Subgroups — C₁₉×#24467 #18030426

Order 4864.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3488	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#455	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3007	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×#2037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2007	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2004	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1896	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1792	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#550	—	2	1	no	—
23	C₁₉×#548	—	2	1	no	—
24	C₁₉×#546	—	2	1	no	—
25	C₁₉×#546	—	2	2	no	—
26	D₄²×C₁₉	—	2	2	no	—
27	D₄²×C₁₉	—	2	1	no	—
28	C₁₉×#537	—	2	1	no	—
29	C₁₉×#537	C₂²	1	1	yes	characteristic
30	C₁₉×#535	—	2	1	no	—
31	C₁₉×#535	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	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₉×#121	—	2	1	no	—
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, complemented
40	C₁₉×#470	—	2	1	no	—
41	C₁₉×#468	—	2	1	no	—
42	C₁₉×#467	—	2	1	no	—
43	C₁₉×#465	—	2	1	no	—
44	C₁₉×#455	—	2	4	no	—
45	C₁₉×#452	—	2	1	no	—
46	C₁₉×#452	—	2	1	no	—
47	C₁₉×#451	—	2	1	no	—
48	C₁₉×#450	—	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, complemented
54	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#417	C₂²	1	1	yes	characteristic
59	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
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×H(5,𝔽₂)	—	2	2	no	—
74	C₁₉×H(5,𝔽₂)	—	2	2	no	—
75	C₁₉×H(5,𝔽₂)	—	4	1	no	—
76	C₁₉×H(5,𝔽₂)	—	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	1	no	—
81	C₂×#41×C₁₉	—	2	2	no	—
82	C₂×#41×C₁₉	—	2	2	no	—
83	C₂×#41×C₁₉	—	4	1	no	—
84	C₂×#41×C₁₉	—	4	1	no	—
85	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
86	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
87	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
91	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₉	—	2	1	no	—
93	C₂²×D₄×C₁₉	—	2	2	no	—
94	C₂²×D₄×C₁₉	—	2	2	no	—
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	D₄	1	2	yes	—
99	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₉	—	2	1	no	—
101	C₂³×C₄×C₁₉	—	2	1	no	—
102	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×#137	—	2	2	no	—
104	C₁₉×#137	—	2	2	no	—
105	C₁₉×#137	—	2	2	no	—
106	C₁₉×#137	—	4	1	no	—
107	C₁₉×#137	—	4	1	no	—
108	C₁₉×#137	—	4	1	no	—
109	C₂×Q₁₆×C₁₉	—	2	1	no	—
110	C₂×Q₁₆×C₁₉	—	2	1	no	—
111	C₂×Q₁₆×C₁₉	—	2	1	no	—
112	C₂×SD₁₆×C₁₉	—	2	1	no	—
113	C₂×SD₁₆×C₁₉	—	2	1	no	—
114	C₂×SD₁₆×C₁₉	—	2	1	no	—
115	C₂×M₁₆×C₁₉	—	2	1	no	—
116	C₂×M₁₆×C₁₉	—	2	2	no	—
117	C₂×M₁₆×C₁₉	—	4	1	no	—
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	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₁₉	—	2	1	no	—
123	C₁₉×#127	—	2	2	no	—
124	C₁₉×#127	—	2	1	no	—
125	C₁₉×#124	—	2	2	no	—
126	C₁₉×#124	—	2	1	no	—
127	C₁₉×#124	—	2	2	no	—
128	C₁₉×#124	—	4	1	no	—
129	C₁₉×#123	—	2	2	no	—
130	C₁₉×#123	—	2	1	no	—
131	C₁₉×C₂²⋊Q₈	—	2	2	no	—
132	C₁₉×C₂²⋊Q₈	—	2	1	no	—
133	C₁₉×C₂²⋊Q₈	—	2	1	no	—
134	C₁₉×C₂²⋊Q₈	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	—	2	1	no	—
136	C₁₉×C₂²⋊Q₈	—	2	1	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
140	C₁₉×#121	—	2	2	no	—
141	C₁₉×#121	—	2	2	no	—
142	C₁₉×#121	—	2	2	no	—
143	C₁₉×#121	—	2	2	no	—
144	C₁₉×#121	—	2	2	no	—
145	C₁₉×#121	—	2	1	no	—
146	C₁₉×#121	—	2	1	no	—
147	C₁₉×#121	—	2	1	no	—
148	C₁₉×#121	—	2	1	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	D₄	1	1	yes	characteristic
155	C₁₉×#121	D₄	1	1	yes	characteristic
156	C₁₉×#120	—	2	2	no	—
157	C₁₉×#120	—	2	2	no	—
158	C₁₉×#120	—	2	2	no	—
159	C₁₉×#120	—	2	1	no	—
160	C₁₉×#120	—	2	2	no	—
161	C₄×Q₈×C₁₉	—	2	1	no	—
162	C₄×D₄×C₁₉	—	2	2	no	—
163	C₄×D₄×C₁₉	—	2	2	no	—
164	C₄×D₄×C₁₉	—	2	1	no	—
165	C₄×D₄×C₁₉	—	2	2	no	—
166	C₄×D₄×C₁₉	—	2	1	no	—
167	C₄×D₄×C₁₉	—	2	1	no	—
168	C₁₉×#117	—	2	1	no	—
169	C₁₉×#117	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	1	no	—
176	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂×C₂²⋊C₄×C₁₉	—	2	2	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×#103	—	2	1	no	—
196	C₁₉×#103	—	2	1	no	—
197	C₁₉×#102	—	2	1	no	—
198	C₁₉×#102	—	2	1	no	—
199	C₁₉×#102	—	2	1	no	—
200	C₁₉×#100	—	2	2	no	—
201	C₁₉×#100	—	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	2	no	—
207	C₂⁴×C₁₉	—	2	1	no	—
208	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
210	#41×C₁₉	—	2	1	no	—
211	#41×C₁₉	—	2	1	no	—
212	#41×C₁₉	—	2	2	no	—
213	#41×C₁₉	—	2	2	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	—	2	1	no	—
222	#41×C₁₉	—	4	2	no	—
223	#41×C₁₉	—	4	2	no	—
224	#41×C₁₉	—	4	1	no	—
225	#41×C₁₉	—	4	1	no	—
226	#41×C₁₉	—	4	2	no	—
227	#41×C₁₉	—	4	2	no	—
228	#41×C₁₉	—	4	2	no	—
229	#41×C₁₉	—	4	2	no	—
230	#41×C₁₉	—	4	2	no	—
231	#41×C₁₉	—	4	2	no	—
232	#41×C₁₉	C₂×D₄	1	2	yes	—
233	#41×C₁₉	#41	1	2	yes	—
234	C₂×Q₈×C₁₉	—	2	1	no	—
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	—	4	1	no	—
243	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂×D₄×C₁₉	—	2	1	no	—
247	C₂×D₄×C₁₉	—	2	2	no	—
248	C₂×D₄×C₁₉	—	2	2	no	—
249	C₂×D₄×C₁₉	—	2	2	no	—
250	C₂×D₄×C₁₉	—	2	2	no	—
251	C₂×D₄×C₁₉	—	2	1	no	—
252	C₂×D₄×C₁₉	—	2	1	no	—
253	C₂×D₄×C₁₉	—	2	1	no	—
254	C₂×D₄×C₁₉	—	2	1	no	—
255	C₂×D₄×C₁₉	—	2	1	no	—
256	C₂×D₄×C₁₉	—	2	2	no	—
257	C₂×D₄×C₁₉	—	2	2	no	—
258	C₂×D₄×C₁₉	—	2	2	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	—	4	1	no	—
269	C₂×D₄×C₁₉	—	4	2	no	—
270	C₂×D₄×C₁₉	—	4	2	no	—
271	C₂×D₄×C₁₉	—	4	2	no	—
272	C₂×D₄×C₁₉	—	4	2	no	—
273	C₂×D₄×C₁₉	—	4	4	no	—
274	C₂×D₄×C₁₉	—	4	4	no	—
275	C₂×D₄×C₁₉	—	4	2	no	—
276	C₂×D₄×C₁₉	—	4	2	no	—
277	C₂×D₄×C₁₉	—	4	4	no	—
278	C₂×D₄×C₁₉	—	8	4	no	—
279	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
280	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
281	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₉	—	2	1	no	—
283	C₂²×C₄×C₁₉	—	2	1	no	—
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	2	no	—
288	C₂²×C₄×C₁₉	—	2	1	no	—
289	C₂²×C₄×C₁₉	—	2	1	no	—
290	C₂²×C₄×C₁₉	—	2	1	no	—
291	C₂²×C₄×C₁₉	—	2	2	no	—
292	C₂²×C₄×C₁₉	—	2	1	no	—
293	C₂²×C₄×C₁₉	—	2	1	no	—
294	C₂²×C₄×C₁₉	—	2	1	no	—
295	C₂²×C₄×C₁₉	—	2	1	no	—
296	C₂²×C₄×C₁₉	—	2	1	no	—
297	C₂²×C₄×C₁₉	—	2	1	no	—
298	C₂²×C₄×C₁₉	—	4	2	no	—
299	C₂²×C₄×C₁₉	—	4	2	no	—
300	C₂²×C₄×C₁₉	—	4	2	no	—
301	C₂²×C₄×C₁₉	—	4	2	no	—
302	C₂²×C₄×C₁₉	—	4	2	no	—
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	1	yes	characteristic
306	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
310	Q₁₆×C₁₉	—	4	2	no	—
311	Q₁₆×C₁₉	—	4	2	no	—
312	Q₁₆×C₁₉	—	4	2	no	—
313	SD₁₆×C₁₉	—	4	2	no	—
314	SD₁₆×C₁₉	—	4	2	no	—
315	SD₁₆×C₁₉	—	4	2	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	—	2	1	no	—
321	M₁₆×C₁₉	—	2	1	no	—
322	M₁₆×C₁₉	—	2	1	no	—
323	M₁₆×C₁₉	—	4	2	no	—
324	M₁₆×C₁₉	C₂×D₄	1	2	yes	complemented
325	C₂×C₈×C₁₉	—	2	1	no	—
326	C₂×C₈×C₁₉	—	2	1	no	—
327	C₂×C₈×C₁₉	—	2	1	no	—
328	C₂×C₈×C₁₉	—	2	1	no	—
329	C₂×C₈×C₁₉	—	4	2	no	—
330	C₄⋊C₄×C₁₉	—	2	2	no	—
331	C₄⋊C₄×C₁₉	—	2	2	no	—
332	C₄⋊C₄×C₁₉	—	2	1	no	—
333	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
339	C₄⋊C₄×C₁₉	—	4	1	no	—
340	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
347	C₂²⋊C₄×C₁₉	—	2	1	no	—
348	C₂²⋊C₄×C₁₉	—	2	1	no	—
349	C₂²⋊C₄×C₁₉	—	2	1	no	—
350	C₂²⋊C₄×C₁₉	—	2	1	no	—
351	C₂²⋊C₄×C₁₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₉	—	2	1	no	—
354	C₂²⋊C₄×C₁₉	—	4	4	no	—
355	C₂²⋊C₄×C₁₉	—	4	4	no	—
356	C₂²⋊C₄×C₁₉	—	4	1	no	—
357	C₂²⋊C₄×C₁₉	—	4	1	no	—
358	C₄²×C₁₉	—	2	2	no	—
359	C₄²×C₁₉	—	2	1	no	—
360	C₄²×C₁₉	—	2	1	no	—
361	C₄²×C₁₉	—	2	1	no	—
362	C₄²×C₁₉	—	2	1	no	—
363	C₄²×C₁₉	—	4	2	no	—
364	C₄²×C₁₉	C₂×D₄	1	2	yes	complemented
365	#24467	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
366	C₂³×C₁₉	—	2	1	no	—
367	C₂³×C₁₉	—	2	1	no	—
368	C₂³×C₁₉	—	2	1	no	—
369	C₂³×C₁₉	—	2	2	no	—
370	C₂³×C₁₉	—	2	2	no	—
371	C₂³×C₁₉	—	2	1	no	—
372	C₂³×C₁₉	—	2	1	no	—
373	C₂³×C₁₉	—	2	2	no	—
374	C₂³×C₁₉	—	2	2	no	—
375	C₂³×C₁₉	—	4	1	no	—
376	C₂³×C₁₉	—	4	2	no	—
377	C₂³×C₁₉	—	4	4	no	—
378	C₂³×C₁₉	—	4	2	no	—
379	C₂³×C₁₉	—	4	2	no	—
380	C₂³×C₁₉	—	4	2	no	—
381	C₂³×C₁₉	—	8	1	no	—
382	C₂³×C₁₉	—	8	2	no	—
383	C₂³×C₁₉	—	8	2	no	—
384	C₂³×C₁₉	#120	1	1	yes	characteristic
385	C₂³×C₁₉	#120	1	1	yes	characteristic
386	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₁₉	—	2	1	no	—
388	Q₈×C₁₉	—	2	1	no	—
389	Q₈×C₁₉	—	2	1	no	—
390	Q₈×C₁₉	—	2	1	no	—
391	Q₈×C₁₉	—	2	1	no	—
392	Q₈×C₁₉	—	4	2	no	—
393	Q₈×C₁₉	—	4	1	no	—
394	Q₈×C₁₉	—	4	1	no	—
395	Q₈×C₁₉	—	4	1	no	—
396	Q₈×C₁₉	—	4	1	no	—
397	Q₈×C₁₉	#121	1	2	yes	—
398	D₄×C₁₉	—	2	2	no	—
399	D₄×C₁₉	—	2	2	no	—
400	D₄×C₁₉	—	2	1	no	—
401	D₄×C₁₉	—	2	1	no	—
402	D₄×C₁₉	—	2	1	no	—
403	D₄×C₁₉	—	2	1	no	—
404	D₄×C₁₉	—	2	1	no	—
405	D₄×C₁₉	—	4	2	no	—
406	D₄×C₁₉	—	4	2	no	—
407	D₄×C₁₉	—	4	4	no	—
408	D₄×C₁₉	—	4	2	no	—
409	D₄×C₁₉	—	4	4	no	—
410	D₄×C₁₉	—	4	1	no	—
411	D₄×C₁₉	—	4	1	no	—
412	D₄×C₁₉	—	4	1	no	—
413	D₄×C₁₉	—	4	1	no	—
414	D₄×C₁₉	—	4	4	no	—
415	D₄×C₁₉	—	4	2	no	—
416	D₄×C₁₉	—	4	1	no	—
417	D₄×C₁₉	—	4	1	no	—
418	D₄×C₁₉	—	4	1	no	—
419	D₄×C₁₉	—	4	1	no	—
420	D₄×C₁₉	—	8	1	no	—
421	D₄×C₁₉	—	8	2	no	—
422	D₄×C₁₉	—	8	2	no	—
423	D₄×C₁₉	—	8	2	no	—
424	D₄×C₁₉	—	8	2	no	—
425	D₄×C₁₉	#121	1	2	yes	—
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	1	no	—
430	C₂×C₄×C₁₉	—	2	1	no	—
431	C₂×C₄×C₁₉	—	2	1	no	—
432	C₂×C₄×C₁₉	—	2	1	no	—
433	C₂×C₄×C₁₉	—	2	1	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	2	no	—
440	C₂×C₄×C₁₉	—	2	1	no	—
441	C₂×C₄×C₁₉	—	2	2	no	—
442	C₂×C₄×C₁₉	—	2	1	no	—
443	C₂×C₄×C₁₉	—	2	1	no	—
444	C₂×C₄×C₁₉	—	2	1	no	—
445	C₂×C₄×C₁₉	—	2	2	no	—
446	C₂×C₄×C₁₉	—	4	2	no	—
447	C₂×C₄×C₁₉	—	4	2	no	—
448	C₂×C₄×C₁₉	—	4	2	no	—
449	C₂×C₄×C₁₉	—	4	4	no	—
450	C₂×C₄×C₁₉	—	4	1	no	—
451	C₂×C₄×C₁₉	—	4	1	no	—
452	C₂×C₄×C₁₉	—	4	1	no	—
453	C₂×C₄×C₁₉	—	4	8	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	1	no	—
458	C₂×C₄×C₁₉	—	4	1	no	—
459	C₂×C₄×C₁₉	—	4	2	no	—
460	C₂×C₄×C₁₉	—	4	2	no	—
461	C₂×C₄×C₁₉	—	4	1	no	—
462	C₂×C₄×C₁₉	—	4	1	no	—
463	C₂×C₄×C₁₉	—	4	1	no	—
464	C₂×C₄×C₁₉	—	4	1	no	—
465	C₂×C₄×C₁₉	—	8	2	no	—
466	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
467	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
468	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
472	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
473	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
474	C₈×C₁₉	—	2	2	no	—
475	C₈×C₁₉	—	4	1	no	—
476	C₈×C₁₉	—	4	1	no	—
477	C₈×C₁₉	—	4	1	no	—
478	#3488	C₂×C₁₉	1	1	yes	characteristic
479	#3056	C₂×C₁₉	1	1	yes	characteristic, complemented
480	C₂×#455	C₂×C₁₉	1	1	yes	characteristic, complemented
481	#3007	C₂×C₁₉	1	1	yes	characteristic, complemented
482	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic, complemented
483	#2850	C₂×C₁₉	1	1	yes	characteristic, complemented
484	#2040	C₂×C₁₉	1	1	yes	characteristic, complemented
485	#2037	C₂×C₁₉	1	1	yes	characteristic, complemented
486	#2007	C₂×C₁₉	1	1	yes	characteristic, complemented
487	#2004	C₂×C₁₉	1	1	yes	characteristic, complemented
488	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
489	#1896	C₂×C₁₉	1	1	yes	characteristic, complemented
490	#1882	C₂×C₁₉	1	1	yes	characteristic, complemented
491	#1860	C₂×C₁₉	1	1	yes	characteristic, complemented
492	#1792	C₂×C₁₉	1	1	yes	characteristic, complemented
493	C₂²×C₁₉	—	2	1	no	—
494	C₂²×C₁₉	—	2	1	no	—
495	C₂²×C₁₉	—	2	1	no	—
496	C₂²×C₁₉	—	2	1	no	—
497	C₂²×C₁₉	—	2	1	no	—
498	C₂²×C₁₉	—	2	2	no	—
499	C₂²×C₁₉	—	2	1	no	—
500	C₂²×C₁₉	—	2	1	no	—
501	C₂²×C₁₉	—	4	2	no	—
502	C₂²×C₁₉	—	4	2	no	—
503	C₂²×C₁₉	—	4	1	no	—
504	C₂²×C₁₉	—	4	1	no	—
505	C₂²×C₁₉	—	4	1	no	—
506	C₂²×C₁₉	—	4	1	no	—
507	C₂²×C₁₉	—	4	2	no	—
508	C₂²×C₁₉	—	4	2	no	—
509	C₂²×C₁₉	—	4	1	no	—
510	C₂²×C₁₉	—	4	1	no	—
511	C₂²×C₁₉	—	4	1	no	—
512	C₂²×C₁₉	—	4	2	no	—
513	C₂²×C₁₉	—	4	1	no	—
514	C₂²×C₁₉	—	8	4	no	—
515	C₂²×C₁₉	—	8	2	no	—
516	C₂²×C₁₉	—	8	2	no	—
517	C₂²×C₁₉	—	16	4	no	—
518	C₂²×C₁₉	#455	1	2	yes	complemented
519	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
520	C₂²×C₁₉	D₄²	1	1	yes	characteristic
521	C₂²×C₁₉	#546	1	1	yes	characteristic
522	C₄×C₁₉	—	2	1	no	—
523	C₄×C₁₉	—	2	1	no	—
524	C₄×C₁₉	—	2	2	no	—
525	C₄×C₁₉	—	4	2	no	—
526	C₄×C₁₉	—	4	2	no	—
527	C₄×C₁₉	—	4	1	no	—
528	C₄×C₁₉	—	4	1	no	—
529	C₄×C₁₉	—	4	2	no	—
530	C₄×C₁₉	—	4	1	no	—
531	C₄×C₁₉	—	4	1	no	—
532	C₄×C₁₉	—	8	1	no	—
533	C₄×C₁₉	—	8	1	no	—
534	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
535	C₄×C₁₉	#534	1	1	yes	characteristic
536	C₄×C₁₉	D₄²	1	1	yes	characteristic
537	C₄×C₁₉	#546	1	1	yes	characteristic
538	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
539	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
540	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
541	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic, complemented
542	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic, complemented
543	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
544	#550	—	2	1	no	—
545	#548	—	2	1	no	—
546	#546	—	2	1	no	—
547	#546	—	2	2	no	—
548	D₄²	—	2	2	no	—
549	D₄²	—	2	1	no	—
550	#537	—	2	1	no	—
551	#537	C₂²×C₁₉	1	1	yes	characteristic
552	#535	—	2	1	no	—
553	#535	C₂²×C₁₉	1	1	yes	characteristic
554	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
555	#525	—	2	1	no	—
556	#525	C₂²×C₁₉	1	1	yes	characteristic
557	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
558	C₂×#121	—	2	1	no	—
559	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
560	#520	C₂²×C₁₉	1	1	yes	characteristic
561	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
562	#470	—	2	1	no	—
563	#468	—	2	1	no	—
564	#467	—	2	1	no	—
565	#465	—	2	1	no	—
566	#455	—	2	4	no	—
567	#452	—	2	1	no	—
568	#452	—	2	1	no	—
569	#451	—	2	1	no	—
570	#450	—	2	1	no	—
571	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
572	C₂×#104	—	2	4	no	—
573	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
574	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
575	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
576	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
577	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
578	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
579	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
580	#417	C₂²×C₁₉	1	1	yes	characteristic
581	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
582	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
583	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
584	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic, complemented
585	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
586	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
587	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
588	#388	—	2	2	no	—
589	#386	—	2	2	no	—
590	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
591	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
592	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
593	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
594	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
595	C₂×C₁₉	—	2	1	no	—
596	C₂×C₁₉	—	2	1	no	—
597	C₂×C₁₉	—	2	2	no	—
598	C₂×C₁₉	—	4	1	no	—
599	C₂×C₁₉	—	4	2	no	—
600	C₂×C₁₉	—	8	1	no	—
601	C₂×C₁₉	—	8	2	no	—
602	C₂×C₁₉	—	8	1	no	—
603	C₂×C₁₉	#2410	1	1	yes	characteristic
604	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
605	C₂×C₁₉	#3018	1	1	yes	characteristic
606	H(5,𝔽₂)	—	2	2	no	—
607	H(5,𝔽₂)	—	2	2	no	—
608	H(5,𝔽₂)	—	4	1	no	—
609	H(5,𝔽₂)	—	4	1	no	—
610	C₂×#41	—	2	1	no	—
611	C₂×#41	—	2	1	no	—
612	C₂×#41	—	2	1	no	—
613	C₂×#41	—	2	1	no	—
614	C₂×#41	—	2	2	no	—
615	C₂×#41	—	2	2	no	—
616	C₂×#41	—	4	1	no	—
617	C₂×#41	—	4	1	no	—
618	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
619	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
620	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
621	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
622	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
623	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
624	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
625	C₂²×D₄	—	2	1	no	—
626	C₂²×D₄	—	2	2	no	—
627	C₂²×D₄	—	2	2	no	—
628	C₂²×D₄	—	2	1	no	—
629	C₂²×D₄	—	2	1	no	—
630	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
631	C₂²×D₄	D₄×C₁₉	1	2	yes	—
632	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
633	C₂³×C₄	—	2	1	no	—
634	C₂³×C₄	—	2	1	no	—
635	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
636	#137	—	2	2	no	—
637	#137	—	2	2	no	—
638	#137	—	2	2	no	—
639	#137	—	4	1	no	—
640	#137	—	4	1	no	—
641	#137	—	4	1	no	—
642	C₂×Q₁₆	—	2	1	no	—
643	C₂×Q₁₆	—	2	1	no	—
644	C₂×Q₁₆	—	2	1	no	—
645	C₂×SD₁₆	—	2	1	no	—
646	C₂×SD₁₆	—	2	1	no	—
647	C₂×SD₁₆	—	2	1	no	—
648	C₂×M₁₆	—	2	1	no	—
649	C₂×M₁₆	—	2	2	no	—
650	C₂×M₁₆	—	4	1	no	—
651	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
652	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
653	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
654	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
655	C₂²×C₈	—	2	1	no	—
656	#127	—	2	2	no	—
657	#127	—	2	1	no	—
658	#124	—	2	2	no	—
659	#124	—	2	1	no	—
660	#124	—	2	2	no	—
661	#124	—	4	1	no	—
662	#123	—	2	2	no	—
663	#123	—	2	1	no	—
664	C₂²⋊Q₈	—	2	2	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	2	no	—
677	#121	—	2	2	no	—
678	#121	—	2	1	no	—
679	#121	—	2	1	no	—
680	#121	—	2	1	no	—
681	#121	—	2	1	no	—
682	#121	—	2	1	no	—
683	#121	—	2	1	no	—
684	#121	—	2	2	no	—
685	#121	—	2	1	no	—
686	#121	—	2	1	no	—
687	#121	D₄×C₁₉	1	1	yes	characteristic
688	#121	D₄×C₁₉	1	1	yes	characteristic
689	#120	—	2	2	no	—
690	#120	—	2	2	no	—
691	#120	—	2	2	no	—
692	#120	—	2	1	no	—
693	#120	—	2	2	no	—
694	C₄×Q₈	—	2	1	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	—	2	2	no	—
699	C₄×D₄	—	2	1	no	—
700	C₄×D₄	—	2	1	no	—
701	#117	—	2	1	no	—
702	#117	C₂³×C₁₉	1	1	yes	characteristic
703	C₂×C₄⋊C₄	—	2	1	no	—
704	C₂×C₄⋊C₄	—	2	1	no	—
705	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	—	2	2	no	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₂²⋊C₄	—	2	2	no	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
712	C₂×C₄²	—	2	2	no	—
713	C₂×C₄²	—	2	1	no	—
714	C₂×C₄²	—	4	1	no	—
715	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
717	#107	—	2	1	no	—
718	#106	—	2	1	no	—
719	#104	—	2	2	no	—
720	#104	—	2	2	no	—
721	#104	—	2	2	no	—
722	#104	—	2	2	no	—
723	#104	—	4	1	no	—
724	#104	D₄×C₁₉	1	4	yes	complemented
725	#103	—	2	1	no	—
726	#103	—	2	1	no	—
727	#103	—	2	1	no	—
728	#103	—	2	1	no	—
729	#103	—	2	1	no	—
730	#102	—	2	1	no	—
731	#102	—	2	1	no	—
732	#102	—	2	1	no	—
733	#100	—	2	2	no	—
734	#100	—	4	1	no	—
735	C₂²⋊C₈	—	2	1	no	—
736	C₂²⋊C₈	—	2	1	no	—
737	#95	—	2	2	no	—
738	#95	—	2	2	no	—
739	C₁₉	#24467	1	1	yes	characteristic, direct product factor, Sylow
740	C₂⁴	—	2	2	no	—
741	C₂⁴	—	2	1	no	—
742	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
743	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
744	#41	—	2	1	no	—
745	#41	—	2	1	no	—
746	#41	—	2	2	no	—
747	#41	—	2	2	no	—
748	#41	—	2	1	no	—
749	#41	—	2	1	no	—
750	#41	—	2	1	no	—
751	#41	—	2	1	no	—
752	#41	—	2	1	no	—
753	#41	—	2	1	no	—
754	#41	—	2	1	no	—
755	#41	—	2	1	no	—
756	#41	—	4	2	no	—
757	#41	—	4	2	no	—
758	#41	—	4	1	no	—
759	#41	—	4	1	no	—
760	#41	—	4	2	no	—
761	#41	—	4	2	no	—
762	#41	—	4	2	no	—
763	#41	—	4	2	no	—
764	#41	—	4	2	no	—
765	#41	—	4	2	no	—
766	#41	C₂×D₄×C₁₉	1	2	yes	—
767	#41	#41×C₁₉	1	2	yes	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	4	1	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	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	4	1	no	—
803	C₂×D₄	—	4	2	no	—
804	C₂×D₄	—	4	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	4	4	no	—
808	C₂×D₄	—	4	4	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	—	4	2	no	—
811	C₂×D₄	—	4	4	no	—
812	C₂×D₄	—	8	4	no	—
813	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
814	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
815	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
816	C₂²×C₄	—	2	1	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	2	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
839	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
840	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
841	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
842	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
844	Q₁₆	—	4	2	no	—
845	Q₁₆	—	4	2	no	—
846	Q₁₆	—	4	2	no	—
847	SD₁₆	—	4	2	no	—
848	SD₁₆	—	4	2	no	—
849	SD₁₆	—	4	2	no	—
850	M₁₆	—	2	1	no	—
851	M₁₆	—	2	1	no	—
852	M₁₆	—	2	1	no	—
853	M₁₆	—	2	1	no	—
854	M₁₆	—	2	1	no	—
855	M₁₆	—	2	1	no	—
856	M₁₆	—	2	1	no	—
857	M₁₆	—	4	2	no	—
858	M₁₆	C₂×D₄×C₁₉	1	2	yes	complemented
859	C₂×C₈	—	2	1	no	—
860	C₂×C₈	—	2	1	no	—
861	C₂×C₈	—	2	1	no	—
862	C₂×C₈	—	2	1	no	—
863	C₂×C₈	—	4	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	4	1	no	—
873	C₄⋊C₄	—	4	1	no	—
874	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
875	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	—	2	1	no	—
884	C₂²⋊C₄	—	2	1	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	4	4	no	—
889	C₂²⋊C₄	—	4	4	no	—
890	C₂²⋊C₄	—	4	1	no	—
891	C₂²⋊C₄	—	4	1	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	1	no	—
894	C₄²	—	2	1	no	—
895	C₄²	—	2	1	no	—
896	C₄²	—	2	1	no	—
897	C₄²	—	4	2	no	—
898	C₄²	C₂×D₄×C₁₉	1	2	yes	complemented
899	C₂³	—	2	2	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	4	1	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	4	4	no	—
911	C₂³	—	4	2	no	—
912	C₂³	—	4	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	8	1	no	—
915	C₂³	—	8	2	no	—
916	C₂³	—	8	2	no	—
917	C₂³	C₁₉×#120	1	1	yes	characteristic
918	C₂³	C₁₉×#120	1	1	yes	characteristic
919	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
920	Q₈	—	2	1	no	—
921	Q₈	—	2	1	no	—
922	Q₈	—	2	1	no	—
923	Q₈	—	2	1	no	—
924	Q₈	—	2	1	no	—
925	Q₈	—	4	2	no	—
926	Q₈	—	4	1	no	—
927	Q₈	—	4	1	no	—
928	Q₈	—	4	1	no	—
929	Q₈	—	4	1	no	—
930	Q₈	C₁₉×#121	1	2	yes	—
931	D₄	—	2	2	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	1	no	—
934	D₄	—	2	1	no	—
935	D₄	—	2	1	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	1	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	4	no	—
943	D₄	—	4	4	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	1	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	1	no	—
948	D₄	—	4	1	no	—
949	D₄	—	4	1	no	—
950	D₄	—	4	1	no	—
951	D₄	—	4	1	no	—
952	D₄	—	4	1	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	1	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	no	—
958	D₄	C₁₉×#121	1	2	yes	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	4	2	no	—
980	C₂×C₄	—	4	2	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	1	no	—
984	C₂×C₄	—	4	1	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	4	8	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	1	no	—
989	C₂×C₄	—	4	1	no	—
990	C₂×C₄	—	4	1	no	—
991	C₂×C₄	—	4	1	no	—
992	C₂×C₄	—	4	2	no	—
993	C₂×C₄	—	4	2	no	—
994	C₂×C₄	—	4	1	no	—
995	C₂×C₄	—	4	1	no	—
996	C₂×C₄	—	4	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	8	2	no	—
999	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1000	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
1001	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1004	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
1005	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1006	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1007	C₈	—	2	2	no	—
1008	C₈	—	4	1	no	—
1009	C₈	—	4	1	no	—
1010	C₈	—	4	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	1	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	8	4	no	—
1033	C₂²	—	8	2	no	—
1034	C₂²	—	8	2	no	—
1035	C₂²	—	16	4	no	—
1036	C₂²	C₁₉×#455	1	2	yes	complemented
1037	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1038	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1039	C₂²	C₁₉×#546	1	1	yes	characteristic
1040	C₄	—	2	1	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	8	1	no	—
1051	C₄	—	8	1	no	—
1052	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
1053	C₄	C₁₉×#534	1	1	yes	characteristic
1054	C₄	D₄²×C₁₉	1	1	yes	characteristic
1055	C₄	C₁₉×#546	1	1	yes	characteristic
1056	C₂	—	2	1	no	—
1057	C₂	—	2	2	no	—
1058	C₂	—	2	1	no	—
1059	C₂	—	4	1	no	—
1060	C₂	—	4	2	no	—
1061	C₂	—	8	1	no	—
1062	C₂	—	8	2	no	—
1063	C₂	—	8	1	no	—
1064	C₂	C₁₉×#2410	1	1	yes	characteristic
1065	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
1066	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3488	C₂
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
2. C₁₉×#3056	C₂	semidirect
3. C₂×C₁₉×#455	C₂	semidirect
4. C₁₉×#3007	C₂	semidirect
5. C₂²×C₁₉×#104	C₂	semidirect
6. C₁₉×#2850	C₂	semidirect
7. C₁₉×#2040	C₂	semidirect
8. C₁₉×#2037	C₂	semidirect
9. C₁₉×#2007	C₂	semidirect
10. C₁₉×#2004	C₂	semidirect
11. C₁₉×#1900	C₂	semidirect
12. C₁₉×#1896	C₂	semidirect
13. C₁₉×#1882	C₂	semidirect
14. C₁₉×#1860	C₂	semidirect
15. C₁₉×#1792	C₂	semidirect
19. C₂×C₁₉×#137	C₂²	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
21. C₂²×M₁₆×C₁₉	C₂²	semidirect
32. C₂×C₁₉×#124	C₂²	semidirect
35. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
39. C₂²×C₄²×C₁₉	C₂²	semidirect
49. C₁₉×#428	C₂²	semidirect
53. C₂×C₁₉×#104	C₂²	semidirect
54. C₂×C₁₉×#104	C₂²	semidirect
55. C₂×C₁₉×#104	C₂²	semidirect
56. C₂×C₁₉×#104	C₂²	semidirect
57. C₁₉×#419	C₂²	semidirect
59. C₁₉×#417	C₂²	semidirect
60. C₁₉×#417	C₂²	semidirect
61. C₂×C₁₉×#100	C₂²	semidirect
62. C₂×C₁₉×#100	C₂²	semidirect
63. C₁₉×#407	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
324. M₁₆×C₁₉	C₂×D₄	semidirect
364. C₄²×C₁₉	C₂×D₄	semidirect
365. #24467	C₁₉	direct (N × H)
479. #3056	C₂×C₁₉	semidirect
480. C₂×#455	C₂×C₁₉	semidirect
481. #3007	C₂×C₁₉	semidirect
482. C₂²×#104	C₂×C₁₉	semidirect
483. #2850	C₂×C₁₉	semidirect
484. #2040	C₂×C₁₉	semidirect
485. #2037	C₂×C₁₉	semidirect
486. #2007	C₂×C₁₉	semidirect
487. #2004	C₂×C₁₉	semidirect
488. #1900	C₂×C₁₉	semidirect
489. #1896	C₂×C₁₉	semidirect
490. #1882	C₂×C₁₉	semidirect
491. #1860	C₂×C₁₉	semidirect
492. #1792	C₂×C₁₉	semidirect
518. C₂²×C₁₉	#455	semidirect
541. C₂×#137	C₂²×C₁₉	semidirect
542. C₂×#137	C₂²×C₁₉	semidirect
543. C₂²×M₁₆	C₂²×C₁₉	semidirect
554. C₂×#124	C₂²×C₁₉	semidirect
557. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
561. C₂²×C₄²	C₂²×C₁₉	semidirect
571. #428	C₂²×C₁₉	semidirect
575. C₂×#104	C₂²×C₁₉	semidirect
576. C₂×#104	C₂²×C₁₉	semidirect
577. C₂×#104	C₂²×C₁₉	semidirect
578. C₂×#104	C₂²×C₁₉	semidirect
579. #419	C₂²×C₁₉	semidirect
581. #417	C₂²×C₁₉	semidirect
582. #417	C₂²×C₁₉	semidirect
583. C₂×#100	C₂²×C₁₉	semidirect
584. C₂×#100	C₂²×C₁₉	semidirect
585. #407	C₂²×C₁₉	semidirect
586. #391	C₂²×C₁₉	semidirect
587. #390	C₂²×C₁₉	semidirect
590. #382	C₂²×C₁₉	semidirect
591. #343	C₂²×C₁₉	semidirect
592. #343	C₂²×C₁₉	semidirect
593. #339	C₂²×C₁₉	semidirect
594. #339	C₂²×C₁₉	semidirect
724. #104	D₄×C₁₉	semidirect
739. C₁₉	#24467	direct (N × H)
858. M₁₆	C₂×D₄×C₁₉	semidirect
898. C₄²	C₂×D₄×C₁₉	semidirect
1036. C₂²	C₁₉×#455	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3488	2
C₁₉×#3056	2
C₂×C₁₉×#455	2
C₁₉×#3007	2
C₂²×C₁₉×#104	2
C₁₉×#2850	2
C₁₉×#2040	2
C₁₉×#2037	2
C₁₉×#2007	2
C₁₉×#2004	2
C₁₉×#1900	2
C₁₉×#1896	2
C₁₉×#1882	2
C₁₉×#1860	2
C₁₉×#1792	2
#24467	19

Subgroups — C19×#24467 #18030426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24467 #18030426