Subgroups — C₁₉×#32709 #18038668

Order 4864.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#120	—	2	1	no	—
25	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₉×#386	—	2	1	no	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#386	—	2	1	no	—
43	C₁₉×#385	—	2	1	no	—
44	C₁₉×#385	—	2	1	no	—
45	C₁₉×#385	—	2	1	no	—
46	C₁₉×#380	C₂²	1	1	yes	characteristic
47	C₁₉×#380	C₂²	1	1	yes	characteristic
48	C₁₉×#380	C₂²	1	1	yes	characteristic
49	C₁₉×#380	C₂²	1	1	yes	characteristic
50	C₁₉×#380	C₂²	1	1	yes	characteristic
51	C₁₉×#380	C₂²	1	1	yes	characteristic
52	C₁₉×#379	—	2	1	no	—
53	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
59	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	—	2	1	no	—
64	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	—	4	1	no	—
66	C₂³×C₄×C₁₉	—	4	1	no	—
67	C₂³×C₄×C₁₉	—	4	1	no	—
68	C₂³×C₄×C₁₉	—	4	1	no	—
69	C₂³×C₄×C₁₉	—	4	1	no	—
70	C₂³×C₄×C₁₉	—	4	1	no	—
71	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×SD₁₆×C₁₉	—	4	1	no	—
78	C₂×SD₁₆×C₁₉	—	4	1	no	—
79	C₂×SD₁₆×C₁₉	—	4	1	no	—
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×C₂²⋊Q₈	—	4	1	no	—
85	C₁₉×C₂²⋊Q₈	—	4	1	no	—
86	C₁₉×C₂²⋊Q₈	—	4	1	no	—
87	C₁₉×C₂²⋊Q₈	—	4	1	no	—
88	C₁₉×C₂²⋊Q₈	—	4	1	no	—
89	C₁₉×C₂²⋊Q₈	—	4	1	no	—
90	C₁₉×#121	—	4	1	no	—
91	C₁₉×#121	—	4	1	no	—
92	C₁₉×#121	—	4	1	no	—
93	C₁₉×#121	—	4	1	no	—
94	C₁₉×#121	—	4	1	no	—
95	C₁₉×#121	—	4	1	no	—
96	C₁₉×#120	—	4	4	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₁₉×#107	—	4	1	no	—
119	C₁₉×#107	—	4	1	no	—
120	C₁₉×#106	—	4	1	no	—
121	C₁₉×#103	—	4	1	no	—
122	C₁₉×#103	—	4	1	no	—
123	C₁₉×#103	—	4	1	no	—
124	C₁₉×#102	—	4	1	no	—
125	C₁₉×#102	—	4	1	no	—
126	C₁₉×#102	—	4	1	no	—
127	C₁₉×C₂²⋊C₈	—	4	1	no	—
128	C₁₉×C₂²⋊C₈	—	4	1	no	—
129	C₁₉×C₂²⋊C₈	—	4	1	no	—
130	C₁₉×C₂²⋊C₈	—	4	1	no	—
131	C₁₉×C₂²⋊C₈	—	4	1	no	—
132	C₁₉×C₂²⋊C₈	—	4	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	—	2	1	no	—
137	C₁₉×#95	—	2	1	no	—
138	C₁₉×#95	—	2	1	no	—
139	C₂⁴×C₁₉	—	2	2	no	—
140	C₂⁴×C₁₉	—	2	2	no	—
141	C₂⁴×C₁₉	—	2	2	no	—
142	C₂⁴×C₁₉	—	2	1	no	—
143	C₂⁴×C₁₉	—	4	1	no	—
144	C₂⁴×C₁₉	—	4	1	no	—
145	C₂⁴×C₁₉	—	4	1	no	—
146	C₂⁴×C₁₉	—	4	1	no	—
147	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	4	2	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	4	2	no	—
170	C₂×D₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	4	1	no	—
197	C₂²×C₄×C₁₉	—	4	1	no	—
198	C₂²×C₄×C₁₉	—	4	1	no	—
199	C₂²×C₄×C₁₉	—	4	1	no	—
200	C₂²×C₄×C₁₉	—	4	1	no	—
201	C₂²×C₄×C₁₉	—	4	1	no	—
202	C₂²×C₄×C₁₉	—	4	1	no	—
203	C₂²×C₄×C₁₉	—	4	1	no	—
204	C₂²×C₄×C₁₉	—	4	1	no	—
205	C₂²×C₄×C₁₉	—	4	4	no	—
206	C₂²×C₄×C₁₉	—	4	4	no	—
207	C₂²×C₄×C₁₉	—	4	4	no	—
208	C₂²×C₄×C₁₉	—	4	4	no	—
209	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
213	SD₁₆×C₁₉	—	4	4	no	—
214	C₂×C₈×C₁₉	—	2	1	no	—
215	C₂×C₈×C₁₉	—	2	1	no	—
216	C₂×C₈×C₁₉	—	2	1	no	—
217	C₂×C₈×C₁₉	—	2	1	no	—
218	C₂×C₈×C₁₉	—	2	1	no	—
219	C₂×C₈×C₁₉	—	2	1	no	—
220	C₂×C₈×C₁₉	—	2	1	no	—
221	C₂×C₈×C₁₉	—	2	1	no	—
222	C₂×C₈×C₁₉	—	2	1	no	—
223	C₂×C₈×C₁₉	—	2	1	no	—
224	C₂×C₈×C₁₉	—	2	1	no	—
225	C₂×C₈×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	2	1	no	—
233	C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₄⋊C₄×C₁₉	—	2	1	no	—
236	C₄⋊C₄×C₁₉	—	2	1	no	—
237	C₄⋊C₄×C₁₉	—	2	1	no	—
238	C₄⋊C₄×C₁₉	—	4	2	no	—
239	C₄⋊C₄×C₁₉	—	4	2	no	—
240	C₄⋊C₄×C₁₉	—	4	2	no	—
241	C₂²⋊C₄×C₁₉	—	4	2	no	—
242	C₂²⋊C₄×C₁₉	—	4	2	no	—
243	C₂²⋊C₄×C₁₉	—	4	2	no	—
244	C₂²⋊C₄×C₁₉	—	4	2	no	—
245	C₂²⋊C₄×C₁₉	—	4	2	no	—
246	C₂²⋊C₄×C₁₉	—	4	2	no	—
247	C₂²⋊C₄×C₁₉	—	4	2	no	—
248	C₂²⋊C₄×C₁₉	—	4	2	no	—
249	C₂²⋊C₄×C₁₉	—	4	2	no	—
250	C₂²⋊C₄×C₁₉	—	4	2	no	—
251	C₂²⋊C₄×C₁₉	—	4	2	no	—
252	C₂²⋊C₄×C₁₉	—	4	2	no	—
253	#32709	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂³×C₁₉	—	2	1	no	—
255	C₂³×C₁₉	—	2	1	no	—
256	C₂³×C₁₉	—	2	1	no	—
257	C₂³×C₁₉	—	2	1	no	—
258	C₂³×C₁₉	—	2	1	no	—
259	C₂³×C₁₉	—	2	1	no	—
260	C₂³×C₁₉	—	2	1	no	—
261	C₂³×C₁₉	—	2	1	no	—
262	C₂³×C₁₉	—	2	1	no	—
263	C₂³×C₁₉	—	2	1	no	—
264	C₂³×C₁₉	—	2	1	no	—
265	C₂³×C₁₉	—	2	1	no	—
266	C₂³×C₁₉	—	2	1	no	—
267	C₂³×C₁₉	—	2	1	no	—
268	C₂³×C₁₉	—	2	1	no	—
269	C₂³×C₁₉	—	2	1	no	—
270	C₂³×C₁₉	—	2	1	no	—
271	C₂³×C₁₉	—	2	1	no	—
272	C₂³×C₁₉	—	4	4	no	—
273	C₂³×C₁₉	—	4	4	no	—
274	C₂³×C₁₉	—	4	4	no	—
275	C₂³×C₁₉	—	4	4	no	—
276	C₂³×C₁₉	—	4	4	no	—
277	C₂³×C₁₉	—	4	4	no	—
278	C₂³×C₁₉	—	4	4	no	—
279	C₂³×C₁₉	—	4	1	no	—
280	C₂³×C₁₉	—	4	1	no	—
281	C₂³×C₁₉	—	4	1	no	—
282	C₂³×C₁₉	—	4	1	no	—
283	C₂³×C₁₉	—	4	1	no	—
284	C₂³×C₁₉	—	4	1	no	—
285	C₂³×C₁₉	—	4	1	no	—
286	C₂³×C₁₉	#135	1	2	yes	—
287	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
288	C₂³×C₁₉	#137	1	2	yes	—
289	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₁₉	—	4	1	no	—
291	Q₈×C₁₉	—	4	1	no	—
292	Q₈×C₁₉	—	4	1	no	—
293	Q₈×C₁₉	—	4	1	no	—
294	D₄×C₁₉	—	4	1	no	—
295	D₄×C₁₉	—	4	1	no	—
296	D₄×C₁₉	—	4	1	no	—
297	D₄×C₁₉	—	4	1	no	—
298	D₄×C₁₉	—	8	4	no	—
299	D₄×C₁₉	—	8	4	no	—
300	D₄×C₁₉	—	8	4	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	2	1	no	—
310	C₂×C₄×C₁₉	—	4	4	no	—
311	C₂×C₄×C₁₉	—	4	4	no	—
312	C₂×C₄×C₁₉	—	4	4	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	1	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	1	no	—
325	C₂×C₄×C₁₉	—	4	1	no	—
326	C₂×C₄×C₁₉	—	4	1	no	—
327	C₂×C₄×C₁₉	—	4	1	no	—
328	C₂×C₄×C₁₉	—	4	1	no	—
329	C₂×C₄×C₁₉	—	4	1	no	—
330	C₂×C₄×C₁₉	—	4	1	no	—
331	C₂×C₄×C₁₉	—	4	1	no	—
332	C₂×C₄×C₁₉	—	4	1	no	—
333	C₂×C₄×C₁₉	—	4	1	no	—
334	C₂×C₄×C₁₉	—	4	1	no	—
335	C₂×C₄×C₁₉	—	4	1	no	—
336	C₂×C₄×C₁₉	—	4	1	no	—
337	C₂×C₄×C₁₉	—	4	1	no	—
338	C₂×C₄×C₁₉	—	4	1	no	—
339	C₂×C₄×C₁₉	—	4	1	no	—
340	C₂×C₄×C₁₉	—	4	1	no	—
341	C₂×C₄×C₁₉	—	4	1	no	—
342	C₂×C₄×C₁₉	—	4	1	no	—
343	C₂×C₄×C₁₉	—	4	1	no	—
344	C₂×C₄×C₁₉	—	4	1	no	—
345	C₂×C₄×C₁₉	—	4	1	no	—
346	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
352	C₈×C₁₉	—	4	1	no	—
353	C₈×C₁₉	—	4	1	no	—
354	C₈×C₁₉	—	4	1	no	—
355	C₈×C₁₉	—	4	1	no	—
356	#2848	C₂×C₁₉	1	1	yes	characteristic, complemented
357	#2847	C₂×C₁₉	1	1	yes	characteristic
358	#2077	C₂×C₁₉	1	1	yes	characteristic, complemented
359	#2076	C₂×C₁₉	1	1	yes	characteristic, complemented
360	#2075	C₂×C₁₉	1	1	yes	characteristic, complemented
361	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
362	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
363	#2035	C₂×C₁₉	1	1	yes	characteristic, complemented
364	#2034	C₂×C₁₉	1	1	yes	characteristic, complemented
365	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
366	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
367	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
368	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
369	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
370	#1779	C₂×C₁₉	1	1	yes	characteristic, complemented
371	C₂²×C₁₉	—	2	2	no	—
372	C₂²×C₁₉	—	2	2	no	—
373	C₂²×C₁₉	—	2	2	no	—
374	C₂²×C₁₉	—	2	2	no	—
375	C₂²×C₁₉	—	2	2	no	—
376	C₂²×C₁₉	—	2	2	no	—
377	C₂²×C₁₉	—	2	2	no	—
378	C₂²×C₁₉	—	2	2	no	—
379	C₂²×C₁₉	—	2	2	no	—
380	C₂²×C₁₉	—	4	16	no	—
381	C₂²×C₁₉	—	4	1	no	—
382	C₂²×C₁₉	—	4	1	no	—
383	C₂²×C₁₉	—	4	1	no	—
384	C₂²×C₁₉	—	4	1	no	—
385	C₂²×C₁₉	—	4	1	no	—
386	C₂²×C₁₉	—	4	1	no	—
387	C₂²×C₁₉	—	4	1	no	—
388	C₂²×C₁₉	—	4	1	no	—
389	C₂²×C₁₉	—	4	1	no	—
390	C₂²×C₁₉	—	4	1	no	—
391	C₂²×C₁₉	—	4	1	no	—
392	C₂²×C₁₉	—	4	1	no	—
393	C₂²×C₁₉	—	8	1	no	—
394	C₂²×C₁₉	—	8	1	no	—
395	C₂²×C₁₉	—	8	1	no	—
396	C₂²×C₁₉	—	8	1	no	—
397	C₂²×C₁₉	—	8	1	no	—
398	C₂²×C₁₉	—	8	1	no	—
399	C₂²×C₁₉	—	8	1	no	—
400	C₂²×C₁₉	#534	1	1	yes	characteristic
401	C₂²×C₁₉	#534	1	1	yes	characteristic
402	C₂²×C₁₉	#534	1	1	yes	characteristic
403	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
404	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
406	C₂²×C₁₉	#575	1	1	yes	characteristic
407	C₄×C₁₉	—	4	1	no	—
408	C₄×C₁₉	—	4	1	no	—
409	C₄×C₁₉	—	4	1	no	—
410	C₄×C₁₉	—	8	1	no	—
411	C₄×C₁₉	—	8	1	no	—
412	C₄×C₁₉	—	8	1	no	—
413	C₄×C₁₉	—	8	1	no	—
414	C₄×C₁₉	—	8	1	no	—
415	C₄×C₁₉	—	8	1	no	—
416	C₄×C₁₉	—	8	1	no	—
417	C₄×C₁₉	#560	1	1	yes	characteristic
418	C₄×C₁₉	#560	1	1	yes	characteristic
419	C₄×C₁₉	#560	1	1	yes	characteristic
420	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
421	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
422	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
425	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
426	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
428	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
429	C₂×#120	—	2	1	no	—
430	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
431	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
432	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
433	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
434	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
435	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
436	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
437	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
438	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
439	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
445	#386	—	2	1	no	—
446	#386	—	2	1	no	—
447	#386	—	2	1	no	—
448	#385	—	2	1	no	—
449	#385	—	2	1	no	—
450	#385	—	2	1	no	—
451	#380	C₂²×C₁₉	1	1	yes	characteristic
452	#380	C₂²×C₁₉	1	1	yes	characteristic
453	#380	C₂²×C₁₉	1	1	yes	characteristic
454	#380	C₂²×C₁₉	1	1	yes	characteristic
455	#380	C₂²×C₁₉	1	1	yes	characteristic
456	#380	C₂²×C₁₉	1	1	yes	characteristic
457	#379	—	2	1	no	—
458	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
459	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
460	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
461	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
462	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
463	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
464	C₂×C₁₉	—	4	2	no	—
465	C₂×C₁₉	—	4	2	no	—
466	C₂×C₁₉	—	4	2	no	—
467	C₂×C₁₉	—	16	1	no	—
468	C₂×C₁₉	#2812	1	1	yes	characteristic
469	C₂×C₁₉	#3188	1	1	yes	characteristic
470	C₂×C₁₉	#3190	1	1	yes	characteristic
471	C₂×C₁₉	#3191	1	1	yes	characteristic
472	C₂×C₁₉	#3193	1	1	yes	characteristic
473	C₂×C₁₉	#3194	1	1	yes	characteristic
474	C₂×C₁₉	#3196	1	1	yes	characteristic
475	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
481	C₂³×C₄	—	4	1	no	—
482	C₂³×C₄	—	4	1	no	—
483	C₂³×C₄	—	4	1	no	—
484	C₂³×C₄	—	4	1	no	—
485	C₂³×C₄	—	4	1	no	—
486	C₂³×C₄	—	4	1	no	—
487	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
488	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
489	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
493	C₂×SD₁₆	—	4	1	no	—
494	C₂×SD₁₆	—	4	1	no	—
495	C₂×SD₁₆	—	4	1	no	—
496	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
500	C₂²⋊Q₈	—	4	1	no	—
501	C₂²⋊Q₈	—	4	1	no	—
502	C₂²⋊Q₈	—	4	1	no	—
503	C₂²⋊Q₈	—	4	1	no	—
504	C₂²⋊Q₈	—	4	1	no	—
505	C₂²⋊Q₈	—	4	1	no	—
506	#121	—	4	1	no	—
507	#121	—	4	1	no	—
508	#121	—	4	1	no	—
509	#121	—	4	1	no	—
510	#121	—	4	1	no	—
511	#121	—	4	1	no	—
512	#120	—	4	4	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	#107	—	4	1	no	—
535	#107	—	4	1	no	—
536	#106	—	4	1	no	—
537	#103	—	4	1	no	—
538	#103	—	4	1	no	—
539	#103	—	4	1	no	—
540	#102	—	4	1	no	—
541	#102	—	4	1	no	—
542	#102	—	4	1	no	—
543	C₂²⋊C₈	—	4	1	no	—
544	C₂²⋊C₈	—	4	1	no	—
545	C₂²⋊C₈	—	4	1	no	—
546	C₂²⋊C₈	—	4	1	no	—
547	C₂²⋊C₈	—	4	1	no	—
548	C₂²⋊C₈	—	4	1	no	—
549	#95	—	2	1	no	—
550	#95	—	2	1	no	—
551	#95	—	2	1	no	—
552	#95	—	2	1	no	—
553	#95	—	2	1	no	—
554	#95	—	2	1	no	—
555	C₁₉	#32709	1	1	yes	characteristic, direct product factor, Sylow
556	C₂⁴	—	2	2	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	—	4	1	no	—
561	C₂⁴	—	4	1	no	—
562	C₂⁴	—	4	1	no	—
563	C₂⁴	—	4	1	no	—
564	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
566	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	1	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	4	1	no	—
618	C₂²×C₄	—	4	1	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
630	SD₁₆	—	4	4	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	4	4	no	—
689	C₂³	—	4	4	no	—
690	C₂³	—	4	4	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	4	1	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	C₁₉×#135	1	2	yes	—
703	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
704	C₂³	C₁₉×#137	1	2	yes	—
705	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
706	Q₈	—	4	1	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	1	no	—
710	D₄	—	4	1	no	—
711	D₄	—	4	1	no	—
712	D₄	—	4	1	no	—
713	D₄	—	4	1	no	—
714	D₄	—	8	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	4	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
764	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
765	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
766	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
767	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
768	C₈	—	4	1	no	—
769	C₈	—	4	1	no	—
770	C₈	—	4	1	no	—
771	C₈	—	4	1	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	4	16	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	8	1	no	—
795	C₂²	—	8	1	no	—
796	C₂²	—	8	1	no	—
797	C₂²	—	8	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	C₁₉×#534	1	1	yes	characteristic
802	C₂²	C₁₉×#534	1	1	yes	characteristic
803	C₂²	C₁₉×#534	1	1	yes	characteristic
804	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
805	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
806	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
807	C₂²	C₁₉×#575	1	1	yes	characteristic
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	8	1	no	—
812	C₄	—	8	1	no	—
813	C₄	—	8	1	no	—
814	C₄	—	8	1	no	—
815	C₄	—	8	1	no	—
816	C₄	—	8	1	no	—
817	C₄	—	8	1	no	—
818	C₄	C₁₉×#560	1	1	yes	characteristic
819	C₄	C₁₉×#560	1	1	yes	characteristic
820	C₄	C₁₉×#560	1	1	yes	characteristic
821	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
822	C₂	—	4	2	no	—
823	C₂	—	4	2	no	—
824	C₂	—	4	2	no	—
825	C₂	—	16	1	no	—
826	C₂	C₁₉×#2812	1	1	yes	characteristic
827	C₂	C₁₉×#3188	1	1	yes	characteristic
828	C₂	C₁₉×#3190	1	1	yes	characteristic
829	C₂	C₁₉×#3191	1	1	yes	characteristic
830	C₂	C₁₉×#3193	1	1	yes	characteristic
831	C₂	C₁₉×#3194	1	1	yes	characteristic
832	C₂	C₁₉×#3196	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2848	C₂	semidirect
3. C₁₉×#2077	C₂	semidirect
4. C₁₉×#2076	C₂	semidirect
5. C₁₉×#2075	C₂	semidirect
6. C₁₉×#2036	C₂	semidirect
7. C₁₉×#2036	C₂	semidirect
8. C₁₉×#2035	C₂	semidirect
9. C₁₉×#2034	C₂	semidirect
10. C₁₉×#2033	C₂	semidirect
11. C₁₉×#2033	C₂	semidirect
12. C₁₉×#2000	C₂	semidirect
13. C₁₉×#2000	C₂	semidirect
14. C₁₉×#2000	C₂	semidirect
15. C₁₉×#1779	C₂	semidirect
17. C₂²×SD₁₆×C₁₉	C₂²	semidirect
25. C₂×C₁₉×#107	C₂²	semidirect
26. C₂×C₁₉×#107	C₂²	semidirect
27. C₂×C₁₉×#106	C₂²	semidirect
28. C₂×C₁₉×#103	C₂²	semidirect
29. C₂×C₁₉×#103	C₂²	semidirect
30. C₂×C₁₉×#103	C₂²	semidirect
31. C₂×C₁₉×#102	C₂²	semidirect
32. C₂×C₁₉×#102	C₂²	semidirect
33. C₂×C₁₉×#102	C₂²	semidirect
53. C₁₉×#340	C₂²	semidirect
54. C₁₉×#340	C₂²	semidirect
55. C₁₉×#340	C₂²	semidirect
56. C₁₉×#340	C₂²	semidirect
57. C₁₉×#340	C₂²	semidirect
58. C₁₉×#340	C₂²	semidirect
253. #32709	C₁₉	direct (N × H)
356. #2848	C₂×C₁₉	semidirect
358. #2077	C₂×C₁₉	semidirect
359. #2076	C₂×C₁₉	semidirect
360. #2075	C₂×C₁₉	semidirect
361. #2036	C₂×C₁₉	semidirect
362. #2036	C₂×C₁₉	semidirect
363. #2035	C₂×C₁₉	semidirect
364. #2034	C₂×C₁₉	semidirect
365. #2033	C₂×C₁₉	semidirect
366. #2033	C₂×C₁₉	semidirect
367. #2000	C₂×C₁₉	semidirect
368. #2000	C₂×C₁₉	semidirect
369. #2000	C₂×C₁₉	semidirect
370. #1779	C₂×C₁₉	semidirect
422. C₂²×SD₁₆	C₂²×C₁₉	semidirect
430. C₂×#107	C₂²×C₁₉	semidirect
431. C₂×#107	C₂²×C₁₉	semidirect
432. C₂×#106	C₂²×C₁₉	semidirect
433. C₂×#103	C₂²×C₁₉	semidirect
434. C₂×#103	C₂²×C₁₉	semidirect
435. C₂×#103	C₂²×C₁₉	semidirect
436. C₂×#102	C₂²×C₁₉	semidirect
437. C₂×#102	C₂²×C₁₉	semidirect
438. C₂×#102	C₂²×C₁₉	semidirect
458. #340	C₂²×C₁₉	semidirect
459. #340	C₂²×C₁₉	semidirect
460. #340	C₂²×C₁₉	semidirect
461. #340	C₂²×C₁₉	semidirect
462. #340	C₂²×C₁₉	semidirect
463. #340	C₂²×C₁₉	semidirect
555. C₁₉	#32709	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2848	2
C₁₉×#2847	2
C₁₉×#2077	2
C₁₉×#2076	2
C₁₉×#2075	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#2000	2
C₁₉×#1779	2
#32709	19

Subgroups — C19×#32709 #18038668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32709 #18038668