Subgroups — C₁₉×#23881 #18029840

Order 4864.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 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	C₁₉×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#454	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3005	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2432	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2007	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2005	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×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1789	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	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#575	—	2	4	no	—
20	C₁₉×#575	—	2	4	no	—
21	C₂×C₁₉×#137	—	2	1	no	—
22	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
26	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#135	—	2	1	no	—
30	C₂×C₁₉×#135	—	2	1	no	—
31	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	D₄×Q₈×C₁₉	—	2	1	no	—
33	C₁₉×#548	—	2	1	no	—
34	C₁₉×#547	—	2	1	no	—
35	C₁₉×#547	—	2	2	no	—
36	C₁₉×#546	—	2	1	no	—
37	C₁₉×#546	—	2	2	no	—
38	C₁₉×#537	—	2	1	no	—
39	C₁₉×#537	C₂²	1	1	yes	characteristic
40	C₁₉×#536	—	2	1	no	—
41	C₁₉×#536	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#525	—	2	1	no	—
45	C₁₉×#525	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₁₉×#520	C₂²	1	1	yes	characteristic
49	C₁₉×#456	—	2	4	no	—
50	C₁₉×#454	—	2	4	no	—
51	C₁₉×#452	—	2	1	no	—
52	C₁₉×#452	—	2	1	no	—
53	C₁₉×#449	—	2	1	no	—
54	C₁₉×#449	—	2	1	no	—
55	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
58	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#418	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#407	C₂²	1	1	yes	characteristic
66	C₁₉×#394	—	2	2	no	—
67	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#385	—	2	2	no	—
70	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
71	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
75	C₁₉×2₋¹⁺⁴	—	2	2	no	—
76	C₁₉×2₋¹⁺⁴	—	2	2	no	—
77	C₁₉×2₋¹⁺⁴	—	4	1	no	—
78	C₁₉×2₋¹⁺⁴	—	4	1	no	—
79	C₂×#41×C₁₉	—	2	1	no	—
80	C₂×#41×C₁₉	—	2	1	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	—	2	2	no	—
83	C₂×#41×C₁₉	—	2	1	no	—
84	C₂×#41×C₁₉	—	2	2	no	—
85	C₂×#41×C₁₉	—	2	2	no	—
86	C₂×#41×C₁₉	—	2	2	no	—
87	C₂×#41×C₁₉	—	2	2	no	—
88	C₂×#41×C₁₉	—	2	1	no	—
89	C₂×#41×C₁₉	—	2	1	no	—
90	C₂×#41×C₁₉	—	2	1	no	—
91	C₂×#41×C₁₉	—	2	1	no	—
92	C₂×#41×C₁₉	—	4	1	no	—
93	C₂×#41×C₁₉	—	4	1	no	—
94	C₂×#41×C₁₉	—	4	1	no	—
95	C₂×#41×C₁₉	—	4	1	no	—
96	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
97	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
98	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₉	—	2	1	no	—
102	C₂²×Q₈×C₁₉	—	2	1	no	—
103	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
104	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₉	—	2	1	no	—
107	C₂²×D₄×C₁₉	—	2	1	no	—
108	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₉	—	2	1	no	—
111	C₂³×C₄×C₁₉	—	2	1	no	—
112	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#137	—	2	8	no	—
114	C₁₉×#137	—	2	2	no	—
115	C₁₉×#137	—	2	2	no	—
116	C₁₉×#137	—	2	2	no	—
117	C₁₉×#137	—	2	2	no	—
118	C₁₉×#137	—	4	1	no	—
119	C₁₉×#137	D₄	1	4	yes	complemented
120	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
121	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
122	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
123	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
124	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
125	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
126	C₁₉×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
127	C₁₉×#135	—	2	8	no	—
128	C₁₉×#135	—	2	8	no	—
129	C₂×Q₁₆×C₁₉	—	2	1	no	—
130	C₂×Q₁₆×C₁₉	—	2	1	no	—
131	C₂×Q₁₆×C₁₉	—	2	1	no	—
132	C₂×SD₁₆×C₁₉	—	2	1	no	—
133	C₂×SD₁₆×C₁₉	—	2	1	no	—
134	C₂×SD₁₆×C₁₉	—	2	1	no	—
135	C₂×SD₁₆×C₁₉	—	2	1	no	—
136	C₂×SD₁₆×C₁₉	—	2	1	no	—
137	C₂×SD₁₆×C₁₉	—	2	1	no	—
138	C₂×D₈×C₁₉	—	2	1	no	—
139	C₂×D₈×C₁₉	—	2	1	no	—
140	C₂×D₈×C₁₉	—	2	1	no	—
141	C₂×M₁₆×C₁₉	—	2	1	no	—
142	C₂×M₁₆×C₁₉	—	2	2	no	—
143	C₂×M₁₆×C₁₉	—	2	2	no	—
144	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₁₉	—	2	1	no	—
149	C₁₉×C₄⋊Q₈	—	2	2	no	—
150	C₁₉×C₄⋊Q₈	—	2	1	no	—
151	C₁₉×C₄⋊Q₈	—	2	2	no	—
152	C₁₉×C₄⋊Q₈	—	4	1	no	—
153	C₁₉×#124	—	2	2	no	—
154	C₁₉×#124	—	2	1	no	—
155	C₁₉×#124	—	2	2	no	—
156	C₁₉×#124	—	4	1	no	—
157	C₁₉×#123	—	2	2	no	—
158	C₁₉×#123	—	2	2	no	—
159	C₁₉×#123	—	2	2	no	—
160	C₁₉×#123	—	2	1	no	—
161	C₁₉×#123	—	2	2	no	—
162	C₁₉×C₂²⋊Q₈	—	2	2	no	—
163	C₁₉×C₂²⋊Q₈	—	2	2	no	—
164	C₁₉×C₂²⋊Q₈	—	2	2	no	—
165	C₁₉×C₂²⋊Q₈	—	2	1	no	—
166	C₁₉×C₂²⋊Q₈	—	2	1	no	—
167	C₁₉×C₂²⋊Q₈	—	2	1	no	—
168	C₁₉×C₂²⋊Q₈	—	2	1	no	—
169	C₁₉×C₂²⋊Q₈	—	2	1	no	—
170	C₁₉×C₂²⋊Q₈	—	2	1	no	—
171	C₁₉×C₂²⋊Q₈	—	2	1	no	—
172	C₁₉×C₂²⋊Q₈	—	2	1	no	—
173	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
174	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
175	C₁₉×#121	—	2	2	no	—
176	C₁₉×#121	—	2	2	no	—
177	C₁₉×#121	—	2	2	no	—
178	C₁₉×#121	—	2	1	no	—
179	C₁₉×#121	—	2	1	no	—
180	C₁₉×#121	—	2	2	no	—
181	C₁₉×#121	D₄	1	1	yes	characteristic
182	C₁₉×#121	D₄	1	1	yes	characteristic
183	C₁₉×#120	—	2	2	no	—
184	C₁₉×#120	—	2	1	no	—
185	C₄×Q₈×C₁₉	—	2	1	no	—
186	C₄×D₄×C₁₉	—	2	2	no	—
187	C₄×D₄×C₁₉	—	2	2	no	—
188	C₄×D₄×C₁₉	—	2	1	no	—
189	C₄×D₄×C₁₉	—	2	2	no	—
190	C₄×D₄×C₁₉	—	2	1	no	—
191	C₄×D₄×C₁₉	—	2	1	no	—
192	C₁₉×#117	—	2	1	no	—
193	C₁₉×#117	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
198	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
204	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
206	C₁₉×#104	—	2	2	no	—
207	C₁₉×#104	—	2	2	no	—
208	C₁₉×#104	—	2	2	no	—
209	C₁₉×#104	—	2	2	no	—
210	C₁₉×#104	—	4	1	no	—
211	C₁₉×#104	—	4	1	no	—
212	C₁₉×#103	—	2	1	no	—
213	C₁₉×#103	—	2	1	no	—
214	C₁₉×#102	—	2	1	no	—
215	C₁₉×#102	—	2	1	no	—
216	C₁₉×#101	—	2	2	no	—
217	C₁₉×#101	—	2	2	no	—
218	C₁₉×C₂²⋊C₈	—	2	1	no	—
219	C₁₉×C₂²⋊C₈	—	2	1	no	—
220	C₁₉×#95	—	2	1	no	—
221	C₁₉×#95	—	2	2	no	—
222	C₂⁴×C₁₉	—	2	1	no	—
223	C₂⁴×C₁₉	—	2	1	no	—
224	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
225	#41×C₁₉	—	2	1	no	—
226	#41×C₁₉	—	2	1	no	—
227	#41×C₁₉	—	2	4	no	—
228	#41×C₁₉	—	2	4	no	—
229	#41×C₁₉	—	2	2	no	—
230	#41×C₁₉	—	2	2	no	—
231	#41×C₁₉	—	2	1	no	—
232	#41×C₁₉	—	2	1	no	—
233	#41×C₁₉	—	2	1	no	—
234	#41×C₁₉	—	2	1	no	—
235	#41×C₁₉	—	2	1	no	—
236	#41×C₁₉	—	2	1	no	—
237	#41×C₁₉	—	2	1	no	—
238	#41×C₁₉	—	2	1	no	—
239	#41×C₁₉	—	4	2	no	—
240	#41×C₁₉	—	4	2	no	—
241	#41×C₁₉	—	4	1	no	—
242	#41×C₁₉	—	4	1	no	—
243	#41×C₁₉	—	4	2	no	—
244	#41×C₁₉	—	4	2	no	—
245	#41×C₁₉	—	4	2	no	—
246	#41×C₁₉	—	4	2	no	—
247	#41×C₁₉	—	4	2	no	—
248	#41×C₁₉	—	4	2	no	—
249	#41×C₁₉	—	4	4	no	—
250	#41×C₁₉	—	4	4	no	—
251	#41×C₁₉	—	4	2	no	—
252	#41×C₁₉	—	4	2	no	—
253	#41×C₁₉	—	4	2	no	—
254	#41×C₁₉	—	4	2	no	—
255	#41×C₁₉	—	4	2	no	—
256	#41×C₁₉	—	4	2	no	—
257	#41×C₁₉	C₂×D₄	1	2	yes	—
258	#41×C₁₉	C₂×D₄	1	2	yes	—
259	C₂×Q₈×C₁₉	—	2	2	no	—
260	C₂×Q₈×C₁₉	—	2	1	no	—
261	C₂×Q₈×C₁₉	—	2	1	no	—
262	C₂×Q₈×C₁₉	—	2	1	no	—
263	C₂×Q₈×C₁₉	—	2	1	no	—
264	C₂×Q₈×C₁₉	—	2	1	no	—
265	C₂×Q₈×C₁₉	—	2	1	no	—
266	C₂×Q₈×C₁₉	—	2	1	no	—
267	C₂×Q₈×C₁₉	—	2	1	no	—
268	C₂×Q₈×C₁₉	—	2	2	no	—
269	C₂×Q₈×C₁₉	—	2	1	no	—
270	C₂×Q₈×C₁₉	—	2	1	no	—
271	C₂×Q₈×C₁₉	—	2	1	no	—
272	C₂×Q₈×C₁₉	—	2	1	no	—
273	C₂×Q₈×C₁₉	—	4	1	no	—
274	C₂×Q₈×C₁₉	—	4	2	no	—
275	C₂×Q₈×C₁₉	—	4	2	no	—
276	C₂×Q₈×C₁₉	—	4	2	no	—
277	C₂×Q₈×C₁₉	—	4	2	no	—
278	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
279	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
280	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
281	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
282	C₂×D₄×C₁₉	—	2	1	no	—
283	C₂×D₄×C₁₉	—	2	2	no	—
284	C₂×D₄×C₁₉	—	2	2	no	—
285	C₂×D₄×C₁₉	—	2	1	no	—
286	C₂×D₄×C₁₉	—	2	1	no	—
287	C₂×D₄×C₁₉	—	2	1	no	—
288	C₂×D₄×C₁₉	—	2	1	no	—
289	C₂×D₄×C₁₉	—	2	1	no	—
290	C₂×D₄×C₁₉	—	2	2	no	—
291	C₂×D₄×C₁₉	—	2	1	no	—
292	C₂×D₄×C₁₉	—	2	1	no	—
293	C₂×D₄×C₁₉	—	2	1	no	—
294	C₂×D₄×C₁₉	—	2	1	no	—
295	C₂×D₄×C₁₉	—	2	1	no	—
296	C₂×D₄×C₁₉	—	2	1	no	—
297	C₂×D₄×C₁₉	—	2	1	no	—
298	C₂×D₄×C₁₉	—	4	1	no	—
299	C₂×D₄×C₁₉	—	4	2	no	—
300	C₂×D₄×C₁₉	—	4	2	no	—
301	C₂×D₄×C₁₉	—	4	2	no	—
302	C₂×D₄×C₁₉	—	4	2	no	—
303	C₂×D₄×C₁₉	—	4	1	no	—
304	C₂×D₄×C₁₉	—	4	1	no	—
305	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₉	—	2	1	no	—
310	C₂²×C₄×C₁₉	—	2	1	no	—
311	C₂²×C₄×C₁₉	—	2	1	no	—
312	C₂²×C₄×C₁₉	—	2	1	no	—
313	C₂²×C₄×C₁₉	—	2	1	no	—
314	C₂²×C₄×C₁₉	—	2	2	no	—
315	C₂²×C₄×C₁₉	—	2	2	no	—
316	C₂²×C₄×C₁₉	—	2	1	no	—
317	C₂²×C₄×C₁₉	—	2	1	no	—
318	C₂²×C₄×C₁₉	—	2	1	no	—
319	C₂²×C₄×C₁₉	—	2	2	no	—
320	C₂²×C₄×C₁₉	—	2	1	no	—
321	C₂²×C₄×C₁₉	—	2	1	no	—
322	C₂²×C₄×C₁₉	—	2	1	no	—
323	C₂²×C₄×C₁₉	—	2	1	no	—
324	C₂²×C₄×C₁₉	—	2	1	no	—
325	C₂²×C₄×C₁₉	—	4	2	no	—
326	C₂²×C₄×C₁₉	—	4	2	no	—
327	C₂²×C₄×C₁₉	—	4	2	no	—
328	C₂²×C₄×C₁₉	—	4	2	no	—
329	C₂²×C₄×C₁₉	—	4	1	no	—
330	C₂²×C₄×C₁₉	—	4	1	no	—
331	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
332	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
338	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
339	Q₁₆×C₁₉	—	2	4	no	—
340	Q₁₆×C₁₉	—	2	4	no	—
341	Q₁₆×C₁₉	—	4	2	no	—
342	SD₁₆×C₁₉	—	2	4	no	—
343	SD₁₆×C₁₉	—	2	4	no	—
344	SD₁₆×C₁₉	—	2	4	no	—
345	SD₁₆×C₁₉	—	2	4	no	—
346	SD₁₆×C₁₉	—	4	2	no	—
347	SD₁₆×C₁₉	—	4	2	no	—
348	D₈×C₁₉	—	2	4	no	—
349	D₈×C₁₉	—	2	4	no	—
350	D₈×C₁₉	—	4	2	no	—
351	M₁₆×C₁₉	—	2	4	no	—
352	M₁₆×C₁₉	—	2	1	no	—
353	M₁₆×C₁₉	—	2	1	no	—
354	M₁₆×C₁₉	—	2	1	no	—
355	M₁₆×C₁₉	—	2	1	no	—
356	M₁₆×C₁₉	—	2	1	no	—
357	M₁₆×C₁₉	—	2	1	no	—
358	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
359	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
360	C₂×C₈×C₁₉	—	2	4	no	—
361	C₂×C₈×C₁₉	—	2	1	no	—
362	C₂×C₈×C₁₉	—	2	1	no	—
363	C₂×C₈×C₁₉	—	2	1	no	—
364	C₂×C₈×C₁₉	—	2	1	no	—
365	C₄⋊C₄×C₁₉	—	2	2	no	—
366	C₄⋊C₄×C₁₉	—	2	2	no	—
367	C₄⋊C₄×C₁₉	—	2	2	no	—
368	C₄⋊C₄×C₁₉	—	2	2	no	—
369	C₄⋊C₄×C₁₉	—	2	1	no	—
370	C₄⋊C₄×C₁₉	—	2	2	no	—
371	C₄⋊C₄×C₁₉	—	2	2	no	—
372	C₄⋊C₄×C₁₉	—	2	1	no	—
373	C₄⋊C₄×C₁₉	—	2	1	no	—
374	C₄⋊C₄×C₁₉	—	2	1	no	—
375	C₄⋊C₄×C₁₉	—	4	4	no	—
376	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
378	C₂²⋊C₄×C₁₉	—	2	2	no	—
379	C₂²⋊C₄×C₁₉	—	2	2	no	—
380	C₂²⋊C₄×C₁₉	—	2	2	no	—
381	C₂²⋊C₄×C₁₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₉	—	2	2	no	—
383	C₂²⋊C₄×C₁₉	—	2	1	no	—
384	C₂²⋊C₄×C₁₉	—	2	2	no	—
385	C₂²⋊C₄×C₁₉	—	2	2	no	—
386	C₂²⋊C₄×C₁₉	—	2	1	no	—
387	C₂²⋊C₄×C₁₉	—	2	1	no	—
388	C₂²⋊C₄×C₁₉	—	2	1	no	—
389	C₂²⋊C₄×C₁₉	—	2	1	no	—
390	C₂²⋊C₄×C₁₉	—	4	4	no	—
391	C₂²⋊C₄×C₁₉	—	4	4	no	—
392	C₂²⋊C₄×C₁₉	—	4	2	no	—
393	C₄²×C₁₉	—	2	2	no	—
394	C₄²×C₁₉	—	2	1	no	—
395	C₄²×C₁₉	—	2	1	no	—
396	C₄²×C₁₉	—	2	1	no	—
397	C₄²×C₁₉	—	2	1	no	—
398	C₄²×C₁₉	—	2	1	no	—
399	#23881	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₂³×C₁₉	—	2	1	no	—
401	C₂³×C₁₉	—	2	1	no	—
402	C₂³×C₁₉	—	2	1	no	—
403	C₂³×C₁₉	—	2	1	no	—
404	C₂³×C₁₉	—	2	1	no	—
405	C₂³×C₁₉	—	2	2	no	—
406	C₂³×C₁₉	—	4	1	no	—
407	C₂³×C₁₉	—	4	1	no	—
408	C₂³×C₁₉	—	4	2	no	—
409	C₂³×C₁₉	—	4	2	no	—
410	C₂³×C₁₉	—	4	2	no	—
411	C₂³×C₁₉	—	4	2	no	—
412	C₂³×C₁₉	—	4	1	no	—
413	C₂³×C₁₉	—	4	1	no	—
414	C₂³×C₁₉	—	8	1	no	—
415	C₂³×C₁₉	#120	1	1	yes	characteristic
416	C₂³×C₁₉	#120	1	1	yes	characteristic
417	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
418	Q₈×C₁₉	—	2	1	no	—
419	Q₈×C₁₉	—	2	1	no	—
420	Q₈×C₁₉	—	2	2	no	—
421	Q₈×C₁₉	—	2	1	no	—
422	Q₈×C₁₉	—	2	1	no	—
423	Q₈×C₁₉	—	2	2	no	—
424	Q₈×C₁₉	—	2	1	no	—
425	Q₈×C₁₉	—	4	2	no	—
426	Q₈×C₁₉	—	4	4	no	—
427	Q₈×C₁₉	—	4	1	no	—
428	Q₈×C₁₉	—	4	1	no	—
429	Q₈×C₁₉	—	4	1	no	—
430	Q₈×C₁₉	—	4	1	no	—
431	Q₈×C₁₉	—	4	1	no	—
432	Q₈×C₁₉	—	4	1	no	—
433	Q₈×C₁₉	#120	1	2	yes	—
434	D₄×C₁₉	—	2	2	no	—
435	D₄×C₁₉	—	2	2	no	—
436	D₄×C₁₉	—	2	1	no	—
437	D₄×C₁₉	—	2	2	no	—
438	D₄×C₁₉	—	2	1	no	—
439	D₄×C₁₉	—	2	1	no	—
440	D₄×C₁₉	—	2	1	no	—
441	D₄×C₁₉	—	2	2	no	—
442	D₄×C₁₉	—	2	1	no	—
443	D₄×C₁₉	—	4	2	no	—
444	D₄×C₁₉	—	4	2	no	—
445	D₄×C₁₉	—	4	2	no	—
446	D₄×C₁₉	—	4	2	no	—
447	D₄×C₁₉	—	4	4	no	—
448	D₄×C₁₉	—	4	4	no	—
449	D₄×C₁₉	—	4	4	no	—
450	D₄×C₁₉	—	4	1	no	—
451	D₄×C₁₉	—	4	1	no	—
452	D₄×C₁₉	—	4	1	no	—
453	D₄×C₁₉	—	4	1	no	—
454	D₄×C₁₉	—	4	1	no	—
455	D₄×C₁₉	—	4	1	no	—
456	D₄×C₁₉	—	8	1	no	—
457	D₄×C₁₉	—	8	2	no	—
458	D₄×C₁₉	#120	1	2	yes	—
459	C₂×C₄×C₁₉	—	2	1	no	—
460	C₂×C₄×C₁₉	—	2	1	no	—
461	C₂×C₄×C₁₉	—	2	1	no	—
462	C₂×C₄×C₁₉	—	2	1	no	—
463	C₂×C₄×C₁₉	—	2	1	no	—
464	C₂×C₄×C₁₉	—	2	1	no	—
465	C₂×C₄×C₁₉	—	2	1	no	—
466	C₂×C₄×C₁₉	—	2	1	no	—
467	C₂×C₄×C₁₉	—	2	1	no	—
468	C₂×C₄×C₁₉	—	2	1	no	—
469	C₂×C₄×C₁₉	—	2	1	no	—
470	C₂×C₄×C₁₉	—	2	2	no	—
471	C₂×C₄×C₁₉	—	2	2	no	—
472	C₂×C₄×C₁₉	—	2	2	no	—
473	C₂×C₄×C₁₉	—	2	1	no	—
474	C₂×C₄×C₁₉	—	2	2	no	—
475	C₂×C₄×C₁₉	—	2	1	no	—
476	C₂×C₄×C₁₉	—	2	1	no	—
477	C₂×C₄×C₁₉	—	2	2	no	—
478	C₂×C₄×C₁₉	—	2	1	no	—
479	C₂×C₄×C₁₉	—	2	2	no	—
480	C₂×C₄×C₁₉	—	2	2	no	—
481	C₂×C₄×C₁₉	—	2	2	no	—
482	C₂×C₄×C₁₉	—	4	2	no	—
483	C₂×C₄×C₁₉	—	4	2	no	—
484	C₂×C₄×C₁₉	—	4	2	no	—
485	C₂×C₄×C₁₉	—	4	4	no	—
486	C₂×C₄×C₁₉	—	4	4	no	—
487	C₂×C₄×C₁₉	—	4	4	no	—
488	C₂×C₄×C₁₉	—	4	1	no	—
489	C₂×C₄×C₁₉	—	4	4	no	—
490	C₂×C₄×C₁₉	—	4	1	no	—
491	C₂×C₄×C₁₉	—	4	1	no	—
492	C₂×C₄×C₁₉	—	4	1	no	—
493	C₂×C₄×C₁₉	—	4	1	no	—
494	C₂×C₄×C₁₉	—	4	1	no	—
495	C₂×C₄×C₁₉	—	4	1	no	—
496	C₂×C₄×C₁₉	—	4	1	no	—
497	C₂×C₄×C₁₉	—	4	2	no	—
498	C₂×C₄×C₁₉	—	4	1	no	—
499	C₂×C₄×C₁₉	—	4	1	no	—
500	C₂×C₄×C₁₉	—	4	1	no	—
501	C₂×C₄×C₁₉	—	8	2	no	—
502	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
503	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
504	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
509	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
510	C₈×C₁₉	—	2	2	no	—
511	C₈×C₁₉	—	2	2	no	—
512	C₈×C₁₉	—	4	1	no	—
513	C₈×C₁₉	—	4	1	no	—
514	C₂×#575	C₂×C₁₉	1	1	yes	characteristic, complemented
515	#3489	C₂×C₁₉	1	1	yes	characteristic, complemented
516	C₂×#456	C₂×C₁₉	1	1	yes	characteristic, complemented
517	C₂×#454	C₂×C₁₉	1	1	yes	characteristic, complemented
518	#3005	C₂×C₁₉	1	1	yes	characteristic, complemented
519	#2432	C₂×C₁₉	1	1	yes	characteristic, complemented
520	#2007	C₂×C₁₉	1	1	yes	characteristic, complemented
521	#2006	C₂×C₁₉	1	1	yes	characteristic, complemented
522	#2005	C₂×C₁₉	1	1	yes	characteristic, complemented
523	#2003	C₂×C₁₉	1	1	yes	characteristic, complemented
524	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
525	#1883	C₂×C₁₉	1	1	yes	characteristic, complemented
526	#1882	C₂×C₁₉	1	1	yes	characteristic, complemented
527	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
528	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
529	C₂²×C₁₉	—	2	1	no	—
530	C₂²×C₁₉	—	2	1	no	—
531	C₂²×C₁₉	—	2	1	no	—
532	C₂²×C₁₉	—	2	1	no	—
533	C₂²×C₁₉	—	2	2	no	—
534	C₂²×C₁₉	—	2	1	no	—
535	C₂²×C₁₉	—	2	1	no	—
536	C₂²×C₁₉	—	2	1	no	—
537	C₂²×C₁₉	—	2	1	no	—
538	C₂²×C₁₉	—	4	4	no	—
539	C₂²×C₁₉	—	4	1	no	—
540	C₂²×C₁₉	—	4	1	no	—
541	C₂²×C₁₉	—	4	1	no	—
542	C₂²×C₁₉	—	4	1	no	—
543	C₂²×C₁₉	—	4	2	no	—
544	C₂²×C₁₉	—	4	1	no	—
545	C₂²×C₁₉	—	4	1	no	—
546	C₂²×C₁₉	—	4	1	no	—
547	C₂²×C₁₉	—	4	1	no	—
548	C₂²×C₁₉	—	8	1	no	—
549	C₂²×C₁₉	—	8	1	no	—
550	C₂²×C₁₉	—	8	2	no	—
551	C₂²×C₁₉	—	8	4	no	—
552	C₂²×C₁₉	—	8	1	no	—
553	C₂²×C₁₉	—	8	1	no	—
554	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
555	C₂²×C₁₉	D₄²	1	1	yes	characteristic
556	C₂²×C₁₉	D₄²	1	1	yes	characteristic
557	C₄×C₁₉	—	2	1	no	—
558	C₄×C₁₉	—	2	1	no	—
559	C₄×C₁₉	—	2	2	no	—
560	C₄×C₁₉	—	4	2	no	—
561	C₄×C₁₉	—	4	2	no	—
562	C₄×C₁₉	—	4	1	no	—
563	C₄×C₁₉	—	4	2	no	—
564	C₄×C₁₉	—	4	1	no	—
565	C₄×C₁₉	—	4	2	no	—
566	C₄×C₁₉	—	4	1	no	—
567	C₄×C₁₉	—	4	1	no	—
568	C₄×C₁₉	—	8	1	no	—
569	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
570	C₄×C₁₉	#534	1	1	yes	characteristic
571	C₄×C₁₉	D₄²	1	1	yes	characteristic
572	C₄×C₁₉	D₄²	1	1	yes	characteristic
573	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
574	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
575	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
576	#575	—	2	4	no	—
577	#575	—	2	4	no	—
578	C₂×#137	—	2	1	no	—
579	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
580	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
581	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic, complemented
582	C₂×AGL(1,ℤ/8)	—	2	1	no	—
583	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
584	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
585	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic, complemented
586	C₂×#135	—	2	1	no	—
587	C₂×#135	—	2	1	no	—
588	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
589	D₄×Q₈	—	2	1	no	—
590	#548	—	2	1	no	—
591	#547	—	2	1	no	—
592	#547	—	2	2	no	—
593	#546	—	2	1	no	—
594	#546	—	2	2	no	—
595	#537	—	2	1	no	—
596	#537	C₂²×C₁₉	1	1	yes	characteristic
597	#536	—	2	1	no	—
598	#536	C₂²×C₁₉	1	1	yes	characteristic
599	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
600	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
601	#525	—	2	1	no	—
602	#525	C₂²×C₁₉	1	1	yes	characteristic
603	C₂×C₂²⋊Q₈	—	2	1	no	—
604	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
605	#520	C₂²×C₁₉	1	1	yes	characteristic
606	#456	—	2	4	no	—
607	#454	—	2	4	no	—
608	#452	—	2	1	no	—
609	#452	—	2	1	no	—
610	#449	—	2	1	no	—
611	#449	—	2	1	no	—
612	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
613	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
614	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
615	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
616	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
617	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
618	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
619	#418	C₂²×C₁₉	1	1	yes	characteristic, complemented
620	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
621	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
622	#407	C₂²×C₁₉	1	1	yes	characteristic
623	#394	—	2	2	no	—
624	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
625	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
626	#385	—	2	2	no	—
627	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
628	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
629	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
630	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
631	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
632	C₂×C₁₉	—	2	1	no	—
633	C₂×C₁₉	—	2	1	no	—
634	C₂×C₁₉	—	4	1	no	—
635	C₂×C₁₉	—	4	1	no	—
636	C₂×C₁₉	—	4	2	no	—
637	C₂×C₁₉	—	8	1	no	—
638	C₂×C₁₉	—	8	2	no	—
639	C₂×C₁₉	—	8	1	no	—
640	C₂×C₁₉	#2403	1	1	yes	characteristic
641	C₂×C₁₉	#3018	1	1	yes	characteristic
642	C₂×C₁₉	#3020	1	1	yes	characteristic
643	2₋¹⁺⁴	—	2	2	no	—
644	2₋¹⁺⁴	—	2	2	no	—
645	2₋¹⁺⁴	—	4	1	no	—
646	2₋¹⁺⁴	—	4	1	no	—
647	C₂×#41	—	2	1	no	—
648	C₂×#41	—	2	1	no	—
649	C₂×#41	—	2	1	no	—
650	C₂×#41	—	2	2	no	—
651	C₂×#41	—	2	1	no	—
652	C₂×#41	—	2	2	no	—
653	C₂×#41	—	2	2	no	—
654	C₂×#41	—	2	2	no	—
655	C₂×#41	—	2	2	no	—
656	C₂×#41	—	2	1	no	—
657	C₂×#41	—	2	1	no	—
658	C₂×#41	—	2	1	no	—
659	C₂×#41	—	2	1	no	—
660	C₂×#41	—	4	1	no	—
661	C₂×#41	—	4	1	no	—
662	C₂×#41	—	4	1	no	—
663	C₂×#41	—	4	1	no	—
664	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
665	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
666	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
667	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
668	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
669	C₂²×Q₈	—	2	1	no	—
670	C₂²×Q₈	—	2	1	no	—
671	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
672	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
673	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
674	C₂²×D₄	—	2	1	no	—
675	C₂²×D₄	—	2	1	no	—
676	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
678	C₂³×C₄	—	2	1	no	—
679	C₂³×C₄	—	2	1	no	—
680	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
681	#137	—	2	8	no	—
682	#137	—	2	2	no	—
683	#137	—	2	2	no	—
684	#137	—	2	2	no	—
685	#137	—	2	2	no	—
686	#137	—	4	1	no	—
687	#137	D₄×C₁₉	1	4	yes	complemented
688	AGL(1,ℤ/8)	—	2	8	no	—
689	AGL(1,ℤ/8)	—	2	2	no	—
690	AGL(1,ℤ/8)	—	2	2	no	—
691	AGL(1,ℤ/8)	—	2	2	no	—
692	AGL(1,ℤ/8)	—	2	2	no	—
693	AGL(1,ℤ/8)	—	4	1	no	—
694	AGL(1,ℤ/8)	D₄×C₁₉	1	4	yes	complemented
695	#135	—	2	8	no	—
696	#135	—	2	8	no	—
697	C₂×Q₁₆	—	2	1	no	—
698	C₂×Q₁₆	—	2	1	no	—
699	C₂×Q₁₆	—	2	1	no	—
700	C₂×SD₁₆	—	2	1	no	—
701	C₂×SD₁₆	—	2	1	no	—
702	C₂×SD₁₆	—	2	1	no	—
703	C₂×SD₁₆	—	2	1	no	—
704	C₂×SD₁₆	—	2	1	no	—
705	C₂×SD₁₆	—	2	1	no	—
706	C₂×D₈	—	2	1	no	—
707	C₂×D₈	—	2	1	no	—
708	C₂×D₈	—	2	1	no	—
709	C₂×M₁₆	—	2	1	no	—
710	C₂×M₁₆	—	2	2	no	—
711	C₂×M₁₆	—	2	2	no	—
712	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
713	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
714	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
715	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
716	C₂²×C₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	2	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	—	4	1	no	—
721	#124	—	2	2	no	—
722	#124	—	2	1	no	—
723	#124	—	2	2	no	—
724	#124	—	4	1	no	—
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	#123	—	2	1	no	—
729	#123	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
742	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
743	#121	—	2	2	no	—
744	#121	—	2	2	no	—
745	#121	—	2	2	no	—
746	#121	—	2	1	no	—
747	#121	—	2	1	no	—
748	#121	—	2	2	no	—
749	#121	D₄×C₁₉	1	1	yes	characteristic
750	#121	D₄×C₁₉	1	1	yes	characteristic
751	#120	—	2	2	no	—
752	#120	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	1	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	1	no	—
760	#117	—	2	1	no	—
761	#117	C₂³×C₁₉	1	1	yes	characteristic
762	C₂×C₄⋊C₄	—	2	2	no	—
763	C₂×C₄⋊C₄	—	2	1	no	—
764	C₂×C₄⋊C₄	—	2	2	no	—
765	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	—	2	2	no	—
768	C₂×C₂²⋊C₄	—	2	1	no	—
769	C₂×C₂²⋊C₄	—	2	2	no	—
770	C₂×C₂²⋊C₄	—	2	2	no	—
771	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
772	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
774	#104	—	2	2	no	—
775	#104	—	2	2	no	—
776	#104	—	2	2	no	—
777	#104	—	2	2	no	—
778	#104	—	4	1	no	—
779	#104	—	4	1	no	—
780	#103	—	2	1	no	—
781	#103	—	2	1	no	—
782	#102	—	2	1	no	—
783	#102	—	2	1	no	—
784	#101	—	2	2	no	—
785	#101	—	2	2	no	—
786	C₂²⋊C₈	—	2	1	no	—
787	C₂²⋊C₈	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	2	no	—
790	C₁₉	#23881	1	1	yes	characteristic, direct product factor, Sylow
791	C₂⁴	—	2	1	no	—
792	C₂⁴	—	2	1	no	—
793	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
794	#41	—	2	1	no	—
795	#41	—	2	1	no	—
796	#41	—	2	4	no	—
797	#41	—	2	4	no	—
798	#41	—	2	2	no	—
799	#41	—	2	2	no	—
800	#41	—	2	1	no	—
801	#41	—	2	1	no	—
802	#41	—	2	1	no	—
803	#41	—	2	1	no	—
804	#41	—	2	1	no	—
805	#41	—	2	1	no	—
806	#41	—	2	1	no	—
807	#41	—	2	1	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	1	no	—
811	#41	—	4	1	no	—
812	#41	—	4	2	no	—
813	#41	—	4	2	no	—
814	#41	—	4	2	no	—
815	#41	—	4	2	no	—
816	#41	—	4	2	no	—
817	#41	—	4	2	no	—
818	#41	—	4	4	no	—
819	#41	—	4	4	no	—
820	#41	—	4	2	no	—
821	#41	—	4	2	no	—
822	#41	—	4	2	no	—
823	#41	—	4	2	no	—
824	#41	—	4	2	no	—
825	#41	—	4	2	no	—
826	#41	C₂×D₄×C₁₉	1	2	yes	—
827	#41	C₂×D₄×C₁₉	1	2	yes	—
828	C₂×Q₈	—	2	2	no	—
829	C₂×Q₈	—	2	1	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	2	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	4	1	no	—
843	C₂×Q₈	—	4	2	no	—
844	C₂×Q₈	—	4	2	no	—
845	C₂×Q₈	—	4	2	no	—
846	C₂×Q₈	—	4	2	no	—
847	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
848	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
849	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
850	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	—	2	1	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	1	no	—
861	C₂×D₄	—	2	1	no	—
862	C₂×D₄	—	2	1	no	—
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	—	4	1	no	—
868	C₂×D₄	—	4	2	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	—	4	2	no	—
871	C₂×D₄	—	4	2	no	—
872	C₂×D₄	—	4	1	no	—
873	C₂×D₄	—	4	1	no	—
874	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
875	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
876	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
877	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	4	2	no	—
895	C₂²×C₄	—	4	2	no	—
896	C₂²×C₄	—	4	2	no	—
897	C₂²×C₄	—	4	2	no	—
898	C₂²×C₄	—	4	1	no	—
899	C₂²×C₄	—	4	1	no	—
900	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
901	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
902	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
904	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
905	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
908	Q₁₆	—	2	4	no	—
909	Q₁₆	—	2	4	no	—
910	Q₁₆	—	4	2	no	—
911	SD₁₆	—	2	4	no	—
912	SD₁₆	—	2	4	no	—
913	SD₁₆	—	2	4	no	—
914	SD₁₆	—	2	4	no	—
915	SD₁₆	—	4	2	no	—
916	SD₁₆	—	4	2	no	—
917	D₈	—	2	4	no	—
918	D₈	—	2	4	no	—
919	D₈	—	4	2	no	—
920	M₁₆	—	2	4	no	—
921	M₁₆	—	2	1	no	—
922	M₁₆	—	2	1	no	—
923	M₁₆	—	2	1	no	—
924	M₁₆	—	2	1	no	—
925	M₁₆	—	2	1	no	—
926	M₁₆	—	2	1	no	—
927	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
928	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
929	C₂×C₈	—	2	4	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	4	4	no	—
945	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
946	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	4	4	no	—
960	C₂²⋊C₄	—	4	4	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	4	1	no	—
975	C₂³	—	4	1	no	—
976	C₂³	—	4	2	no	—
977	C₂³	—	4	2	no	—
978	C₂³	—	4	2	no	—
979	C₂³	—	4	2	no	—
980	C₂³	—	4	1	no	—
981	C₂³	—	4	1	no	—
982	C₂³	—	8	1	no	—
983	C₂³	C₁₉×#120	1	1	yes	characteristic
984	C₂³	C₁₉×#120	1	1	yes	characteristic
985	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
986	Q₈	—	2	1	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	2	2	no	—
989	Q₈	—	2	1	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	4	2	no	—
994	Q₈	—	4	4	no	—
995	Q₈	—	4	1	no	—
996	Q₈	—	4	1	no	—
997	Q₈	—	4	1	no	—
998	Q₈	—	4	1	no	—
999	Q₈	—	4	1	no	—
1000	Q₈	—	4	1	no	—
1001	Q₈	C₁₉×#120	1	2	yes	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	2	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	4	2	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	4	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	4	no	—
1018	D₄	—	4	1	no	—
1019	D₄	—	4	1	no	—
1020	D₄	—	4	1	no	—
1021	D₄	—	4	1	no	—
1022	D₄	—	4	1	no	—
1023	D₄	—	4	1	no	—
1024	D₄	—	8	1	no	—
1025	D₄	—	8	2	no	—
1026	D₄	C₁₉×#120	1	2	yes	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	4	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	1	no	—
1060	C₂×C₄	—	4	1	no	—
1061	C₂×C₄	—	4	1	no	—
1062	C₂×C₄	—	4	1	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	1	no	—
1067	C₂×C₄	—	4	1	no	—
1068	C₂×C₄	—	4	1	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1071	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1076	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1077	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1078	C₈	—	2	2	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	4	1	no	—
1081	C₈	—	4	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	4	4	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	8	1	no	—
1102	C₂²	—	8	1	no	—
1103	C₂²	—	8	2	no	—
1104	C₂²	—	8	4	no	—
1105	C₂²	—	8	1	no	—
1106	C₂²	—	8	1	no	—
1107	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1108	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1109	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	8	1	no	—
1122	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
1123	C₄	C₁₉×#534	1	1	yes	characteristic
1124	C₄	D₄²×C₁₉	1	1	yes	characteristic
1125	C₄	D₄²×C₁₉	1	1	yes	characteristic
1126	C₂	—	2	1	no	—
1127	C₂	—	2	1	no	—
1128	C₂	—	4	1	no	—
1129	C₂	—	4	1	no	—
1130	C₂	—	4	2	no	—
1131	C₂	—	8	2	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	1	no	—
1134	C₂	C₁₉×#2403	1	1	yes	characteristic
1135	C₂	C₁₉×#3018	1	1	yes	characteristic
1136	C₂	C₁₉×#3020	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. C₂×C₁₉×#575	C₂	semidirect
2. C₁₉×#3489	C₂	semidirect
3. C₂×C₁₉×#456	C₂	semidirect
4. C₂×C₁₉×#454	C₂	semidirect
5. C₁₉×#3005	C₂	semidirect
6. C₁₉×#2432	C₂	semidirect
7. C₁₉×#2007	C₂	semidirect
8. C₁₉×#2006	C₂	semidirect
9. C₁₉×#2005	C₂	semidirect
10. C₁₉×#2003	C₂	semidirect
11. C₁₉×#1901	C₂	semidirect
12. C₁₉×#1883	C₂	semidirect
13. C₁₉×#1882	C₂	semidirect
14. C₁₉×#1871	C₂	semidirect
15. C₁₉×#1789	C₂	semidirect
24. C₂×C₁₉×#137	C₂²	semidirect
28. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
42. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
43. C₂×C₁₉×#124	C₂²	semidirect
59. C₂×C₁₉×#104	C₂²	semidirect
60. C₂×C₁₉×#104	C₂²	semidirect
61. C₁₉×#419	C₂²	semidirect
62. C₁₉×#418	C₂²	semidirect
63. C₂×C₁₉×#101	C₂²	semidirect
64. C₂×C₁₉×#101	C₂²	semidirect
67. C₁₉×#391	C₂²	semidirect
68. C₁₉×#390	C₂²	semidirect
71. C₁₉×#343	C₂²	semidirect
72. C₁₉×#343	C₂²	semidirect
73. C₁₉×#339	C₂²	semidirect
74. C₁₉×#339	C₂²	semidirect
119. C₁₉×#137	D₄	semidirect
126. C₁₉×AGL(1,ℤ/8)	D₄	semidirect
399. #23881	C₁₉	direct (N × H)
514. C₂×#575	C₂×C₁₉	semidirect
515. #3489	C₂×C₁₉	semidirect
516. C₂×#456	C₂×C₁₉	semidirect
517. C₂×#454	C₂×C₁₉	semidirect
518. #3005	C₂×C₁₉	semidirect
519. #2432	C₂×C₁₉	semidirect
520. #2007	C₂×C₁₉	semidirect
521. #2006	C₂×C₁₉	semidirect
522. #2005	C₂×C₁₉	semidirect
523. #2003	C₂×C₁₉	semidirect
524. #1901	C₂×C₁₉	semidirect
525. #1883	C₂×C₁₉	semidirect
526. #1882	C₂×C₁₉	semidirect
527. #1871	C₂×C₁₉	semidirect
528. #1789	C₂×C₁₉	semidirect
581. C₂×#137	C₂²×C₁₉	semidirect
585. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
599. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
600. C₂×#124	C₂²×C₁₉	semidirect
616. C₂×#104	C₂²×C₁₉	semidirect
617. C₂×#104	C₂²×C₁₉	semidirect
618. #419	C₂²×C₁₉	semidirect
619. #418	C₂²×C₁₉	semidirect
620. C₂×#101	C₂²×C₁₉	semidirect
621. C₂×#101	C₂²×C₁₉	semidirect
624. #391	C₂²×C₁₉	semidirect
625. #390	C₂²×C₁₉	semidirect
628. #343	C₂²×C₁₉	semidirect
629. #343	C₂²×C₁₉	semidirect
630. #339	C₂²×C₁₉	semidirect
631. #339	C₂²×C₁₉	semidirect
687. #137	D₄×C₁₉	semidirect
694. AGL(1,ℤ/8)	D₄×C₁₉	semidirect
790. C₁₉	#23881	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
C₁₉×#3489	2
C₂×C₁₉×#456	2
C₂×C₁₉×#454	2
C₁₉×#3005	2
C₁₉×#2432	2
C₁₉×#2007	2
C₁₉×#2006	2
C₁₉×#2005	2
C₁₉×#2003	2
C₁₉×#1901	2
C₁₉×#1883	2
C₁₉×#1882	2
C₁₉×#1871	2
C₁₉×#1789	2
#23881	19

Subgroups — C19×#23881 #18029840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23881 #18029840