Subgroups — C₁₉×#25147 #18031106

Order 4864.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3005	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1978	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#137	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	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#525	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₁₉×#471	—	2	4	no	—
28	C₁₉×#469	—	2	1	no	—
29	C₁₉×#468	—	2	1	no	—
30	C₁₉×#466	—	2	1	no	—
31	C₁₉×#465	—	2	1	no	—
32	C₁₉×#452	—	2	1	no	—
33	C₁₉×#452	—	2	1	no	—
34	C₁₉×#449	—	2	1	no	—
35	C₁₉×#449	—	2	1	no	—
36	C₁₉×#449	—	2	1	no	—
37	C₁₉×#449	—	2	1	no	—
38	C₁₉×#449	—	2	1	no	—
39	C₁₉×#449	—	2	1	no	—
40	C₁₉×#436	—	2	1	no	—
41	C₁₉×#435	—	2	1	no	—
42	C₁₉×#435	—	2	1	no	—
43	C₈×D₄×C₁₉	—	2	1	no	—
44	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
46	C₁₉×#428	C₂²	1	1	yes	characteristic
47	C₁₉×#424	C₂²	1	1	yes	characteristic
48	C₁₉×#419	C₂²	1	1	yes	characteristic
49	C₁₉×#418	C₂²	1	1	yes	characteristic
50	C₁₉×#418	C₂²	1	1	yes	characteristic
51	C₁₉×#417	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
54	C₁₉×#413	—	2	4	no	—
55	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
58	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
60	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
61	C₁₉×#408	C₂²	1	1	yes	characteristic
62	C₁₉×#407	C₂²	1	1	yes	characteristic
63	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×#405	C₂²	1	1	yes	characteristic
65	C₁₉×#343	C₂²	1	1	yes	characteristic
66	C₁₉×#343	C₂²	1	1	yes	characteristic
67	C₁₉×#341	C₂²	1	1	yes	characteristic
68	C₁₉×#341	C₂²	1	1	yes	characteristic
69	C₂×#41×C₁₉	—	2	2	no	—
70	C₂×#41×C₁₉	—	2	2	no	—
71	C₂×#41×C₁₉	—	2	1	no	—
72	C₂×#41×C₁₉	—	2	1	no	—
73	C₂×#41×C₁₉	—	2	1	no	—
74	C₂×#41×C₁₉	—	2	1	no	—
75	C₂×#41×C₁₉	—	4	1	no	—
76	C₂×#41×C₁₉	—	4	1	no	—
77	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	—	2	1	no	—
81	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	—	2	1	no	—
84	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#137	—	2	2	no	—
86	C₁₉×#137	—	4	1	no	—
87	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
88	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
89	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
90	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
91	C₂×Q₁₆×C₁₉	—	2	1	no	—
92	C₂×SD₁₆×C₁₉	—	2	1	no	—
93	C₂×SD₁₆×C₁₉	—	2	1	no	—
94	C₂×SD₁₆×C₁₉	—	2	2	no	—
95	C₂×SD₁₆×C₁₉	—	2	1	no	—
96	C₂×SD₁₆×C₁₉	—	2	1	no	—
97	C₂×SD₁₆×C₁₉	—	2	1	no	—
98	C₂×SD₁₆×C₁₉	—	4	1	no	—
99	C₂×D₈×C₁₉	—	2	1	no	—
100	C₂×D₈×C₁₉	—	2	1	no	—
101	C₂×D₈×C₁₉	—	2	2	no	—
102	C₂×D₈×C₁₉	—	2	1	no	—
103	C₂×D₈×C₁₉	—	2	1	no	—
104	C₂×D₈×C₁₉	—	4	1	no	—
105	C₁₉×#131	—	2	2	no	—
106	C₁₉×#131	—	4	1	no	—
107	C₂×M₁₆×C₁₉	—	2	1	no	—
108	C₂×M₁₆×C₁₉	—	2	1	no	—
109	C₂×M₁₆×C₁₉	—	2	1	no	—
110	C₂×M₁₆×C₁₉	—	2	2	no	—
111	C₂×M₁₆×C₁₉	—	2	2	no	—
112	C₂×M₁₆×C₁₉	—	4	1	no	—
113	C₂×M₁₆×C₁₉	—	4	1	no	—
114	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₉	—	2	1	no	—
121	C₂²×C₈×C₁₉	—	2	1	no	—
122	C₂²×C₈×C₁₉	—	2	1	no	—
123	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₁₉×#123	—	2	1	no	—
126	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₁₉×#121	—	2	1	no	—
129	C₁₉×#121	—	2	1	no	—
130	C₁₉×#121	—	2	1	no	—
131	C₁₉×#121	—	2	1	no	—
132	C₁₉×#121	D₄	1	1	yes	characteristic
133	C₁₉×#121	D₄	1	1	yes	characteristic
134	C₁₉×#120	—	2	1	no	—
135	C₄×D₄×C₁₉	—	2	1	no	—
136	C₄×D₄×C₁₉	—	2	1	no	—
137	C₁₉×#117	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
140	C₁₉×#108	—	2	2	no	—
141	C₁₉×#108	—	4	1	no	—
142	C₁₉×#107	—	2	1	no	—
143	C₁₉×#106	—	2	1	no	—
144	C₁₉×C₄⋊C₈	—	2	1	no	—
145	C₁₉×C₄⋊C₈	—	2	1	no	—
146	C₁₉×#103	—	2	1	no	—
147	C₁₉×#103	—	2	1	no	—
148	C₁₉×#103	—	2	1	no	—
149	C₁₉×#103	—	2	1	no	—
150	C₁₉×#103	—	2	1	no	—
151	C₁₉×#102	—	2	1	no	—
152	C₁₉×#102	—	2	1	no	—
153	C₁₉×#102	—	2	1	no	—
154	C₁₉×#102	—	2	1	no	—
155	C₁₉×#102	—	2	1	no	—
156	C₁₉×#102	—	2	1	no	—
157	C₁₉×#102	—	2	1	no	—
158	C₁₉×#101	—	2	2	no	—
159	C₁₉×#101	D₄	1	4	yes	complemented
160	C₁₉×#100	—	2	2	no	—
161	C₁₉×#100	—	2	2	no	—
162	C₁₉×#100	—	2	2	no	—
163	C₁₉×#100	—	4	1	no	—
164	C₁₉×C₂²⋊C₈	—	2	1	no	—
165	C₁₉×C₂²⋊C₈	—	2	1	no	—
166	C₁₉×C₂²⋊C₈	—	2	1	no	—
167	C₁₉×C₂²⋊C₈	—	2	1	no	—
168	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
171	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
172	C₁₉×#97	—	2	1	no	—
173	C₄×C₈×C₁₉	—	2	1	no	—
174	C₂⁴×C₁₉	—	2	1	no	—
175	C₂⁴×C₁₉	—	2	1	no	—
176	C₂⁴×C₁₉	#41	1	1	yes	characteristic
177	#41×C₁₉	—	2	1	no	—
178	#41×C₁₉	—	2	1	no	—
179	#41×C₁₉	—	2	1	no	—
180	#41×C₁₉	—	2	1	no	—
181	#41×C₁₉	—	4	2	no	—
182	#41×C₁₉	—	4	2	no	—
183	#41×C₁₉	—	4	2	no	—
184	#41×C₁₉	—	4	2	no	—
185	#41×C₁₉	—	4	2	no	—
186	#41×C₁₉	—	4	2	no	—
187	#41×C₁₉	—	4	2	no	—
188	#41×C₁₉	—	4	2	no	—
189	C₂×Q₈×C₁₉	—	2	1	no	—
190	C₂×Q₈×C₁₉	—	2	1	no	—
191	C₂×Q₈×C₁₉	—	2	1	no	—
192	C₂×Q₈×C₁₉	—	2	1	no	—
193	C₂×Q₈×C₁₉	—	2	1	no	—
194	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₁₉	—	2	4	no	—
197	C₂×D₄×C₁₉	—	2	1	no	—
198	C₂×D₄×C₁₉	—	2	1	no	—
199	C₂×D₄×C₁₉	—	2	1	no	—
200	C₂×D₄×C₁₉	—	2	1	no	—
201	C₂×D₄×C₁₉	—	2	1	no	—
202	C₂×D₄×C₁₉	—	2	1	no	—
203	C₂×D₄×C₁₉	—	2	1	no	—
204	C₂×D₄×C₁₉	—	2	1	no	—
205	C₂×D₄×C₁₉	—	2	1	no	—
206	C₂×D₄×C₁₉	—	2	1	no	—
207	C₂×D₄×C₁₉	—	2	1	no	—
208	C₂×D₄×C₁₉	—	2	1	no	—
209	C₂×D₄×C₁₉	—	2	1	no	—
210	C₂×D₄×C₁₉	—	2	1	no	—
211	C₂×D₄×C₁₉	—	4	2	no	—
212	C₂×D₄×C₁₉	—	4	1	no	—
213	C₂×D₄×C₁₉	—	4	1	no	—
214	C₂×D₄×C₁₉	—	4	1	no	—
215	C₂×D₄×C₁₉	—	4	1	no	—
216	C₂×D₄×C₁₉	—	8	2	no	—
217	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₁₉	#41	1	2	yes	—
219	C₂²×C₄×C₁₉	—	2	1	no	—
220	C₂²×C₄×C₁₉	—	2	1	no	—
221	C₂²×C₄×C₁₉	—	2	1	no	—
222	C₂²×C₄×C₁₉	—	2	1	no	—
223	C₂²×C₄×C₁₉	—	2	4	no	—
224	C₂²×C₄×C₁₉	—	2	1	no	—
225	C₂²×C₄×C₁₉	—	2	1	no	—
226	C₂²×C₄×C₁₉	—	2	1	no	—
227	C₂²×C₄×C₁₉	—	4	2	no	—
228	C₂²×C₄×C₁₉	—	4	1	no	—
229	C₂²×C₄×C₁₉	—	4	1	no	—
230	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
235	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₁₉	—	4	2	no	—
237	SD₁₆×C₁₉	—	4	2	no	—
238	SD₁₆×C₁₉	—	4	2	no	—
239	SD₁₆×C₁₉	—	4	2	no	—
240	SD₁₆×C₁₉	—	4	2	no	—
241	SD₁₆×C₁₉	—	4	2	no	—
242	D₈×C₁₉	—	4	2	no	—
243	D₈×C₁₉	—	4	2	no	—
244	D₈×C₁₉	—	4	2	no	—
245	D₈×C₁₉	—	4	2	no	—
246	M₁₆×C₁₉	—	2	1	no	—
247	M₁₆×C₁₉	—	2	1	no	—
248	M₁₆×C₁₉	—	2	1	no	—
249	M₁₆×C₁₉	—	2	1	no	—
250	M₁₆×C₁₉	—	2	1	no	—
251	M₁₆×C₁₉	—	2	1	no	—
252	M₁₆×C₁₉	—	2	1	no	—
253	M₁₆×C₁₉	—	2	1	no	—
254	M₁₆×C₁₉	—	2	1	no	—
255	M₁₆×C₁₉	—	2	1	no	—
256	M₁₆×C₁₉	—	4	2	no	—
257	M₁₆×C₁₉	—	4	2	no	—
258	M₁₆×C₁₉	—	4	2	no	—
259	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
260	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
261	C₂×C₈×C₁₉	—	2	1	no	—
262	C₂×C₈×C₁₉	—	2	1	no	—
263	C₂×C₈×C₁₉	—	2	1	no	—
264	C₂×C₈×C₁₉	—	2	1	no	—
265	C₂×C₈×C₁₉	—	2	1	no	—
266	C₂×C₈×C₁₉	—	2	1	no	—
267	C₂×C₈×C₁₉	—	2	1	no	—
268	C₂×C₈×C₁₉	—	2	1	no	—
269	C₂×C₈×C₁₉	—	2	1	no	—
270	C₂×C₈×C₁₉	—	2	1	no	—
271	C₂×C₈×C₁₉	—	4	2	no	—
272	C₂×C₈×C₁₉	—	4	2	no	—
273	C₂×C₈×C₁₉	—	4	2	no	—
274	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
275	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
277	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	1	no	—
280	C₄⋊C₄×C₁₉	—	2	1	no	—
281	C₄⋊C₄×C₁₉	—	2	1	no	—
282	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
283	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
284	C₂²⋊C₄×C₁₉	—	2	1	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	1	no	—
289	C₂²⋊C₄×C₁₉	—	4	1	no	—
290	C₂²⋊C₄×C₁₉	—	4	1	no	—
291	C₄²×C₁₉	—	2	1	no	—
292	#25147	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂³×C₁₉	—	2	1	no	—
294	C₂³×C₁₉	—	2	1	no	—
295	C₂³×C₁₉	—	2	1	no	—
296	C₂³×C₁₉	—	2	2	no	—
297	C₂³×C₁₉	—	4	1	no	—
298	C₂³×C₁₉	—	4	1	no	—
299	C₂³×C₁₉	—	4	1	no	—
300	C₂³×C₁₉	—	4	1	no	—
301	C₂³×C₁₉	—	4	1	no	—
302	C₂³×C₁₉	—	4	1	no	—
303	C₂³×C₁₉	—	4	1	no	—
304	C₂³×C₁₉	—	8	1	no	—
305	C₂³×C₁₉	—	8	1	no	—
306	C₂³×C₁₉	—	8	1	no	—
307	C₂³×C₁₉	—	8	1	no	—
308	C₂³×C₁₉	#121	1	1	yes	characteristic
309	C₂³×C₁₉	#121	1	1	yes	characteristic
310	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
311	Q₈×C₁₉	—	2	1	no	—
312	Q₈×C₁₉	—	2	2	no	—
313	Q₈×C₁₉	—	2	2	no	—
314	Q₈×C₁₉	—	2	1	no	—
315	Q₈×C₁₉	—	4	1	no	—
316	Q₈×C₁₉	—	4	1	no	—
317	D₄×C₁₉	—	2	1	no	—
318	D₄×C₁₉	—	2	2	no	—
319	D₄×C₁₉	—	2	1	no	—
320	D₄×C₁₉	—	2	2	no	—
321	D₄×C₁₉	—	4	2	no	—
322	D₄×C₁₉	—	4	4	no	—
323	D₄×C₁₉	—	4	4	no	—
324	D₄×C₁₉	—	4	1	no	—
325	D₄×C₁₉	—	4	1	no	—
326	D₄×C₁₉	—	4	1	no	—
327	D₄×C₁₉	—	4	1	no	—
328	D₄×C₁₉	—	4	1	no	—
329	D₄×C₁₉	—	4	1	no	—
330	D₄×C₁₉	—	4	1	no	—
331	D₄×C₁₉	—	4	1	no	—
332	D₄×C₁₉	—	8	1	no	—
333	D₄×C₁₉	—	8	2	no	—
334	D₄×C₁₉	—	8	2	no	—
335	C₂×C₄×C₁₉	—	2	1	no	—
336	C₂×C₄×C₁₉	—	2	1	no	—
337	C₂×C₄×C₁₉	—	2	1	no	—
338	C₂×C₄×C₁₉	—	2	1	no	—
339	C₂×C₄×C₁₉	—	2	1	no	—
340	C₂×C₄×C₁₉	—	2	1	no	—
341	C₂×C₄×C₁₉	—	2	1	no	—
342	C₂×C₄×C₁₉	—	2	1	no	—
343	C₂×C₄×C₁₉	—	2	1	no	—
344	C₂×C₄×C₁₉	—	2	1	no	—
345	C₂×C₄×C₁₉	—	2	1	no	—
346	C₂×C₄×C₁₉	—	2	1	no	—
347	C₂×C₄×C₁₉	—	2	1	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	4	4	no	—
350	C₂×C₄×C₁₉	—	4	4	no	—
351	C₂×C₄×C₁₉	—	4	1	no	—
352	C₂×C₄×C₁₉	—	4	1	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	8	1	no	—
357	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
358	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
359	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
363	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
365	C₈×C₁₉	—	2	1	no	—
366	C₈×C₁₉	—	2	1	no	—
367	C₈×C₁₉	—	2	2	no	—
368	C₈×C₁₉	—	2	2	no	—
369	C₈×C₁₉	—	2	1	no	—
370	C₈×C₁₉	—	2	1	no	—
371	C₈×C₁₉	—	4	1	no	—
372	C₈×C₁₉	—	4	1	no	—
373	C₈×C₁₉	—	4	1	no	—
374	C₈×C₁₉	—	4	1	no	—
375	C₂×#471	C₂×C₁₉	1	1	yes	characteristic, complemented
376	#3055	C₂×C₁₉	1	1	yes	characteristic, complemented
377	#3005	C₂×C₁₉	1	1	yes	characteristic, complemented
378	C₂×#449	C₂×C₁₉	1	1	yes	characteristic, complemented
379	#2933	C₂×C₁₉	1	1	yes	characteristic, complemented
380	C₂×#413	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#2052	C₂×C₁₉	1	1	yes	characteristic, complemented
383	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
384	#2018	C₂×C₁₉	1	1	yes	characteristic, complemented
385	#1978	C₂×C₁₉	1	1	yes	characteristic, complemented
386	#1930	C₂×C₁₉	1	1	yes	characteristic, complemented
387	#1907	C₂×C₁₉	1	1	yes	characteristic, complemented
388	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
390	C₂²×C₁₉	—	2	1	no	—
391	C₂²×C₁₉	—	2	1	no	—
392	C₂²×C₁₉	—	2	1	no	—
393	C₂²×C₁₉	—	2	1	no	—
394	C₂²×C₁₉	—	2	1	no	—
395	C₂²×C₁₉	—	2	1	no	—
396	C₂²×C₁₉	—	2	1	no	—
397	C₂²×C₁₉	—	2	1	no	—
398	C₂²×C₁₉	—	4	2	no	—
399	C₂²×C₁₉	—	4	1	no	—
400	C₂²×C₁₉	—	4	1	no	—
401	C₂²×C₁₉	—	4	1	no	—
402	C₂²×C₁₉	—	8	1	no	—
403	C₂²×C₁₉	—	8	1	no	—
404	C₂²×C₁₉	—	8	2	no	—
405	C₂²×C₁₉	—	8	2	no	—
406	C₂²×C₁₉	—	8	1	no	—
407	C₂²×C₁₉	—	8	1	no	—
408	C₂²×C₁₉	—	8	1	no	—
409	C₂²×C₁₉	—	8	1	no	—
410	C₂²×C₁₉	—	8	1	no	—
411	C₂²×C₁₉	—	16	1	no	—
412	C₂²×C₁₉	—	16	1	no	—
413	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
414	C₂²×C₁₉	#525	1	1	yes	characteristic
415	C₂²×C₁₉	#538	1	1	yes	characteristic
416	C₄×C₁₉	—	2	1	no	—
417	C₄×C₁₉	—	2	1	no	—
418	C₄×C₁₉	—	4	2	no	—
419	C₄×C₁₉	—	4	1	no	—
420	C₄×C₁₉	—	4	1	no	—
421	C₄×C₁₉	—	4	1	no	—
422	C₄×C₁₉	—	8	1	no	—
423	C₄×C₁₉	D₄²	1	1	yes	characteristic
424	C₄×C₁₉	D₄²	1	1	yes	characteristic
425	C₄×C₁₉	#546	1	1	yes	characteristic
426	C₄×C₁₉	#546	1	1	yes	characteristic
427	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
428	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
429	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
431	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
432	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
434	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
435	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
436	#525	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
438	#471	—	2	4	no	—
439	#469	—	2	1	no	—
440	#468	—	2	1	no	—
441	#466	—	2	1	no	—
442	#465	—	2	1	no	—
443	#452	—	2	1	no	—
444	#452	—	2	1	no	—
445	#449	—	2	1	no	—
446	#449	—	2	1	no	—
447	#449	—	2	1	no	—
448	#449	—	2	1	no	—
449	#449	—	2	1	no	—
450	#449	—	2	1	no	—
451	#436	—	2	1	no	—
452	#435	—	2	1	no	—
453	#435	—	2	1	no	—
454	C₈×D₄	—	2	1	no	—
455	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
457	#428	C₂²×C₁₉	1	1	yes	characteristic
458	#424	C₂²×C₁₉	1	1	yes	characteristic
459	#419	C₂²×C₁₉	1	1	yes	characteristic
460	#418	C₂²×C₁₉	1	1	yes	characteristic
461	#418	C₂²×C₁₉	1	1	yes	characteristic
462	#417	C₂²×C₁₉	1	1	yes	characteristic
463	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
464	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
465	#413	—	2	4	no	—
466	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
467	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
468	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
469	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
470	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
471	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
472	#408	C₂²×C₁₉	1	1	yes	characteristic
473	#407	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
475	#405	C₂²×C₁₉	1	1	yes	characteristic
476	#343	C₂²×C₁₉	1	1	yes	characteristic
477	#343	C₂²×C₁₉	1	1	yes	characteristic
478	#341	C₂²×C₁₉	1	1	yes	characteristic
479	#341	C₂²×C₁₉	1	1	yes	characteristic
480	C₂×C₁₉	—	2	1	no	—
481	C₂×C₁₉	—	2	1	no	—
482	C₂×C₁₉	—	4	1	no	—
483	C₂×C₁₉	—	4	1	no	—
484	C₂×C₁₉	—	8	1	no	—
485	C₂×C₁₉	—	8	2	no	—
486	C₂×C₁₉	—	16	1	no	—
487	C₂×C₁₉	#2424	1	1	yes	characteristic
488	C₂×C₁₉	#3067	1	1	yes	characteristic
489	C₂×C₁₉	#3068	1	1	yes	characteristic
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	—	2	1	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	—	4	1	no	—
497	C₂×#41	—	4	1	no	—
498	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
499	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
506	#137	—	2	2	no	—
507	#137	—	4	1	no	—
508	AGL(1,ℤ/8)	—	2	2	no	—
509	AGL(1,ℤ/8)	—	2	2	no	—
510	AGL(1,ℤ/8)	—	4	1	no	—
511	AGL(1,ℤ/8)	—	4	1	no	—
512	C₂×Q₁₆	—	2	1	no	—
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	2	1	no	—
515	C₂×SD₁₆	—	2	1	no	—
516	C₂×SD₁₆	—	2	1	no	—
517	C₂×SD₁₆	—	2	1	no	—
518	C₂×SD₁₆	—	2	1	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×D₈	—	2	1	no	—
521	C₂×D₈	—	2	1	no	—
522	C₂×D₈	—	2	2	no	—
523	C₂×D₈	—	2	1	no	—
524	C₂×D₈	—	2	1	no	—
525	C₂×D₈	—	4	1	no	—
526	#131	—	2	2	no	—
527	#131	—	4	1	no	—
528	C₂×M₁₆	—	2	1	no	—
529	C₂×M₁₆	—	2	1	no	—
530	C₂×M₁₆	—	2	1	no	—
531	C₂×M₁₆	—	2	2	no	—
532	C₂×M₁₆	—	2	2	no	—
533	C₂×M₁₆	—	4	1	no	—
534	C₂×M₁₆	—	4	1	no	—
535	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
536	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
537	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
538	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
539	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
540	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
541	C₂²×C₈	—	2	1	no	—
542	C₂²×C₈	—	2	1	no	—
543	C₂²×C₈	—	2	1	no	—
544	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
545	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
546	#123	—	2	1	no	—
547	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
548	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
549	#121	—	2	1	no	—
550	#121	—	2	1	no	—
551	#121	—	2	1	no	—
552	#121	—	2	1	no	—
553	#121	D₄×C₁₉	1	1	yes	characteristic
554	#121	D₄×C₁₉	1	1	yes	characteristic
555	#120	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	#117	C₂³×C₁₉	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	#108	—	2	2	no	—
562	#108	—	4	1	no	—
563	#107	—	2	1	no	—
564	#106	—	2	1	no	—
565	C₄⋊C₈	—	2	1	no	—
566	C₄⋊C₈	—	2	1	no	—
567	#103	—	2	1	no	—
568	#103	—	2	1	no	—
569	#103	—	2	1	no	—
570	#103	—	2	1	no	—
571	#103	—	2	1	no	—
572	#102	—	2	1	no	—
573	#102	—	2	1	no	—
574	#102	—	2	1	no	—
575	#102	—	2	1	no	—
576	#102	—	2	1	no	—
577	#102	—	2	1	no	—
578	#102	—	2	1	no	—
579	#101	—	2	2	no	—
580	#101	D₄×C₁₉	1	4	yes	complemented
581	#100	—	2	2	no	—
582	#100	—	2	2	no	—
583	#100	—	2	2	no	—
584	#100	—	4	1	no	—
585	C₂²⋊C₈	—	2	1	no	—
586	C₂²⋊C₈	—	2	1	no	—
587	C₂²⋊C₈	—	2	1	no	—
588	C₂²⋊C₈	—	2	1	no	—
589	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
590	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
591	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
592	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
593	#97	—	2	1	no	—
594	C₄×C₈	—	2	1	no	—
595	C₁₉	#25147	1	1	yes	characteristic, direct product factor, Sylow
596	C₂⁴	—	2	1	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	#41×C₁₉	1	1	yes	characteristic
599	#41	—	2	1	no	—
600	#41	—	2	1	no	—
601	#41	—	2	1	no	—
602	#41	—	2	1	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	—	4	2	no	—
606	#41	—	4	2	no	—
607	#41	—	4	2	no	—
608	#41	—	4	2	no	—
609	#41	—	4	2	no	—
610	#41	—	4	2	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
617	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	1	no	—
637	C₂×D₄	—	4	1	no	—
638	C₂×D₄	—	8	2	no	—
639	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
640	C₂×D₄	#41×C₁₉	1	2	yes	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	1	no	—
652	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
656	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
658	Q₁₆	—	4	2	no	—
659	SD₁₆	—	4	2	no	—
660	SD₁₆	—	4	2	no	—
661	SD₁₆	—	4	2	no	—
662	SD₁₆	—	4	2	no	—
663	SD₁₆	—	4	2	no	—
664	D₈	—	4	2	no	—
665	D₈	—	4	2	no	—
666	D₈	—	4	2	no	—
667	D₈	—	4	2	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	2	1	no	—
670	M₁₆	—	2	1	no	—
671	M₁₆	—	2	1	no	—
672	M₁₆	—	2	1	no	—
673	M₁₆	—	2	1	no	—
674	M₁₆	—	2	1	no	—
675	M₁₆	—	2	1	no	—
676	M₁₆	—	2	1	no	—
677	M₁₆	—	2	1	no	—
678	M₁₆	—	4	2	no	—
679	M₁₆	—	4	2	no	—
680	M₁₆	—	4	2	no	—
681	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
682	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	4	2	no	—
694	C₂×C₈	—	4	2	no	—
695	C₂×C₈	—	4	2	no	—
696	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
697	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
698	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
699	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
705	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	4	1	no	—
712	C₂²⋊C₄	—	4	1	no	—
713	C₄²	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	8	1	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	1	no	—
729	C₂³	C₁₉×#121	1	1	yes	characteristic
730	C₂³	C₁₉×#121	1	1	yes	characteristic
731	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
732	Q₈	—	2	1	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	2	2	no	—
735	Q₈	—	2	1	no	—
736	Q₈	—	4	1	no	—
737	Q₈	—	4	1	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	1	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	8	1	no	—
754	D₄	—	8	2	no	—
755	D₄	—	8	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	8	1	no	—
778	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
779	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
783	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
784	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
785	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
786	C₈	—	2	1	no	—
787	C₈	—	2	1	no	—
788	C₈	—	2	2	no	—
789	C₈	—	2	2	no	—
790	C₈	—	2	1	no	—
791	C₈	—	2	1	no	—
792	C₈	—	4	1	no	—
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	2	no	—
811	C₂²	—	8	2	no	—
812	C₂²	—	8	1	no	—
813	C₂²	—	8	1	no	—
814	C₂²	—	8	1	no	—
815	C₂²	—	8	1	no	—
816	C₂²	—	8	1	no	—
817	C₂²	—	16	1	no	—
818	C₂²	—	16	1	no	—
819	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
820	C₂²	C₁₉×#525	1	1	yes	characteristic
821	C₂²	C₁₉×#538	1	1	yes	characteristic
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	8	1	no	—
829	C₄	D₄²×C₁₉	1	1	yes	characteristic
830	C₄	D₄²×C₁₉	1	1	yes	characteristic
831	C₄	C₁₉×#546	1	1	yes	characteristic
832	C₄	C₁₉×#546	1	1	yes	characteristic
833	C₂	—	2	1	no	—
834	C₂	—	2	1	no	—
835	C₂	—	4	1	no	—
836	C₂	—	4	1	no	—
837	C₂	—	8	1	no	—
838	C₂	—	8	2	no	—
839	C₂	—	16	1	no	—
840	C₂	C₁₉×#2424	1	1	yes	characteristic
841	C₂	C₁₉×#3067	1	1	yes	characteristic
842	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
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×#471	C₂	semidirect
2. C₁₉×#3055	C₂	semidirect
3. C₁₉×#3005	C₂	semidirect
4. C₂×C₁₉×#449	C₂	semidirect
5. C₁₉×#2933	C₂	semidirect
6. C₂×C₁₉×#413	C₂	semidirect
7. C₁₉×#2063	C₂	semidirect
8. C₁₉×#2052	C₂	semidirect
9. C₁₉×#2046	C₂	semidirect
10. C₁₉×#2018	C₂	semidirect
11. C₁₉×#1978	C₂	semidirect
12. C₁₉×#1930	C₂	semidirect
13. C₁₉×#1907	C₂	semidirect
14. C₁₉×#1900	C₂	semidirect
15. C₁₉×#1855	C₂	semidirect
159. C₁₉×#101	D₄	semidirect
292. #25147	C₁₉	direct (N × H)
375. C₂×#471	C₂×C₁₉	semidirect
376. #3055	C₂×C₁₉	semidirect
377. #3005	C₂×C₁₉	semidirect
378. C₂×#449	C₂×C₁₉	semidirect
379. #2933	C₂×C₁₉	semidirect
380. C₂×#413	C₂×C₁₉	semidirect
381. #2063	C₂×C₁₉	semidirect
382. #2052	C₂×C₁₉	semidirect
383. #2046	C₂×C₁₉	semidirect
384. #2018	C₂×C₁₉	semidirect
385. #1978	C₂×C₁₉	semidirect
386. #1930	C₂×C₁₉	semidirect
387. #1907	C₂×C₁₉	semidirect
388. #1900	C₂×C₁₉	semidirect
389. #1855	C₂×C₁₉	semidirect
580. #101	D₄×C₁₉	semidirect
595. C₁₉	#25147	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×#471	2
C₁₉×#3055	2
C₁₉×#3005	2
C₂×C₁₉×#449	2
C₁₉×#2933	2
C₂×C₁₉×#413	2
C₁₉×#2063	2
C₁₉×#2052	2
C₁₉×#2046	2
C₁₉×#2018	2
C₁₉×#1978	2
C₁₉×#1930	2
C₁₉×#1907	2
C₁₉×#1900	2
C₁₉×#1855	2
#25147	19

Subgroups — C19×#25147 #18031106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#25147 #18031106