1	2	yes	—
35	C₁₉×#536	C₂²	1	2	yes	complemented
36	C₁₉×#535	C₂²	1	2	yes	—
37	C₁₉×#535	C₂²	1	2	yes	complemented
38	C₁₉×#534	—	2	2	no	—
39	C₁₉×#532	C₂²	1	4	yes	complemented
40	C₁₉×#525	—	2	2	no	—
41	C₁₉×#525	—	2	2	no	—
42	C₁₉×#520	—	2	2	no	—
43	C₁₉×#520	C₂²	1	4	yes	complemented
44	C₁₉×#519	C₂²	1	2	yes	complemented
45	C₁₉×#518	—	2	2	no	—
46	C₁₉×#518	C₂²	1	2	yes	complemented
47	C₄×#41×C₁₉	—	2	2	no	—
48	C₄×#41×C₁₉	C₂²	1	4	yes	complemented
49	C₂×C₁₉×#117	—	2	2	no	—
50	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
52	C₁₉×#464	C₂²	1	8	yes	complemented
53	C₁₉×#464	C₂²	1	8	yes	complemented
54	C₁₉×#463	C₂²	1	8	yes	complemented
55	C₁₉×#463	C₂²	1	8	yes	complemented
56	C₁₉×#462	C₂²	1	8	yes	complemented
57	C₁₉×#461	C₂²	1	8	yes	complemented
58	C₁₉×#460	C₂²	1	8	yes	complemented
59	C₁₉×#459	C₂²	1	8	yes	complemented
60	C₁₉×#424	C₂²	1	2	yes	complemented
61	C₁₉×#424	C₂²	1	2	yes	complemented
62	C₁₉×#424	C₂²	1	4	yes	complemented
63	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	complemented
64	C₁₉×#419	C₂²	1	2	yes	complemented
65	C₁₉×#418	C₂²	1	2	yes	complemented
66	C₁₉×#417	C₂²	1	4	yes	complemented
67	C₁₉×#416	C₂²	1	2	yes	—
68	C₁₉×#416	C₂²	1	2	yes	—
69	C₁₉×#416	C₂²	1	4	yes	complemented
70	C₁₉×#416	C₂²	1	4	yes	complemented
71	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
72	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
73	C₂×#41×C₁₉	—	2	1	no	—
74	C₂×#41×C₁₉	—	2	1	no	—
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×#41×C₁₉	—	2	1	no	—
77	C₂×#41×C₁₉	—	2	1	no	—
78	C₂×#41×C₁₉	—	2	1	no	—
79	C₂×#41×C₁₉	—	2	4	no	—
80	C₂×#41×C₁₉	—	2	4	no	—
81	C₂×#41×C₁₉	—	2	4	no	—
82	C₂×#41×C₁₉	—	2	4	no	—
83	C₂×#41×C₁₉	—	2	4	no	—
84	C₂×#41×C₁₉	D₄	1	8	yes	complemented
85	C₂×#41×C₁₉	C₂³	1	2	yes	—
86	C₂×#41×C₁₉	C₂³	1	2	yes	—
87	C₂×#41×C₁₉	C₂³	1	2	yes	—
88	C₂×#41×C₁₉	C₂³	1	2	yes	—
89	C₂×#41×C₁₉	C₂³	1	2	yes	—
90	C₂×#41×C₁₉	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₉	—	2	1	no	—
95	C₂²×D₄×C₁₉	—	2	1	no	—
96	C₂²×D₄×C₁₉	—	2	1	no	—
97	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₉	—	2	1	no	—
101	C₂³×C₄×C₁₉	—	2	1	no	—
102	C₂³×C₄×C₁₉	—	2	1	no	—
103	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#137	—	2	8	no	—
105	C₁₉×#137	—	2	8	no	—
106	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
107	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
108	C₁₉×#135	—	2	16	no	—
109	C₁₉×#135	—	2	16	no	—
110	C₁₉×#135	—	2	16	no	—
111	C₂×Q₁₆×C₁₉	—	2	4	no	—
112	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₁₉	—	2	4	no	—
115	C₂×SD₁₆×C₁₉	—	2	4	no	—
116	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
120	C₂×D₈×C₁₉	—	2	4	no	—
121	C₂×D₈×C₁₉	C₂³	1	4	yes	—
122	C₂×D₈×C₁₉	C₂³	1	4	yes	—
123	C₂×M₁₆×C₁₉	—	2	4	no	—
124	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
125	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
126	C₂²×C₈×C₁₉	—	2	4	no	—
127	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
131	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
132	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₁₉×#127	C₂³	1	4	yes	—
134	C₁₉×#124	C₂³	1	4	yes	—
135	C₁₉×#124	C₂³	1	4	yes	—
136	C₁₉×#123	—	2	4	no	—
137	C₁₉×#123	—	2	4	no	—
138	C₁₉×C₂²⋊Q₈	—	2	4	no	—
139	C₁₉×C₂²⋊Q₈	—	2	4	no	—
140	C₁₉×#121	—	2	8	no	—
141	C₁₉×#121	—	2	4	no	—
142	C₁₉×#121	—	2	4	no	—
143	C₁₉×#120	—	2	4	no	—
144	C₁₉×#120	—	2	4	no	—
145	C₄×Q₈×C₁₉	—	2	4	no	—
146	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
147	C₄×D₄×C₁₉	—	2	8	no	—
148	C₄×D₄×C₁₉	—	2	4	no	—
149	C₄×D₄×C₁₉	—	2	8	no	—
150	C₄×D₄×C₁₉	—	2	8	no	—
151	C₄×D₄×C₁₉	C₂³	1	8	yes	—
152	C₁₉×#117	—	2	1	no	—
153	C₁₉×#117	—	2	1	no	—
154	C₁₉×#117	—	2	4	no	—
155	C₁₉×#117	—	2	4	no	—
156	C₁₉×#117	—	2	4	no	—
157	C₁₉×#117	D₄	1	2	yes	—
158	C₁₉×#117	D₄	1	2	yes	—
159	C₁₉×#117	C₂³	1	2	yes	—
160	C₁₉×#117	C₂³	1	2	yes	—
161	C₁₉×#117	C₂³	1	2	yes	—
162	C₁₉×#117	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
168	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
169	C₂×C₄²×C₁₉	—	2	1	no	—
170	C₂×C₄²×C₁₉	—	2	4	no	—
171	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
172	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
173	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
174	C₁₉×#103	C₂³	1	4	yes	—
175	C₁₉×#103	C₂³	1	4	yes	—
176	C₁₉×#103	C₂³	1	8	yes	—
177	C₁₉×#102	C₂³	1	4	yes	—
178	C₁₉×#102	C₂³	1	4	yes	—
179	C₁₉×#102	C₂³	1	8	yes	—
180	C₂⁴×C₁₉	—	2	1	no	—
181	C₂⁴×C₁₉	—	2	1	no	—
182	C₂⁴×C₁₉	—	2	1	no	—
183	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
184	#41×C₁₉	—	2	8	no	—
185	#41×C₁₉	—	2	8	no	—
186	#41×C₁₉	—	2	4	no	—
187	#41×C₁₉	—	2	4	no	—
188	#41×C₁₉	—	2	4	no	—
189	#41×C₁₉	—	2	4	no	—
190	#41×C₁₉	—	2	4	no	—
191	#41×C₁₉	—	2	4	no	—
192	#41×C₁₉	—	2	4	no	—
193	#41×C₁₉	—	2	4	no	—
194	#41×C₁₉	—	2	4	no	—
195	#41×C₁₉	—	2	4	no	—
196	#41×C₁₉	—	4	4	no	—
197	#41×C₁₉	—	4	4	no	—
198	#41×C₁₉	—	4	4	no	—
199	#41×C₁₉	—	4	4	no	—
200	#41×C₁₉	C₂×D₄	1	8	yes	—
201	#41×C₁₉	C₂×D₄	1	8	yes	—
202	C₂×Q₈×C₁₉	—	2	1	no	—
203	C₂×Q₈×C₁₉	—	2	1	no	—
204	C₂×Q₈×C₁₉	—	2	1	no	—
205	C₂×Q₈×C₁₉	—	2	2	no	—
206	C₂×Q₈×C₁₉	—	2	2	no	—
207	C₂×Q₈×C₁₉	—	2	2	no	—
208	C₂×Q₈×C₁₉	—	2	2	no	—
209	C₂×Q₈×C₁₉	—	2	2	no	—
210	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
211	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
213	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
214	C₂×D₄×C₁₉	—	2	8	no	—
215	C₂×D₄×C₁₉	—	2	2	no	—
216	C₂×D₄×C₁₉	—	2	2	no	—
217	C₂×D₄×C₁₉	—	2	2	no	—
218	C₂×D₄×C₁₉	—	2	2	no	—
219	C₂×D₄×C₁₉	—	2	2	no	—
220	C₂×D₄×C₁₉	—	2	2	no	—
221	C₂×D₄×C₁₉	—	2	1	no	—
222	C₂×D₄×C₁₉	—	2	2	no	—
223	C₂×D₄×C₁₉	—	2	2	no	—
224	C₂×D₄×C₁₉	—	2	1	no	—
225	C₂×D₄×C₁₉	—	2	1	no	—
226	C₂×D₄×C₁₉	—	2	8	no	—
227	C₂×D₄×C₁₉	—	2	2	no	—
228	C₂×D₄×C₁₉	—	2	2	no	—
229	C₂×D₄×C₁₉	—	2	2	no	—
230	C₂×D₄×C₁₉	—	4	4	no	—
231	C₂×D₄×C₁₉	—	4	4	no	—
232	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
233	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
234	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₉	—	2	1	no	—
237	C₂²×C₄×C₁₉	—	2	8	no	—
238	C₂²×C₄×C₁₉	—	2	2	no	—
239	C₂²×C₄×C₁₉	—	2	2	no	—
240	C₂²×C₄×C₁₉	—	2	1	no	—
241	C₂²×C₄×C₁₉	—	2	1	no	—
242	C₂²×C₄×C₁₉	—	2	2	no	—
243	C₂²×C₄×C₁₉	—	2	2	no	—
244	C₂²×C₄×C₁₉	—	2	2	no	—
245	C₂²×C₄×C₁₉	—	2	2	no	—
246	C₂²×C₄×C₁₉	—	2	2	no	—
247	C₂²×C₄×C₁₉	—	2	8	no	—
248	C₂²×C₄×C₁₉	—	4	4	no	—
249	C₂²×C₄×C₁₉	—	4	4	no	—
250	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
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	1	yes	characteristic
254	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
255	C₂²×C₄×C₁₉	#41	1	4	yes	—
256	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₁₉	—	2	8	no	—
260	Q₁₆×C₁₉	—	2	8	no	—
261	SD₁₆×C₁₉	—	2	8	no	—
262	SD₁₆×C₁₉	—	2	8	no	—
263	SD₁₆×C₁₉	—	2	8	no	—
264	SD₁₆×C₁₉	—	2	8	no	—
265	D₈×C₁₉	—	2	8	no	—
266	D₈×C₁₉	—	2	8	no	—
267	M₁₆×C₁₉	—	2	4	no	—
268	M₁₆×C₁₉	—	2	4	no	—
269	C₂×C₈×C₁₉	—	2	2	no	—
270	C₂×C₈×C₁₉	—	2	2	no	—
271	C₂×C₈×C₁₉	—	2	4	no	—
272	C₂×C₈×C₁₉	—	2	4	no	—
273	C₂×C₈×C₁₉	—	2	4	no	—
274	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₁₉	—	2	2	no	—
278	C₄⋊C₄×C₁₉	—	2	8	no	—
279	C₄⋊C₄×C₁₉	—	2	8	no	—
280	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
282	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
283	C₂²⋊C₄×C₁₉	—	2	2	no	—
284	C₂²⋊C₄×C₁₉	—	2	2	no	—
285	C₂²⋊C₄×C₁₉	—	2	8	no	—
286	C₂²⋊C₄×C₁₉	—	2	8	no	—
287	C₂²⋊C₄×C₁₉	—	2	8	no	—
288	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
289	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
290	C₄²×C₁₉	—	2	8	no	—
291	C₄²×C₁₉	—	2	2	no	—
292	C₄²×C₁₉	—	2	2	no	—
293	C₄²×C₁₉	C₂×D₄	1	4	yes	—
294	C₄²×C₁₉	C₂⁴	1	4	yes	—
295	#60422	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂³×C₁₉	—	2	2	no	—
297	C₂³×C₁₉	—	2	4	no	—
298	C₂³×C₁₉	—	2	2	no	—
299	C₂³×C₁₉	—	2	2	no	—
300	C₂³×C₁₉	—	4	2	no	—
301	C₂³×C₁₉	—	4	2	no	—
302	C₂³×C₁₉	—	4	2	no	—
303	C₂³×C₁₉	—	8	2	no	—
304	C₂³×C₁₉	—	8	2	no	—
305	C₂³×C₁₉	—	8	2	no	—
306	C₂³×C₁₉	#121	1	4	yes	—
307	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
308	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
309	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₁₉	—	2	4	no	—
311	Q₈×C₁₉	—	2	2	no	—
312	Q₈×C₁₉	—	2	2	no	—
313	Q₈×C₁₉	—	2	2	no	—
314	Q₈×C₁₉	—	2	2	no	—
315	Q₈×C₁₉	—	2	2	no	—
316	Q₈×C₁₉	—	4	2	no	—
317	Q₈×C₁₉	—	4	2	no	—
318	Q₈×C₁₉	C₂²×D₄	1	4	yes	—
319	D₄×C₁₉	—	2	8	no	—
320	D₄×C₁₉	—	2	8	no	—
321	D₄×C₁₉	—	2	4	no	—
322	D₄×C₁₉	—	2	2	no	—
323	D₄×C₁₉	—	2	2	no	—
324	D₄×C₁₉	—	2	2	no	—
325	D₄×C₁₉	—	2	2	no	—
326	D₄×C₁₉	—	2	2	no	—
327	D₄×C₁₉	—	4	4	no	—
328	D₄×C₁₉	—	4	4	no	—
329	D₄×C₁₉	—	4	4	no	—
330	D₄×C₁₉	—	4	4	no	—
331	D₄×C₁₉	—	4	2	no	—
332	D₄×C₁₉	—	4	2	no	—
333	D₄×C₁₉	—	8	8	no	—
334	D₄×C₁₉	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₁₉	—	2	4	no	—
336	C₂×C₄×C₁₉	—	2	2	no	—
337	C₂×C₄×C₁₉	—	2	8	no	—
338	C₂×C₄×C₁₉	—	2	8	no	—
339	C₂×C₄×C₁₉	—	2	4	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	2	no	—
342	C₂×C₄×C₁₉	—	4	4	no	—
343	C₂×C₄×C₁₉	—	4	2	no	—
344	C₂×C₄×C₁₉	—	4	2	no	—
345	C₂×C₄×C₁₉	—	4	4	no	—
346	C₂×C₄×C₁₉	—	4	4	no	—
347	C₂×C₄×C₁₉	—	4	4	no	—
348	C₂×C₄×C₁₉	—	4	4	no	—
349	C₂×C₄×C₁₉	—	8	8	no	—
350	C₂×C₄×C₁₉	—	8	2	no	—
351	C₂×C₄×C₁₉	#121	1	4	yes	—
352	C₂×C₄×C₁₉	#121	1	4	yes	—
353	C₂×C₄×C₁₉	#121	1	4	yes	—
354	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
355	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
363	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
364	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
365	C₈×C₁₉	—	2	2	no	—
366	C₈×C₁₉	—	2	2	no	—
367	C₈×C₁₉	—	2	4	no	—
368	C₂×#575	C₂×C₁₉	1	1	yes	characteristic, complemented
369	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic, complemented
370	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
371	#3428	C₂×C₁₉	1	1	yes	characteristic, complemented
372	#3046	C₂×C₁₉	1	4	yes	complemented
373	#3045	C₂×C₁₉	1	4	yes	complemented
374	#3044	C₂×C₁₉	1	2	yes	complemented
375	#3043	C₂×C₁₉	1	2	yes	complemented
376	#3042	C₂×C₁₉	1	2	yes	complemented
377	#3041	C₂×C₁₉	1	2	yes	complemented
378	#3035	C₂×C₁₉	1	8	yes	complemented
379	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
380	#2896	C₂×C₁₉	1	1	yes	characteristic, complemented
381	C₂×#416	C₂×C₁₉	1	1	yes	characteristic, complemented
382	C₂²×C₁₉	—	2	2	no	—
383	C₂²×C₁₉	—	2	2	no	—
384	C₂²×C₁₉	—	2	2	no	—
385	C₂²×C₁₉	—	2	4	no	—
386	C₂²×C₁₉	—	4	4	no	—
387	C₂²×C₁₉	—	4	4	no	—
388	C₂²×C₁₉	—	4	4	no	—
389	C₂²×C₁₉	—	4	4	no	—
390	C₂²×C₁₉	—	4	2	no	—
391	C₂²×C₁₉	—	4	2	no	—
392	C₂²×C₁₉	—	8	4	no	—
393	C₂²×C₁₉	—	8	4	no	—
394	C₂²×C₁₉	—	8	4	no	—
395	C₂²×C₁₉	C₂×#121	1	2	yes	—
396	C₂²×C₁₉	C₂×#121	1	2	yes	—
397	C₂²×C₁₉	C₂×#121	1	2	yes	—
398	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
399	C₄×C₁₉	—	2	8	no	—
400	C₄×C₁₉	—	2	4	no	—
401	C₄×C₁₉	—	4	4	no	—
402	C₄×C₁₉	—	4	2	no	—
403	C₄×C₁₉	—	4	2	no	—
404	C₄×C₁₉	C₂×#121	1	2	yes	—
405	C₄×C₁₉	C₂×#121	1	2	yes	—
406	C₄×C₁₉	C₂×#121	1	2	yes	—
407	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
408	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
409	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
410	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
411	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
412	#575	—	2	8	no	—
413	C₂×#137	C₂²×C₁₉	1	2	yes	—
414	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
415	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
416	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
417	C₂×#135	—	2	8	no	—
418	C₂×#135	C₂²×C₁₉	1	4	yes	—
419	C₂×#135	C₂²×C₁₉	1	4	yes	complemented
420	C₂×#135	C₂²×C₁₉	1	4	yes	complemented
421	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
422	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
423	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
425	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
426	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
427	#537	—	2	2	no	—
428	#536	C₂²×C₁₉	1	2	yes	—
429	#536	C₂²×C₁₉	1	2	yes	complemented
430	#535	C₂²×C₁₉	1	2	yes	—
431	#535	C₂²×C₁₉	1	2	yes	complemented
432	#534	—	2	2	no	—
433	#532	C₂²×C₁₉	1	4	yes	complemented
434	#525	—	2	2	no	—
435	#525	—	2	2	no	—
436	#520	—	2	2	no	—
437	#520	C₂²×C₁₉	1	4	yes	complemented
438	#519	C₂²×C₁₉	1	2	yes	complemented
439	#518	—	2	2	no	—
440	#518	C₂²×C₁₉	1	2	yes	complemented
441	C₄×#41	—	2	2	no	—
442	C₄×#41	C₂²×C₁₉	1	4	yes	complemented
443	C₂×#117	—	2	2	no	—
444	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
446	#464	C₂²×C₁₉	1	8	yes	complemented
447	#464	C₂²×C₁₉	1	8	yes	complemented
448	#463	C₂²×C₁₉	1	8	yes	complemented
449	#463	C₂²×C₁₉	1	8	yes	complemented
450	#462	C₂²×C₁₉	1	8	yes	complemented
451	#461	C₂²×C₁₉	1	8	yes	complemented
452	#460	C₂²×C₁₉	1	8	yes	complemented
453	#459	C₂²×C₁₉	1	8	yes	complemented
454	#424	C₂²×C₁₉	1	2	yes	complemented
455	#424	C₂²×C₁₉	1	2	yes	complemented
456	#424	C₂²×C₁₉	1	4	yes	complemented
457	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
458	#419	C₂²×C₁₉	1	2	yes	complemented
459	#418	C₂²×C₁₉	1	2	yes	complemented
460	#417	C₂²×C₁₉	1	4	yes	complemented
461	#416	C₂²×C₁₉	1	2	yes	—
462	#416	C₂²×C₁₉	1	2	yes	—
463	#416	C₂²×C₁₉	1	4	yes	complemented
464	#416	C₂²×C₁₉	1	4	yes	complemented
465	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
466	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
467	C₂×C₁₉	—	2	2	no	—
468	C₂×C₁₉	—	2	2	no	—
469	C₂×C₁₉	—	2	2	no	—
470	C₂×C₁₉	—	4	4	no	—
471	C₂×C₁₉	—	8	2	no	—
472	C₂×C₁₉	—	8	2	no	—
473	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
474	C₂×C₁₉	#3584	1	2	yes	—
475	C₂×#41	—	2	1	no	—
476	C₂×#41	—	2	1	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	1	no	—
480	C₂×#41	—	2	1	no	—
481	C₂×#41	—	2	4	no	—
482	C₂×#41	—	2	4	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	2	4	no	—
485	C₂×#41	—	2	4	no	—
486	C₂×#41	D₄×C₁₉	1	8	yes	complemented
487	C₂×#41	C₂³×C₁₉	1	2	yes	—
488	C₂×#41	C₂³×C₁₉	1	2	yes	—
489	C₂×#41	C₂³×C₁₉	1	2	yes	—
490	C₂×#41	C₂³×C₁₉	1	2	yes	—
491	C₂×#41	C₂³×C₁₉	1	2	yes	—
492	C₂×#41	C₂³×C₁₉	1	2	yes	—
493	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
494	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
506	#137	—	2	8	no	—
507	#137	—	2	8	no	—
508	AGL(1,ℤ/8)	—	2	8	no	—
509	AGL(1,ℤ/8)	—	2	8	no	—
510	#135	—	2	16	no	—
511	#135	—	2	16	no	—
512	#135	—	2	16	no	—
513	C₂×Q₁₆	—	2	4	no	—
514	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
515	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
516	C₂×SD₁₆	—	2	4	no	—
517	C₂×SD₁₆	—	2	4	no	—
518	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
519	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
520	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
521	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
522	C₂×D₈	—	2	4	no	—
523	C₂×D₈	C₂³×C₁₉	1	4	yes	—
524	C₂×D₈	C₂³×C₁₉	1	4	yes	—
525	C₂×M₁₆	—	2	4	no	—
526	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
527	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
528	C₂²×C₈	—	2	4	no	—
529	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
532	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
533	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
535	#127	C₂³×C₁₉	1	4	yes	—
536	#124	C₂³×C₁₉	1	4	yes	—
537	#124	C₂³×C₁₉	1	4	yes	—
538	#123	—	2	4	no	—
539	#123	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	#121	—	2	8	no	—
543	#121	—	2	4	no	—
544	#121	—	2	4	no	—
545	#120	—	2	4	no	—
546	#120	—	2	4	no	—
547	C₄×Q₈	—	2	4	no	—
548	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
549	C₄×D₄	—	2	8	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	2	8	no	—
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	C₂³×C₁₉	1	8	yes	—
554	#117	—	2	1	no	—
555	#117	—	2	1	no	—
556	#117	—	2	4	no	—
557	#117	—	2	4	no	—
558	#117	—	2	4	no	—
559	#117	D₄×C₁₉	1	2	yes	—
560	#117	D₄×C₁₉	1	2	yes	—
561	#117	C₂³×C₁₉	1	2	yes	—
562	#117	C₂³×C₁₉	1	2	yes	—
563	#117	C₂³×C₁₉	1	2	yes	—
564	#117	C₂³×C₁₉	1	2	yes	—
565	C₂×C₄⋊C₄	—	2	4	no	—
566	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
570	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	—	2	4	no	—
573	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
574	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
575	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
576	#103	C₂³×C₁₉	1	4	yes	—
577	#103	C₂³×C₁₉	1	4	yes	—
578	#103	C₂³×C₁₉	1	8	yes	—
579	#102	C₂³×C₁₉	1	4	yes	—
580	#102	C₂³×C₁₉	1	4	yes	—
581	#102	C₂³×C₁₉	1	8	yes	—
582	C₁₉	#60422	1	1	yes	characteristic, direct product factor, Sylow
583	C₂⁴	—	2	1	no	—
584	C₂⁴	—	2	1	no	—
585	C₂⁴	—	2	1	no	—
586	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
587	#41	—	2	8	no	—
588	#41	—	2	8	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	—	2	4	no	—
595	#41	—	2	4	no	—
596	#41	—	2	4	no	—
597	#41	—	2	4	no	—
598	#41	—	2	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	4	no	—
601	#41	—	4	4	no	—
602	#41	—	4	4	no	—
603	#41	C₂×D₄×C₁₉	1	8	yes	—
604	#41	C₂×D₄×C₁₉	1	8	yes	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
636	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
637	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
638	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	8	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
654	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
658	C₂²×C₄	#41×C₁₉	1	4	yes	—
659	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
662	Q₁₆	—	2	8	no	—
663	Q₁₆	—	2	8	no	—
664	SD₁₆	—	2	8	no	—
665	SD₁₆	—	2	8	no	—
666	SD₁₆	—	2	8	no	—
667	SD₁₆	—	2	8	no	—
668	D₈	—	2	8	no	—
669	D₈	—	2	8	no	—
670	M₁₆	—	2	4	no	—
671	M₁₆	—	2	4	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	4	no	—
675	C₂×C₈	—	2	4	no	—
676	C₂×C₈	—	2	4	no	—
677	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
678	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
679	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	8	no	—
682	C₄⋊C₄	—	2	8	no	—
683	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
684	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
685	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	2	8	no	—
691	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
692	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	8	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₁₉	1	4	yes	—
697	C₄²	C₂⁴×C₁₉	1	4	yes	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	4	2	no	—
703	C₂³	—	4	2	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	8	2	no	—
706	C₂³	—	8	2	no	—
707	C₂³	—	8	2	no	—
708	C₂³	C₁₉×#121	1	4	yes	—
709	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
710	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
711	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
712	Q₈	—	2	4	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	4	2	no	—
720	Q₈	C₂²×D₄×C₁₉	1	4	yes	—
721	D₄	—	2	8	no	—
722	D₄	—	2	8	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	4	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	2	no	—
735	D₄	—	8	8	no	—
736	D₄	C₂²×D₄×C₁₉	1	4	yes	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	8	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	8	8	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	C₁₉×#121	1	4	yes	—
754	C₂×C₄	C₁₉×#121	1	4	yes	—
755	C₂×C₄	C₁₉×#121	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
757	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
763	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
764	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
765	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
766	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
767	C₈	—	2	2	no	—
768	C₈	—	2	2	no	—
769	C₈	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	4	4	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	8	4	no	—
781	C₂²	—	8	4	no	—
782	C₂²	—	8	4	no	—
783	C₂²	C₂×C₁₉×#121	1	2	yes	—
784	C₂²	C₂×C₁₉×#121	1	2	yes	—
785	C₂²	C₂×C₁₉×#121	1	2	yes	—
786	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
787	C₄	—	2	4	no	—
788	C₄	—	2	8	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	4	no	—
792	C₄	C₂×C₁₉×#121	1	2	yes	—
793	C₄	C₂×C₁₉×#121	1	2	yes	—
794	C₄	C₂×C₁₉×#121	1	2	yes	—
795	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
796	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
797	C₂	—	2	2	no	—
798	C₂	—	2	2	no	—
799	C₂	—	2	2	no	—
800	C₂	—	4	4	no	—
801	C₂	—	8	2	no	—
802	C₂	—	8	2	no	—
803	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
804	C₂	C₁₉×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#575	C₂	semidirect
2. C₂²×C₁₉×#135	C₂	semidirect
3. C₁₉×#3449	C₂	semidirect
4. C₁₉×#3428	C₂	semidirect
5. C₁₉×#3046	C₂	semidirect
6. C₁₉×#3045	C₂	semidirect
7. C₁₉×#3044	C₂	semidirect
8. C₁₉×#3043	C₂	semidirect
9. C₁₉×#3042	C₂	semidirect
10. C₁₉×#3041	C₂	semidirect
11. C₁₉×#3035	C₂	semidirect
12. C₂×C₁₉×#424	C₂	semidirect
13. C₁₉×#2896	C₂	semidirect
14. C₂×C₁₉×#416	C₂	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
22. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₉×#135	C₂²	semidirect
26. C₂×C₁₉×#135	C₂²	semidirect
27. C₂²×Q₁₆×C₁₉	C₂²	semidirect
28. C₂²×SD₁₆×C₁₉	C₂²	semidirect
29. C₂²×SD₁₆×C₁₉	C₂²	semidirect
30. C₂²×D₈×C₁₉	C₂²	semidirect
35. C₁₉×#536	C₂²	semidirect
37. C₁₉×#535	C₂²	semidirect
39. C₁₉×#532	C₂²	semidirect
43. C₁₉×#520	C₂²	semidirect
44. C₁₉×#519	C₂²	semidirect
46. C₁₉×#518	C₂²	semidirect
48. C₄×#41×C₁₉	C₂²	semidirect
52. C₁₉×#464	C₂²	semidirect
53. C₁₉×#464	C₂²	semidirect
54. C₁₉×#463	C₂²	semidirect
55. C₁₉×#463	C₂²	semidirect
56. C₁₉×#462	C₂²	semidirect
57. C₁₉×#461	C₂²	semidirect
58. C₁₉×#460	C₂²	semidirect
59. C₁₉×#459	C₂²	semidirect
60. C₁₉×#424	C₂²	semidirect
61. C₁₉×#424	C₂²	semidirect
62. C₁₉×#424	C₂²	semidirect
63. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
64. C₁₉×#419	C₂²	semidirect
65. C₁₉×#418	C₂²	semidirect
66. C₁₉×#417	C₂²	semidirect
69. C₁₉×#416	C₂²	semidirect
70. C₁₉×#416	C₂²	semidirect
71. C₂×C₁₉×#103	C₂²	semidirect
72. C₂×C₁₉×#102	C₂²	semidirect
84. C₂×#41×C₁₉	D₄	semidirect
295. #60422	C₁₉	direct (N × H)
368. C₂×#575	C₂×C₁₉	semidirect
369. C₂²×#135	C₂×C₁₉	semidirect
370. #3449	C₂×C₁₉	semidirect
371. #3428	C₂×C₁₉	semidirect
372. #3046	C₂×C₁₉	semidirect
373. #3045	C₂×C₁₉	semidirect
374. #3044	C₂×C₁₉	semidirect
375. #3043	C₂×C₁₉	semidirect
376. #3042	C₂×C₁₉	semidirect
377. #3041	C₂×C₁₉	semidirect
378. #3035	C₂×C₁₉	semidirect
379. C₂×#424	C₂×C₁₉	semidirect
380. #2896	C₂×C₁₉	semidirect
381. C₂×#416	C₂×C₁₉	semidirect
414. C₂×#137	C₂²×C₁₉	semidirect
416. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
419. C₂×#135	C₂²×C₁₉	semidirect
420. C₂×#135	C₂²×C₁₉	semidirect
421. C₂²×Q₁₆	C₂²×C₁₉	semidirect
422. C₂²×SD₁₆	C₂²×C₁₉	semidirect
423. C₂²×SD₁₆	C₂²×C₁₉	semidirect
424. C₂²×D₈	C₂²×C₁₉	semidirect
429. #536	C₂²×C₁₉	semidirect
431. #535	C₂²×C₁₉	semidirect
433. #532	C₂²×C₁₉	semidirect
437. #520	C₂²×C₁₉	semidirect
438. #519	C₂²×C₁₉	semidirect
440. #518	C₂²×C₁₉	semidirect
442. C₄×#41	C₂²×C₁₉	semidirect
446. #464	C₂²×C₁₉	semidirect
447. #464	C₂²×C₁₉	semidirect
448. #463	C₂²×C₁₉	semidirect
449. #463	C₂²×C₁₉	semidirect
450. #462	C₂²×C₁₉	semidirect
451. #461	C₂²×C₁₉	semidirect
452. #460	C₂²×C₁₉	semidirect
453. #459	C₂²×C₁₉	semidirect
454. #424	C₂²×C₁₉	semidirect
455. #424	C₂²×C₁₉	semidirect
456. #424	C₂²×C₁₉	semidirect
457. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
458. #419	C₂²×C₁₉	semidirect
459. #418	C₂²×C₁₉	semidirect
460. #417	C₂²×C₁₉	semidirect
463. #416	C₂²×C₁₉	semidirect
464. #416	C₂²×C₁₉	semidirect
465. C₂×#103	C₂²×C₁₉	semidirect
466. C₂×#102	C₂²×C₁₉	semidirect
486. C₂×#41	D₄×C₁₉	semidirect
582. C₁₉	#60422	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×#575	2
C₂²×C₁₉×#135	2
C₁₉×#3449	2
C₁₉×#3428	2
C₁₉×#3046	2
C₁₉×#3045	2
C₁₉×#3044	2
C₁₉×#3043	2
C₁₉×#3042	2
C₁₉×#3041	2
C₁₉×#3035	2
C₂×C₁₉×#424	2
C₁₉×#2896	2
C₂×C₁₉×#416	2
#60422	19

Subgroups — C19×#60422 #18066381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60422 #18066381