Subgroups — C₁₉×#24465 #18030424

Order 4864.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#454	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3006	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2040	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2038	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2006	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2003	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1896	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₉	—	2	1	no	—
23	C₁₉×#548	—	2	1	no	—
24	C₁₉×#547	—	2	1	no	—
25	C₁₉×#547	—	2	2	no	—
26	C₁₉×#546	—	2	1	no	—
27	C₁₉×#546	—	2	2	no	—
28	C₁₉×#537	—	2	1	no	—
29	C₁₉×#537	C₂²	1	1	yes	characteristic
30	C₁₉×#536	—	2	1	no	—
31	C₁₉×#536	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#525	—	2	1	no	—
34	C₁₉×#525	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₁₉×#520	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#469	—	2	1	no	—
41	C₁₉×#468	—	2	1	no	—
42	C₁₉×#466	—	2	1	no	—
43	C₁₉×#465	—	2	1	no	—
44	C₁₉×#454	—	2	4	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#449	—	2	1	no	—
47	C₁₉×#448	—	2	1	no	—
48	C₁₉×#447	—	2	1	no	—
49	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₉×#104	—	2	4	no	—
51	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#418	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#417	C₂²	1	1	yes	characteristic
59	C₁₉×#417	C₂²	1	1	yes	characteristic
60	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#407	C₂²	1	1	yes	characteristic
64	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#388	—	2	2	no	—
67	C₁₉×#386	—	2	2	no	—
68	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×2₋¹⁺⁴	—	2	2	no	—
74	C₁₉×2₋¹⁺⁴	—	2	2	no	—
75	C₁₉×2₋¹⁺⁴	—	4	1	no	—
76	C₁₉×2₋¹⁺⁴	—	4	1	no	—
77	C₂×#41×C₁₉	—	2	1	no	—
78	C₂×#41×C₁₉	—	2	1	no	—
79	C₂×#41×C₁₉	—	2	1	no	—
80	C₂×#41×C₁₉	—	2	2	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	—	2	2	no	—
83	C₂×#41×C₁₉	—	2	2	no	—
84	C₂×#41×C₁₉	—	4	1	no	—
85	C₂×#41×C₁₉	—	4	1	no	—
86	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
87	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
88	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₉	—	2	1	no	—
92	C₂²×Q₈×C₁₉	—	2	1	no	—
93	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
94	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₉	—	2	1	no	—
96	C₂²×D₄×C₁₉	—	2	1	no	—
97	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₉	—	2	1	no	—
100	C₂³×C₄×C₁₉	—	2	1	no	—
101	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
103	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
104	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
105	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
106	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
107	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
108	C₂×SD₁₆×C₁₉	—	2	1	no	—
109	C₂×SD₁₆×C₁₉	—	2	1	no	—
110	C₂×SD₁₆×C₁₉	—	2	1	no	—
111	C₂×D₈×C₁₉	—	2	1	no	—
112	C₂×D₈×C₁₉	—	2	1	no	—
113	C₂×D₈×C₁₉	—	2	1	no	—
114	C₂×M₁₆×C₁₉	—	2	1	no	—
115	C₂×M₁₆×C₁₉	—	2	2	no	—
116	C₂×M₁₆×C₁₉	—	4	1	no	—
117	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₁₉	—	2	1	no	—
122	C₁₉×C₄⋊Q₈	—	2	2	no	—
123	C₁₉×C₄⋊Q₈	—	2	1	no	—
124	C₁₉×#124	—	2	2	no	—
125	C₁₉×#124	—	2	1	no	—
126	C₁₉×#124	—	2	2	no	—
127	C₁₉×#124	—	4	1	no	—
128	C₁₉×#123	—	2	2	no	—
129	C₁₉×#123	—	2	2	no	—
130	C₁₉×#123	—	2	2	no	—
131	C₁₉×#123	—	2	1	no	—
132	C₁₉×#123	—	2	2	no	—
133	C₁₉×C₂²⋊Q₈	—	2	2	no	—
134	C₁₉×C₂²⋊Q₈	—	2	2	no	—
135	C₁₉×C₂²⋊Q₈	—	2	2	no	—
136	C₁₉×C₂²⋊Q₈	—	2	1	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	—	2	1	no	—
139	C₁₉×C₂²⋊Q₈	—	2	1	no	—
140	C₁₉×C₂²⋊Q₈	—	2	1	no	—
141	C₁₉×C₂²⋊Q₈	—	2	1	no	—
142	C₁₉×C₂²⋊Q₈	—	2	1	no	—
143	C₁₉×C₂²⋊Q₈	—	2	1	no	—
144	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
145	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
146	C₁₉×#121	—	2	2	no	—
147	C₁₉×#121	—	2	2	no	—
148	C₁₉×#121	—	2	2	no	—
149	C₁₉×#121	—	2	1	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	2	no	—
152	C₁₉×#121	—	2	1	no	—
153	C₁₉×#121	—	2	1	no	—
154	C₁₉×#121	—	2	1	no	—
155	C₁₉×#121	—	2	1	no	—
156	C₁₉×#121	D₄	1	1	yes	characteristic
157	C₁₉×#121	D₄	1	1	yes	characteristic
158	C₁₉×#120	—	2	2	no	—
159	C₁₉×#120	—	2	1	no	—
160	C₄×Q₈×C₁₉	—	2	1	no	—
161	C₄×D₄×C₁₉	—	2	2	no	—
162	C₄×D₄×C₁₉	—	2	2	no	—
163	C₄×D₄×C₁₉	—	2	1	no	—
164	C₄×D₄×C₁₉	—	2	2	no	—
165	C₄×D₄×C₁₉	—	2	1	no	—
166	C₄×D₄×C₁₉	—	2	1	no	—
167	C₁₉×#117	—	2	1	no	—
168	C₁₉×#117	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
179	C₂×C₄²×C₁₉	—	2	2	no	—
180	C₂×C₄²×C₁₉	—	2	1	no	—
181	C₂×C₄²×C₁₉	—	4	1	no	—
182	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
184	C₁₉×#107	—	2	1	no	—
185	C₁₉×#106	—	2	1	no	—
186	C₁₉×#104	—	2	2	no	—
187	C₁₉×#104	—	2	2	no	—
188	C₁₉×#104	—	2	2	no	—
189	C₁₉×#104	—	2	2	no	—
190	C₁₉×#104	—	4	1	no	—
191	C₁₉×#104	D₄	1	4	yes	complemented
192	C₁₉×#103	—	2	1	no	—
193	C₁₉×#103	—	2	1	no	—
194	C₁₉×#103	—	2	1	no	—
195	C₁₉×#102	—	2	1	no	—
196	C₁₉×#102	—	2	1	no	—
197	C₁₉×#102	—	2	1	no	—
198	C₁₉×#102	—	2	1	no	—
199	C₁₉×#102	—	2	1	no	—
200	C₁₉×#101	—	2	2	no	—
201	C₁₉×#101	—	4	1	no	—
202	C₁₉×C₂²⋊C₈	—	2	1	no	—
203	C₁₉×C₂²⋊C₈	—	2	1	no	—
204	C₁₉×#95	—	2	2	no	—
205	C₁₉×#95	—	2	2	no	—
206	C₂⁴×C₁₉	—	2	1	no	—
207	C₂⁴×C₁₉	—	2	1	no	—
208	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
209	#41×C₁₉	—	2	1	no	—
210	#41×C₁₉	—	2	1	no	—
211	#41×C₁₉	—	2	2	no	—
212	#41×C₁₉	—	2	2	no	—
213	#41×C₁₉	—	2	1	no	—
214	#41×C₁₉	—	2	1	no	—
215	#41×C₁₉	—	2	1	no	—
216	#41×C₁₉	—	2	1	no	—
217	#41×C₁₉	—	2	1	no	—
218	#41×C₁₉	—	2	1	no	—
219	#41×C₁₉	—	2	1	no	—
220	#41×C₁₉	—	2	1	no	—
221	#41×C₁₉	—	4	2	no	—
222	#41×C₁₉	—	4	2	no	—
223	#41×C₁₉	—	4	1	no	—
224	#41×C₁₉	—	4	1	no	—
225	#41×C₁₉	—	4	2	no	—
226	#41×C₁₉	—	4	2	no	—
227	#41×C₁₉	—	4	2	no	—
228	#41×C₁₉	—	4	2	no	—
229	#41×C₁₉	—	4	4	no	—
230	#41×C₁₉	—	4	4	no	—
231	#41×C₁₉	—	4	2	no	—
232	#41×C₁₉	—	4	2	no	—
233	#41×C₁₉	C₂×D₄	1	2	yes	—
234	#41×C₁₉	#41	1	2	yes	—
235	C₂×Q₈×C₁₉	—	2	2	no	—
236	C₂×Q₈×C₁₉	—	2	1	no	—
237	C₂×Q₈×C₁₉	—	2	1	no	—
238	C₂×Q₈×C₁₉	—	2	1	no	—
239	C₂×Q₈×C₁₉	—	2	1	no	—
240	C₂×Q₈×C₁₉	—	2	1	no	—
241	C₂×Q₈×C₁₉	—	2	1	no	—
242	C₂×Q₈×C₁₉	—	2	1	no	—
243	C₂×Q₈×C₁₉	—	2	2	no	—
244	C₂×Q₈×C₁₉	—	4	1	no	—
245	C₂×Q₈×C₁₉	—	4	2	no	—
246	C₂×Q₈×C₁₉	—	4	2	no	—
247	C₂×Q₈×C₁₉	—	4	2	no	—
248	C₂×Q₈×C₁₉	—	4	2	no	—
249	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₁₉	—	2	1	no	—
253	C₂×D₄×C₁₉	—	2	2	no	—
254	C₂×D₄×C₁₉	—	2	2	no	—
255	C₂×D₄×C₁₉	—	2	1	no	—
256	C₂×D₄×C₁₉	—	2	1	no	—
257	C₂×D₄×C₁₉	—	2	1	no	—
258	C₂×D₄×C₁₉	—	2	1	no	—
259	C₂×D₄×C₁₉	—	2	1	no	—
260	C₂×D₄×C₁₉	—	2	2	no	—
261	C₂×D₄×C₁₉	—	2	1	no	—
262	C₂×D₄×C₁₉	—	2	1	no	—
263	C₂×D₄×C₁₉	—	2	1	no	—
264	C₂×D₄×C₁₉	—	2	1	no	—
265	C₂×D₄×C₁₉	—	2	1	no	—
266	C₂×D₄×C₁₉	—	2	1	no	—
267	C₂×D₄×C₁₉	—	2	1	no	—
268	C₂×D₄×C₁₉	—	2	1	no	—
269	C₂×D₄×C₁₉	—	4	1	no	—
270	C₂×D₄×C₁₉	—	4	2	no	—
271	C₂×D₄×C₁₉	—	4	2	no	—
272	C₂×D₄×C₁₉	—	4	4	no	—
273	C₂×D₄×C₁₉	—	4	1	no	—
274	C₂×D₄×C₁₉	—	4	1	no	—
275	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
277	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₉	—	2	1	no	—
279	C₂²×C₄×C₁₉	—	2	1	no	—
280	C₂²×C₄×C₁₉	—	2	1	no	—
281	C₂²×C₄×C₁₉	—	2	1	no	—
282	C₂²×C₄×C₁₉	—	2	1	no	—
283	C₂²×C₄×C₁₉	—	2	2	no	—
284	C₂²×C₄×C₁₉	—	2	2	no	—
285	C₂²×C₄×C₁₉	—	2	1	no	—
286	C₂²×C₄×C₁₉	—	2	1	no	—
287	C₂²×C₄×C₁₉	—	2	1	no	—
288	C₂²×C₄×C₁₉	—	2	2	no	—
289	C₂²×C₄×C₁₉	—	2	1	no	—
290	C₂²×C₄×C₁₉	—	2	1	no	—
291	C₂²×C₄×C₁₉	—	2	1	no	—
292	C₂²×C₄×C₁₉	—	2	1	no	—
293	C₂²×C₄×C₁₉	—	2	1	no	—
294	C₂²×C₄×C₁₉	—	4	2	no	—
295	C₂²×C₄×C₁₉	—	4	2	no	—
296	C₂²×C₄×C₁₉	—	4	2	no	—
297	C₂²×C₄×C₁₉	—	4	2	no	—
298	C₂²×C₄×C₁₉	—	4	2	no	—
299	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
307	SD₁₆×C₁₉	—	4	2	no	—
308	SD₁₆×C₁₉	—	4	2	no	—
309	SD₁₆×C₁₉	—	4	2	no	—
310	D₈×C₁₉	—	4	2	no	—
311	D₈×C₁₉	—	4	2	no	—
312	D₈×C₁₉	—	4	2	no	—
313	M₁₆×C₁₉	—	2	1	no	—
314	M₁₆×C₁₉	—	2	1	no	—
315	M₁₆×C₁₉	—	2	1	no	—
316	M₁₆×C₁₉	—	2	1	no	—
317	M₁₆×C₁₉	—	2	1	no	—
318	M₁₆×C₁₉	—	2	1	no	—
319	M₁₆×C₁₉	—	2	1	no	—
320	M₁₆×C₁₉	—	4	2	no	—
321	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
322	C₂×C₈×C₁₉	—	2	1	no	—
323	C₂×C₈×C₁₉	—	2	1	no	—
324	C₂×C₈×C₁₉	—	2	1	no	—
325	C₂×C₈×C₁₉	—	2	1	no	—
326	C₂×C₈×C₁₉	—	4	2	no	—
327	C₄⋊C₄×C₁₉	—	2	2	no	—
328	C₄⋊C₄×C₁₉	—	2	2	no	—
329	C₄⋊C₄×C₁₉	—	2	2	no	—
330	C₄⋊C₄×C₁₉	—	2	2	no	—
331	C₄⋊C₄×C₁₉	—	2	1	no	—
332	C₄⋊C₄×C₁₉	—	2	2	no	—
333	C₄⋊C₄×C₁₉	—	2	2	no	—
334	C₄⋊C₄×C₁₉	—	2	1	no	—
335	C₄⋊C₄×C₁₉	—	2	1	no	—
336	C₄⋊C₄×C₁₉	—	2	1	no	—
337	C₄⋊C₄×C₁₉	—	2	1	no	—
338	C₄⋊C₄×C₁₉	—	2	1	no	—
339	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
340	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₉	—	2	1	no	—
347	C₂²⋊C₄×C₁₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	—	2	1	no	—
350	C₂²⋊C₄×C₁₉	—	2	1	no	—
351	C₂²⋊C₄×C₁₉	—	2	1	no	—
352	C₂²⋊C₄×C₁₉	—	2	1	no	—
353	C₂²⋊C₄×C₁₉	—	4	4	no	—
354	C₂²⋊C₄×C₁₉	—	4	4	no	—
355	C₂²⋊C₄×C₁₉	—	4	1	no	—
356	C₂²⋊C₄×C₁₉	—	4	1	no	—
357	C₄²×C₁₉	—	2	2	no	—
358	C₄²×C₁₉	—	2	1	no	—
359	C₄²×C₁₉	—	2	1	no	—
360	C₄²×C₁₉	—	2	1	no	—
361	C₄²×C₁₉	—	2	1	no	—
362	C₄²×C₁₉	—	4	2	no	—
363	C₄²×C₁₉	C₂×D₄	1	2	yes	—
364	#24465	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂³×C₁₉	—	2	1	no	—
366	C₂³×C₁₉	—	2	1	no	—
367	C₂³×C₁₉	—	2	1	no	—
368	C₂³×C₁₉	—	2	2	no	—
369	C₂³×C₁₉	—	2	1	no	—
370	C₂³×C₁₉	—	2	1	no	—
371	C₂³×C₁₉	—	4	1	no	—
372	C₂³×C₁₉	—	4	2	no	—
373	C₂³×C₁₉	—	4	2	no	—
374	C₂³×C₁₉	—	4	2	no	—
375	C₂³×C₁₉	—	4	2	no	—
376	C₂³×C₁₉	—	4	1	no	—
377	C₂³×C₁₉	—	4	1	no	—
378	C₂³×C₁₉	—	4	1	no	—
379	C₂³×C₁₉	—	8	1	no	—
380	C₂³×C₁₉	#120	1	1	yes	characteristic
381	C₂³×C₁₉	#120	1	1	yes	characteristic
382	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₁₉	—	2	1	no	—
384	Q₈×C₁₉	—	2	1	no	—
385	Q₈×C₁₉	—	2	1	no	—
386	Q₈×C₁₉	—	2	1	no	—
387	Q₈×C₁₉	—	2	1	no	—
388	Q₈×C₁₉	—	4	2	no	—
389	Q₈×C₁₉	—	4	4	no	—
390	Q₈×C₁₉	—	4	1	no	—
391	Q₈×C₁₉	—	4	1	no	—
392	Q₈×C₁₉	—	4	1	no	—
393	Q₈×C₁₉	—	4	1	no	—
394	Q₈×C₁₉	#121	1	2	yes	—
395	D₄×C₁₉	—	2	2	no	—
396	D₄×C₁₉	—	2	2	no	—
397	D₄×C₁₉	—	2	1	no	—
398	D₄×C₁₉	—	2	1	no	—
399	D₄×C₁₉	—	2	1	no	—
400	D₄×C₁₉	—	2	1	no	—
401	D₄×C₁₉	—	2	1	no	—
402	D₄×C₁₉	—	4	2	no	—
403	D₄×C₁₉	—	4	2	no	—
404	D₄×C₁₉	—	4	2	no	—
405	D₄×C₁₉	—	4	4	no	—
406	D₄×C₁₉	—	4	1	no	—
407	D₄×C₁₉	—	4	1	no	—
408	D₄×C₁₉	—	4	1	no	—
409	D₄×C₁₉	—	4	1	no	—
410	D₄×C₁₉	—	4	2	no	—
411	D₄×C₁₉	—	4	1	no	—
412	D₄×C₁₉	—	4	1	no	—
413	D₄×C₁₉	—	4	1	no	—
414	D₄×C₁₉	—	4	1	no	—
415	D₄×C₁₉	—	8	1	no	—
416	D₄×C₁₉	—	8	2	no	—
417	D₄×C₁₉	—	8	2	no	—
418	D₄×C₁₉	—	8	2	no	—
419	D₄×C₁₉	#121	1	2	yes	—
420	C₂×C₄×C₁₉	—	2	1	no	—
421	C₂×C₄×C₁₉	—	2	1	no	—
422	C₂×C₄×C₁₉	—	2	1	no	—
423	C₂×C₄×C₁₉	—	2	1	no	—
424	C₂×C₄×C₁₉	—	2	1	no	—
425	C₂×C₄×C₁₉	—	2	1	no	—
426	C₂×C₄×C₁₉	—	2	1	no	—
427	C₂×C₄×C₁₉	—	2	1	no	—
428	C₂×C₄×C₁₉	—	2	1	no	—
429	C₂×C₄×C₁₉	—	2	2	no	—
430	C₂×C₄×C₁₉	—	2	1	no	—
431	C₂×C₄×C₁₉	—	2	1	no	—
432	C₂×C₄×C₁₉	—	2	2	no	—
433	C₂×C₄×C₁₉	—	2	2	no	—
434	C₂×C₄×C₁₉	—	2	1	no	—
435	C₂×C₄×C₁₉	—	2	2	no	—
436	C₂×C₄×C₁₉	—	2	1	no	—
437	C₂×C₄×C₁₉	—	2	1	no	—
438	C₂×C₄×C₁₉	—	2	2	no	—
439	C₂×C₄×C₁₉	—	2	1	no	—
440	C₂×C₄×C₁₉	—	2	2	no	—
441	C₂×C₄×C₁₉	—	2	2	no	—
442	C₂×C₄×C₁₉	—	2	2	no	—
443	C₂×C₄×C₁₉	—	4	2	no	—
444	C₂×C₄×C₁₉	—	4	2	no	—
445	C₂×C₄×C₁₉	—	4	2	no	—
446	C₂×C₄×C₁₉	—	4	4	no	—
447	C₂×C₄×C₁₉	—	4	1	no	—
448	C₂×C₄×C₁₉	—	4	1	no	—
449	C₂×C₄×C₁₉	—	4	1	no	—
450	C₂×C₄×C₁₉	—	4	4	no	—
451	C₂×C₄×C₁₉	—	4	8	no	—
452	C₂×C₄×C₁₉	—	4	1	no	—
453	C₂×C₄×C₁₉	—	4	1	no	—
454	C₂×C₄×C₁₉	—	4	1	no	—
455	C₂×C₄×C₁₉	—	4	1	no	—
456	C₂×C₄×C₁₉	—	4	1	no	—
457	C₂×C₄×C₁₉	—	4	2	no	—
458	C₂×C₄×C₁₉	—	4	2	no	—
459	C₂×C₄×C₁₉	—	4	1	no	—
460	C₂×C₄×C₁₉	—	8	2	no	—
461	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
462	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
463	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
467	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
469	C₈×C₁₉	—	2	2	no	—
470	C₈×C₁₉	—	4	1	no	—
471	C₈×C₁₉	—	4	1	no	—
472	C₈×C₁₉	—	4	1	no	—
473	#3489	C₂×C₁₉	1	1	yes	characteristic, complemented
474	#3055	C₂×C₁₉	1	1	yes	characteristic, complemented
475	C₂×#454	C₂×C₁₉	1	1	yes	characteristic, complemented
476	#3006	C₂×C₁₉	1	1	yes	characteristic, complemented
477	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic, complemented
478	#2850	C₂×C₁₉	1	1	yes	characteristic, complemented
479	#2040	C₂×C₁₉	1	1	yes	characteristic, complemented
480	#2038	C₂×C₁₉	1	1	yes	characteristic, complemented
481	#2006	C₂×C₁₉	1	1	yes	characteristic, complemented
482	#2003	C₂×C₁₉	1	1	yes	characteristic, complemented
483	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
484	#1896	C₂×C₁₉	1	1	yes	characteristic, complemented
485	#1883	C₂×C₁₉	1	1	yes	characteristic, complemented
486	#1860	C₂×C₁₉	1	1	yes	characteristic, complemented
487	#1793	C₂×C₁₉	1	1	yes	characteristic, complemented
488	C₂²×C₁₉	—	2	1	no	—
489	C₂²×C₁₉	—	2	1	no	—
490	C₂²×C₁₉	—	2	1	no	—
491	C₂²×C₁₉	—	2	1	no	—
492	C₂²×C₁₉	—	2	1	no	—
493	C₂²×C₁₉	—	2	2	no	—
494	C₂²×C₁₉	—	2	1	no	—
495	C₂²×C₁₉	—	2	1	no	—
496	C₂²×C₁₉	—	4	2	no	—
497	C₂²×C₁₉	—	4	2	no	—
498	C₂²×C₁₉	—	4	1	no	—
499	C₂²×C₁₉	—	4	1	no	—
500	C₂²×C₁₉	—	4	1	no	—
501	C₂²×C₁₉	—	4	1	no	—
502	C₂²×C₁₉	—	4	1	no	—
503	C₂²×C₁₉	—	4	1	no	—
504	C₂²×C₁₉	—	4	1	no	—
505	C₂²×C₁₉	—	4	1	no	—
506	C₂²×C₁₉	—	8	4	no	—
507	C₂²×C₁₉	—	8	2	no	—
508	C₂²×C₁₉	—	8	2	no	—
509	C₂²×C₁₉	—	8	1	no	—
510	C₂²×C₁₉	—	8	1	no	—
511	C₂²×C₁₉	—	8	1	no	—
512	C₂²×C₁₉	#454	1	2	yes	complemented
513	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
514	C₂²×C₁₉	D₄²	1	1	yes	characteristic
515	C₂²×C₁₉	#546	1	1	yes	characteristic
516	C₄×C₁₉	—	2	1	no	—
517	C₄×C₁₉	—	2	1	no	—
518	C₄×C₁₉	—	2	2	no	—
519	C₄×C₁₉	—	4	2	no	—
520	C₄×C₁₉	—	4	2	no	—
521	C₄×C₁₉	—	4	2	no	—
522	C₄×C₁₉	—	4	1	no	—
523	C₄×C₁₉	—	4	1	no	—
524	C₄×C₁₉	—	4	1	no	—
525	C₄×C₁₉	—	4	2	no	—
526	C₄×C₁₉	—	4	1	no	—
527	C₄×C₁₉	—	8	1	no	—
528	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
529	C₄×C₁₉	#534	1	1	yes	characteristic
530	C₄×C₁₉	D₄²	1	1	yes	characteristic
531	C₄×C₁₉	#546	1	1	yes	characteristic
532	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
533	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
534	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
535	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
536	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic, complemented
537	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
538	D₄×Q₈	—	2	1	no	—
539	#548	—	2	1	no	—
540	#547	—	2	1	no	—
541	#547	—	2	2	no	—
542	#546	—	2	1	no	—
543	#546	—	2	2	no	—
544	#537	—	2	1	no	—
545	#537	C₂²×C₁₉	1	1	yes	characteristic
546	#536	—	2	1	no	—
547	#536	C₂²×C₁₉	1	1	yes	characteristic
548	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
549	#525	—	2	1	no	—
550	#525	C₂²×C₁₉	1	1	yes	characteristic
551	C₂×C₂²⋊Q₈	—	2	1	no	—
552	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
553	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
554	#520	C₂²×C₁₉	1	1	yes	characteristic
555	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
556	#469	—	2	1	no	—
557	#468	—	2	1	no	—
558	#466	—	2	1	no	—
559	#465	—	2	1	no	—
560	#454	—	2	4	no	—
561	#449	—	2	1	no	—
562	#449	—	2	1	no	—
563	#448	—	2	1	no	—
564	#447	—	2	1	no	—
565	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
566	C₂×#104	—	2	4	no	—
567	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
568	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
569	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
570	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
571	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
572	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
573	#418	C₂²×C₁₉	1	1	yes	characteristic, complemented
574	#417	C₂²×C₁₉	1	1	yes	characteristic
575	#417	C₂²×C₁₉	1	1	yes	characteristic
576	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
577	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
578	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
579	#407	C₂²×C₁₉	1	1	yes	characteristic
580	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
581	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
582	#388	—	2	2	no	—
583	#386	—	2	2	no	—
584	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
585	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
586	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
587	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
588	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
589	C₂×C₁₉	—	2	1	no	—
590	C₂×C₁₉	—	2	1	no	—
591	C₂×C₁₉	—	2	2	no	—
592	C₂×C₁₉	—	4	1	no	—
593	C₂×C₁₉	—	4	2	no	—
594	C₂×C₁₉	—	8	1	no	—
595	C₂×C₁₉	—	8	1	no	—
596	C₂×C₁₉	—	16	1	no	—
597	C₂×C₁₉	#2410	1	1	yes	characteristic
598	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
599	C₂×C₁₉	#3018	1	1	yes	characteristic
600	2₋¹⁺⁴	—	2	2	no	—
601	2₋¹⁺⁴	—	2	2	no	—
602	2₋¹⁺⁴	—	4	1	no	—
603	2₋¹⁺⁴	—	4	1	no	—
604	C₂×#41	—	2	1	no	—
605	C₂×#41	—	2	1	no	—
606	C₂×#41	—	2	1	no	—
607	C₂×#41	—	2	2	no	—
608	C₂×#41	—	2	1	no	—
609	C₂×#41	—	2	2	no	—
610	C₂×#41	—	2	2	no	—
611	C₂×#41	—	4	1	no	—
612	C₂×#41	—	4	1	no	—
613	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
614	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
615	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
616	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
617	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
618	C₂²×Q₈	—	2	1	no	—
619	C₂²×Q₈	—	2	1	no	—
620	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
621	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
622	C₂²×D₄	—	2	1	no	—
623	C₂²×D₄	—	2	1	no	—
624	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
626	C₂³×C₄	—	2	1	no	—
627	C₂³×C₄	—	2	1	no	—
628	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
629	AGL(1,ℤ/8)	—	2	2	no	—
630	AGL(1,ℤ/8)	—	2	2	no	—
631	AGL(1,ℤ/8)	—	2	2	no	—
632	AGL(1,ℤ/8)	—	4	1	no	—
633	AGL(1,ℤ/8)	—	4	1	no	—
634	AGL(1,ℤ/8)	—	4	1	no	—
635	C₂×SD₁₆	—	2	1	no	—
636	C₂×SD₁₆	—	2	1	no	—
637	C₂×SD₁₆	—	2	1	no	—
638	C₂×D₈	—	2	1	no	—
639	C₂×D₈	—	2	1	no	—
640	C₂×D₈	—	2	1	no	—
641	C₂×M₁₆	—	2	1	no	—
642	C₂×M₁₆	—	2	2	no	—
643	C₂×M₁₆	—	4	1	no	—
644	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
645	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
646	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
647	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
648	C₂²×C₈	—	2	1	no	—
649	C₄⋊Q₈	—	2	2	no	—
650	C₄⋊Q₈	—	2	1	no	—
651	#124	—	2	2	no	—
652	#124	—	2	1	no	—
653	#124	—	2	2	no	—
654	#124	—	4	1	no	—
655	#123	—	2	2	no	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	1	no	—
659	#123	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	1	no	—
668	C₂²⋊Q₈	—	2	1	no	—
669	C₂²⋊Q₈	—	2	1	no	—
670	C₂²⋊Q₈	—	2	1	no	—
671	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
672	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
673	#121	—	2	2	no	—
674	#121	—	2	2	no	—
675	#121	—	2	2	no	—
676	#121	—	2	1	no	—
677	#121	—	2	1	no	—
678	#121	—	2	2	no	—
679	#121	—	2	1	no	—
680	#121	—	2	1	no	—
681	#121	—	2	1	no	—
682	#121	—	2	1	no	—
683	#121	D₄×C₁₉	1	1	yes	characteristic
684	#121	D₄×C₁₉	1	1	yes	characteristic
685	#120	—	2	2	no	—
686	#120	—	2	1	no	—
687	C₄×Q₈	—	2	1	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	1	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	1	no	—
694	#117	—	2	1	no	—
695	#117	C₂³×C₁₉	1	1	yes	characteristic
696	C₂×C₄⋊C₄	—	2	2	no	—
697	C₂×C₄⋊C₄	—	2	1	no	—
698	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₂²⋊C₄	—	2	1	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	—	2	2	no	—
705	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
706	C₂×C₄²	—	2	2	no	—
707	C₂×C₄²	—	2	1	no	—
708	C₂×C₄²	—	4	1	no	—
709	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
711	#107	—	2	1	no	—
712	#106	—	2	1	no	—
713	#104	—	2	2	no	—
714	#104	—	2	2	no	—
715	#104	—	2	2	no	—
716	#104	—	2	2	no	—
717	#104	—	4	1	no	—
718	#104	D₄×C₁₉	1	4	yes	complemented
719	#103	—	2	1	no	—
720	#103	—	2	1	no	—
721	#103	—	2	1	no	—
722	#102	—	2	1	no	—
723	#102	—	2	1	no	—
724	#102	—	2	1	no	—
725	#102	—	2	1	no	—
726	#102	—	2	1	no	—
727	#101	—	2	2	no	—
728	#101	—	4	1	no	—
729	C₂²⋊C₈	—	2	1	no	—
730	C₂²⋊C₈	—	2	1	no	—
731	#95	—	2	2	no	—
732	#95	—	2	2	no	—
733	C₁₉	#24465	1	1	yes	characteristic, direct product factor, Sylow
734	C₂⁴	—	2	1	no	—
735	C₂⁴	—	2	1	no	—
736	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
737	#41	—	2	1	no	—
738	#41	—	2	1	no	—
739	#41	—	2	2	no	—
740	#41	—	2	2	no	—
741	#41	—	2	1	no	—
742	#41	—	2	1	no	—
743	#41	—	2	1	no	—
744	#41	—	2	1	no	—
745	#41	—	2	1	no	—
746	#41	—	2	1	no	—
747	#41	—	2	1	no	—
748	#41	—	2	1	no	—
749	#41	—	4	2	no	—
750	#41	—	4	2	no	—
751	#41	—	4	1	no	—
752	#41	—	4	1	no	—
753	#41	—	4	2	no	—
754	#41	—	4	2	no	—
755	#41	—	4	2	no	—
756	#41	—	4	2	no	—
757	#41	—	4	4	no	—
758	#41	—	4	4	no	—
759	#41	—	4	2	no	—
760	#41	—	4	2	no	—
761	#41	C₂×D₄×C₁₉	1	2	yes	—
762	#41	#41×C₁₉	1	2	yes	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	1	no	—
767	C₂×Q₈	—	2	1	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	4	1	no	—
773	C₂×Q₈	—	4	2	no	—
774	C₂×Q₈	—	4	2	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
778	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
779	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	4	1	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	4	no	—
801	C₂×D₄	—	4	1	no	—
802	C₂×D₄	—	4	1	no	—
803	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
804	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
805	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
828	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
829	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
833	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
835	SD₁₆	—	4	2	no	—
836	SD₁₆	—	4	2	no	—
837	SD₁₆	—	4	2	no	—
838	D₈	—	4	2	no	—
839	D₈	—	4	2	no	—
840	D₈	—	4	2	no	—
841	M₁₆	—	2	1	no	—
842	M₁₆	—	2	1	no	—
843	M₁₆	—	2	1	no	—
844	M₁₆	—	2	1	no	—
845	M₁₆	—	2	1	no	—
846	M₁₆	—	2	1	no	—
847	M₁₆	—	2	1	no	—
848	M₁₆	—	4	2	no	—
849	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
850	C₂×C₈	—	2	1	no	—
851	C₂×C₈	—	2	1	no	—
852	C₂×C₈	—	2	1	no	—
853	C₂×C₈	—	2	1	no	—
854	C₂×C₈	—	4	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
868	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	1	no	—
881	C₂²⋊C₄	—	4	4	no	—
882	C₂²⋊C₄	—	4	4	no	—
883	C₂²⋊C₄	—	4	1	no	—
884	C₂²⋊C₄	—	4	1	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	1	no	—
887	C₄²	—	2	1	no	—
888	C₄²	—	2	1	no	—
889	C₄²	—	2	1	no	—
890	C₄²	—	4	2	no	—
891	C₄²	C₂×D₄×C₁₉	1	2	yes	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	2	no	—
900	C₂³	—	4	2	no	—
901	C₂³	—	4	2	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	4	1	no	—
905	C₂³	—	4	1	no	—
906	C₂³	—	8	1	no	—
907	C₂³	C₁₉×#120	1	1	yes	characteristic
908	C₂³	C₁₉×#120	1	1	yes	characteristic
909	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
910	Q₈	—	2	1	no	—
911	Q₈	—	2	1	no	—
912	Q₈	—	2	1	no	—
913	Q₈	—	2	1	no	—
914	Q₈	—	2	1	no	—
915	Q₈	—	4	2	no	—
916	Q₈	—	4	4	no	—
917	Q₈	—	4	1	no	—
918	Q₈	—	4	1	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	4	1	no	—
921	Q₈	C₁₉×#121	1	2	yes	—
922	D₄	—	2	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	1	no	—
925	D₄	—	2	1	no	—
926	D₄	—	2	1	no	—
927	D₄	—	2	1	no	—
928	D₄	—	2	1	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	2	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	2	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	1	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	1	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	1	no	—
941	D₄	—	4	1	no	—
942	D₄	—	8	1	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	2	no	—
946	D₄	C₁₉×#121	1	2	yes	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	4	2	no	—
972	C₂×C₄	—	4	2	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	1	no	—
975	C₂×C₄	—	4	1	no	—
976	C₂×C₄	—	4	1	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	1	no	—
982	C₂×C₄	—	4	1	no	—
983	C₂×C₄	—	4	1	no	—
984	C₂×C₄	—	4	2	no	—
985	C₂×C₄	—	4	2	no	—
986	C₂×C₄	—	4	1	no	—
987	C₂×C₄	—	8	2	no	—
988	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
989	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
991	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
992	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
993	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
994	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
995	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
996	C₈	—	2	2	no	—
997	C₈	—	4	1	no	—
998	C₈	—	4	1	no	—
999	C₈	—	4	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	8	4	no	—
1019	C₂²	—	8	2	no	—
1020	C₂²	—	8	2	no	—
1021	C₂²	—	8	1	no	—
1022	C₂²	—	8	1	no	—
1023	C₂²	—	8	1	no	—
1024	C₂²	C₁₉×#454	1	2	yes	complemented
1025	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1026	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1027	C₂²	C₁₉×#546	1	1	yes	characteristic
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	8	1	no	—
1040	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
1041	C₄	C₁₉×#534	1	1	yes	characteristic
1042	C₄	D₄²×C₁₉	1	1	yes	characteristic
1043	C₄	C₁₉×#546	1	1	yes	characteristic
1044	C₂	—	2	1	no	—
1045	C₂	—	2	2	no	—
1046	C₂	—	2	1	no	—
1047	C₂	—	4	1	no	—
1048	C₂	—	4	2	no	—
1049	C₂	—	8	1	no	—
1050	C₂	—	8	1	no	—
1051	C₂	—	16	1	no	—
1052	C₂	C₁₉×#2410	1	1	yes	characteristic
1053	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
1054	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3489	C₂	semidirect
2. C₁₉×#3055	C₂	semidirect
3. C₂×C₁₉×#454	C₂	semidirect
4. C₁₉×#3006	C₂	semidirect
5. C₂²×C₁₉×#104	C₂	semidirect
6. C₁₉×#2850	C₂	semidirect
7. C₁₉×#2040	C₂	semidirect
8. C₁₉×#2038	C₂	semidirect
9. C₁₉×#2006	C₂	semidirect
10. C₁₉×#2003	C₂	semidirect
11. C₁₉×#1901	C₂	semidirect
12. C₁₉×#1896	C₂	semidirect
13. C₁₉×#1883	C₂	semidirect
14. C₁₉×#1860	C₂	semidirect
15. C₁₉×#1793	C₂	semidirect
20. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
32. C₂×C₁₉×#124	C₂²	semidirect
49. C₁₉×#428	C₂²	semidirect
55. C₂×C₁₉×#104	C₂²	semidirect
56. C₂×C₁₉×#104	C₂²	semidirect
57. C₁₉×#418	C₂²	semidirect
60. C₁₉×#417	C₂²	semidirect
61. C₂×C₁₉×#101	C₂²	semidirect
62. C₂×C₁₉×#101	C₂²	semidirect
64. C₁₉×#391	C₂²	semidirect
65. C₁₉×#390	C₂²	semidirect
68. C₁₉×#382	C₂²	semidirect
69. C₁₉×#343	C₂²	semidirect
70. C₁₉×#343	C₂²	semidirect
71. C₁₉×#339	C₂²	semidirect
72. C₁₉×#339	C₂²	semidirect
191. C₁₉×#104	D₄	semidirect
364. #24465	C₁₉	direct (N × H)
473. #3489	C₂×C₁₉	semidirect
474. #3055	C₂×C₁₉	semidirect
475. C₂×#454	C₂×C₁₉	semidirect
476. #3006	C₂×C₁₉	semidirect
477. C₂²×#104	C₂×C₁₉	semidirect
478. #2850	C₂×C₁₉	semidirect
479. #2040	C₂×C₁₉	semidirect
480. #2038	C₂×C₁₉	semidirect
481. #2006	C₂×C₁₉	semidirect
482. #2003	C₂×C₁₉	semidirect
483. #1901	C₂×C₁₉	semidirect
484. #1896	C₂×C₁₉	semidirect
485. #1883	C₂×C₁₉	semidirect
486. #1860	C₂×C₁₉	semidirect
487. #1793	C₂×C₁₉	semidirect
512. C₂²×C₁₉	#454	semidirect
536. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
548. C₂×#124	C₂²×C₁₉	semidirect
565. #428	C₂²×C₁₉	semidirect
571. C₂×#104	C₂²×C₁₉	semidirect
572. C₂×#104	C₂²×C₁₉	semidirect
573. #418	C₂²×C₁₉	semidirect
576. #417	C₂²×C₁₉	semidirect
577. C₂×#101	C₂²×C₁₉	semidirect
578. C₂×#101	C₂²×C₁₉	semidirect
580. #391	C₂²×C₁₉	semidirect
581. #390	C₂²×C₁₉	semidirect
584. #382	C₂²×C₁₉	semidirect
585. #343	C₂²×C₁₉	semidirect
586. #343	C₂²×C₁₉	semidirect
587. #339	C₂²×C₁₉	semidirect
588. #339	C₂²×C₁₉	semidirect
718. #104	D₄×C₁₉	semidirect
733. C₁₉	#24465	direct (N × H)
1024. C₂²	C₁₉×#454	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3489	2
C₁₉×#3055	2
C₂×C₁₉×#454	2
C₁₉×#3006	2
C₂²×C₁₉×#104	2
C₁₉×#2850	2
C₁₉×#2040	2
C₁₉×#2038	2
C₁₉×#2006	2
C₁₉×#2003	2
C₁₉×#1901	2
C₁₉×#1896	2
C₁₉×#1883	2
C₁₉×#1860	2
C₁₉×#1793	2
#24465	19

Subgroups — C19×#24465 #18030424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24465 #18030424