Subgroups — C₁₉×#62051 #18068010

Order 4864.

2020 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3318	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3297	C₂	1	2	yes	maximal, complemented
11	D₄×D₈×C₁₉	C₂	1	2	yes	maximal, complemented
12	D₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3264	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3259	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3220	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3122	C₂	1	2	yes	maximal, complemented
20	C₁₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3041	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂²×D₈×C₁₉	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₁₉	C₂²	1	2	yes	complemented
27	C₁₉×#560	—	2	2	no	—
28	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#555	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#553	—	2	1	no	—
32	C₁₉×#553	C₂²	1	2	yes	complemented
33	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#546	—	2	1	no	—
37	C₁₉×#546	—	2	2	no	—
38	C₁₉×#546	—	2	1	no	—
39	C₁₉×#546	C₂²	1	2	yes	complemented
40	D₄²×C₁₉	—	2	1	no	—
41	D₄²×C₁₉	C₂²	1	2	yes	complemented
42	D₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	D₄²×C₁₉	C₂²	1	2	yes	complemented
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#540	—	2	1	no	—
46	C₁₉×#540	C₂²	1	2	yes	complemented
47	C₁₉×#540	C₂²	1	2	yes	complemented
48	C₁₉×#538	—	2	2	no	—
49	C₁₉×#535	—	2	1	no	—
50	C₁₉×#535	C₂²	1	2	yes	complemented
51	C₁₉×#534	—	2	2	no	—
52	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#529	C₂²	1	1	yes	characteristic
55	C₁₉×#529	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#525	—	2	1	no	—
57	C₂×C₁₉×#121	—	2	1	no	—
58	C₁₉×#518	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#496	C₂²	1	2	yes	complemented
61	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#493	C₂²	1	2	yes	complemented
64	C₁₉×#490	C₂²	1	2	yes	complemented
65	C₁₉×#488	C₂²	1	2	yes	complemented
66	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#484	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#482	C₂²	1	2	yes	complemented
70	C₁₉×#482	C₂²	1	2	yes	complemented
71	C₁₉×#481	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#478	C₂²	1	2	yes	complemented
73	C₁₉×#478	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#478	C₂²	1	2	yes	complemented
75	C₁₉×#478	C₂²	1	2	yes	complemented
76	C₁₉×#478	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#469	C₂²	1	2	yes	complemented
80	C₁₉×#469	C₂²	1	2	yes	complemented
81	C₁₉×#466	C₂²	1	2	yes	complemented
82	C₁₉×#466	C₂²	1	2	yes	complemented
83	C₁₉×#466	C₂²	1	2	yes	complemented
84	C₁₉×#465	C₂²	1	2	yes	complemented
85	C₁₉×#463	C₂²	1	1	yes	characteristic, complemented
86	C₁₉×#463	C₂²	1	2	yes	complemented
87	C₁₉×#463	C₂²	1	2	yes	complemented
88	C₁₉×#463	C₂²	1	1	yes	characteristic, complemented
89	C₁₉×#463	C₂²	1	2	yes	complemented
90	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
91	C₁₉×#459	C₂²	1	1	yes	characteristic
92	C₁₉×#459	C₂²	1	2	yes	complemented
93	C₁₉×#459	C₂²	1	2	yes	complemented
94	C₁₉×#459	C₂²	1	2	yes	complemented
95	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
96	C₁₉×#459	C₂²	1	2	yes	complemented
97	C₁₉×#459	C₂²	1	2	yes	complemented
98	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
99	C₁₉×#459	C₂²	1	2	yes	complemented
100	C₁₉×#459	C₂²	1	2	yes	complemented
101	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
102	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
103	C₁₉×#459	C₂²	1	2	yes	complemented
104	C₁₉×#450	C₂²	1	1	yes	characteristic, complemented
105	C₁₉×#449	C₂²	1	2	yes	complemented
106	C₁₉×#449	C₂²	1	2	yes	complemented
107	C₁₉×#447	C₂²	1	1	yes	characteristic
108	C₁₉×#447	C₂²	1	2	yes	complemented
109	C₁₉×#447	C₂²	1	2	yes	complemented
110	C₁₉×#447	C₂²	1	2	yes	complemented
111	C₁₉×#447	C₂²	1	2	yes	complemented
112	C₁₉×#447	C₂²	1	2	yes	complemented
113	C₁₉×#447	C₂²	1	2	yes	complemented
114	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
116	C₁₉×#442	C₂²	1	2	yes	complemented
117	C₁₉×#442	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
122	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
123	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
124	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
125	C₁₉×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
127	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
128	C₁₉×#433	C₂²	1	2	yes	complemented
129	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
130	C₁₉×#424	C₂²	1	2	yes	complemented
131	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₁₉×#418	C₂²	1	2	yes	complemented
133	C₁₉×#416	C₂²	1	2	yes	complemented
134	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	1	no	—
137	C₂×#41×C₁₉	—	2	1	no	—
138	C₂×#41×C₁₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₉	—	2	1	no	—
140	C₂²×D₄×C₁₉	—	2	2	no	—
141	C₂²×D₄×C₁₉	—	2	2	no	—
142	C₂²×D₄×C₁₉	—	2	1	no	—
143	C₂²×D₄×C₁₉	—	2	1	no	—
144	C₂²×D₄×C₁₉	—	2	1	no	—
145	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
147	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
148	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
149	C₂³×C₄×C₁₉	—	2	1	no	—
150	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
151	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
154	C₂×D₈×C₁₉	—	4	4	no	—
155	C₂×D₈×C₁₉	—	4	4	no	—
156	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₁₉	C₂³	1	2	yes	—
158	C₂×D₈×C₁₉	C₂³	1	2	yes	—
159	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₁₉	C₂³	1	2	yes	—
161	C₂×D₈×C₁₉	C₂³	1	2	yes	—
162	C₂×D₈×C₁₉	C₂³	1	2	yes	—
163	C₂×D₈×C₁₉	C₂³	1	2	yes	—
164	C₂×D₈×C₁₉	C₂³	1	2	yes	—
165	C₂×D₈×C₁₉	C₂³	1	2	yes	—
166	C₂×D₈×C₁₉	C₂³	1	2	yes	—
167	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
168	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
169	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×#127	—	2	1	no	—
172	C₁₉×#127	—	2	1	no	—
173	C₁₉×#127	—	2	1	no	—
174	C₁₉×#127	C₂³	1	1	yes	characteristic
175	C₁₉×#127	C₂³	1	2	yes	—
176	C₁₉×#127	C₂³	1	1	yes	characteristic
177	C₁₉×#127	C₂³	1	2	yes	—
178	C₁₉×#127	C₂³	1	2	yes	—
179	C₁₉×#127	C₂³	1	1	yes	characteristic
180	C₁₉×#126	—	2	2	no	—
181	C₁₉×#126	—	2	1	no	—
182	C₁₉×#126	D₄	1	2	yes	—
183	C₁₉×#125	D₄	1	1	yes	characteristic
184	C₁₉×#125	C₂³	1	1	yes	characteristic
185	C₁₉×#125	C₂³	1	2	yes	—
186	C₁₉×#124	—	2	1	no	—
187	C₁₉×#124	—	2	2	no	—
188	C₁₉×#124	—	2	1	no	—
189	C₁₉×#124	D₄	1	1	yes	characteristic
190	C₁₉×#124	C₂³	1	1	yes	characteristic
191	C₁₉×#124	C₂³	1	2	yes	—
192	C₁₉×#123	—	2	1	no	—
193	C₁₉×#123	—	2	2	no	—
194	C₁₉×#123	—	2	2	no	—
195	C₁₉×#123	—	2	2	no	—
196	C₁₉×#123	—	2	2	no	—
197	C₁₉×#123	—	2	2	no	—
198	C₁₉×#123	—	2	2	no	—
199	C₁₉×#123	—	2	2	no	—
200	C₁₉×#123	D₄	1	2	yes	—
201	C₁₉×C₂²⋊Q₈	—	2	1	no	—
202	C₁₉×C₂²⋊Q₈	—	2	2	no	—
203	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
204	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₁₉×#121	—	2	2	no	—
206	C₁₉×#121	—	2	1	no	—
207	C₁₉×#121	—	2	1	no	—
208	C₁₉×#121	—	2	1	no	—
209	C₁₉×#121	—	2	1	no	—
210	C₁₉×#121	—	2	2	no	—
211	C₁₉×#121	—	2	2	no	—
212	C₁₉×#121	—	2	2	no	—
213	C₁₉×#121	—	2	2	no	—
214	C₁₉×#121	—	2	2	no	—
215	C₁₉×#121	—	2	1	no	—
216	C₁₉×#121	—	2	1	no	—
217	C₁₉×#121	—	2	2	no	—
218	C₁₉×#121	—	2	2	no	—
219	C₁₉×#121	—	2	2	no	—
220	C₁₉×#121	—	2	2	no	—
221	C₁₉×#121	—	2	2	no	—
222	C₁₉×#121	—	2	2	no	—
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	D₄	1	1	yes	characteristic
225	C₁₉×#121	C₂³	1	1	yes	characteristic
226	C₁₉×#121	C₂³	1	2	yes	—
227	C₁₉×#121	C₂³	1	2	yes	—
228	C₁₉×#121	C₂³	1	2	yes	—
229	C₁₉×#121	C₂³	1	2	yes	—
230	C₁₉×#121	C₂³	1	2	yes	—
231	C₁₉×#120	—	2	2	no	—
232	C₁₉×#120	—	2	2	no	—
233	C₁₉×#120	—	2	2	no	—
234	C₁₉×#120	—	2	2	no	—
235	C₁₉×#120	—	2	2	no	—
236	C₁₉×#120	—	2	2	no	—
237	C₁₉×#120	—	2	2	no	—
238	C₁₉×#120	—	2	2	no	—
239	C₁₉×#120	—	2	2	no	—
240	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₉	—	2	1	no	—
243	C₄×D₄×C₁₉	—	2	2	no	—
244	C₄×D₄×C₁₉	—	2	2	no	—
245	C₄×D₄×C₁₉	—	2	1	no	—
246	C₄×D₄×C₁₉	—	2	1	no	—
247	C₄×D₄×C₁₉	—	2	2	no	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	1	no	—
250	C₄×D₄×C₁₉	—	2	1	no	—
251	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₉	C₂³	1	2	yes	—
255	C₄×D₄×C₁₉	C₂³	1	2	yes	—
256	C₄×D₄×C₁₉	C₂³	1	2	yes	—
257	C₄×D₄×C₁₉	C₂³	1	2	yes	—
258	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₁₉	C₂³	1	2	yes	—
261	C₄×D₄×C₁₉	C₂³	1	2	yes	—
262	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
263	C₁₉×#117	—	2	1	no	—
264	C₁₉×#117	—	2	1	no	—
265	C₁₉×#117	C₂³	1	2	yes	—
266	C₁₉×#117	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
273	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
274	C₁₉×#107	C₂³	1	1	yes	characteristic
275	C₁₉×#107	C₂³	1	2	yes	—
276	C₁₉×#107	C₂³	1	1	yes	characteristic
277	C₁₉×#106	C₂³	1	1	yes	characteristic
278	C₁₉×#106	C₂³	1	1	yes	characteristic
279	C₁₉×#106	C₂³	1	2	yes	—
280	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₉×#103	C₂³	1	1	yes	characteristic
288	C₁₉×#103	C₂³	1	2	yes	—
289	C₁₉×#103	C₂³	1	1	yes	characteristic
290	C₁₉×#102	C₂³	1	2	yes	—
291	C₁₉×#102	C₂³	1	2	yes	—
292	C₁₉×#102	C₂³	1	2	yes	—
293	C₁₉×#102	C₂³	1	2	yes	—
294	C₁₉×#102	C₂³	1	2	yes	—
295	C₁₉×#102	C₂³	1	1	yes	characteristic
296	C₁₉×#102	C₂³	1	2	yes	—
297	C₁₉×#102	C₂³	1	2	yes	—
298	C₁₉×#102	C₂³	1	1	yes	characteristic
299	C₁₉×#102	C₂³	1	1	yes	characteristic
300	C₁₉×#102	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	1	yes	characteristic
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	1	yes	characteristic
304	C₁₉×#102	C₂³	1	1	yes	characteristic
305	C₁₉×#102	C₂³	1	2	yes	—
306	C₁₉×#102	C₂³	1	2	yes	—
307	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₉	C₂³	1	2	yes	—
315	C₂⁴×C₁₉	—	2	1	no	—
316	C₂⁴×C₁₉	—	2	2	no	—
317	C₂⁴×C₁₉	—	2	2	no	—
318	C₂⁴×C₁₉	—	2	2	no	—
319	#41×C₁₉	—	4	2	no	—
320	#41×C₁₉	—	4	2	no	—
321	#41×C₁₉	—	8	2	no	—
322	#41×C₁₉	—	8	2	no	—
323	#41×C₁₉	—	8	2	no	—
324	C₂×Q₈×C₁₉	—	2	1	no	—
325	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₁₉	—	2	2	no	—
328	C₂×D₄×C₁₉	—	2	4	no	—
329	C₂×D₄×C₁₉	—	2	1	no	—
330	C₂×D₄×C₁₉	—	2	2	no	—
331	C₂×D₄×C₁₉	—	2	2	no	—
332	C₂×D₄×C₁₉	—	2	2	no	—
333	C₂×D₄×C₁₉	—	2	2	no	—
334	C₂×D₄×C₁₉	—	2	2	no	—
335	C₂×D₄×C₁₉	—	2	2	no	—
336	C₂×D₄×C₁₉	—	2	2	no	—
337	C₂×D₄×C₁₉	—	2	1	no	—
338	C₂×D₄×C₁₉	—	2	1	no	—
339	C₂×D₄×C₁₉	—	2	1	no	—
340	C₂×D₄×C₁₉	—	2	1	no	—
341	C₂×D₄×C₁₉	—	2	2	no	—
342	C₂×D₄×C₁₉	—	2	2	no	—
343	C₂×D₄×C₁₉	—	2	2	no	—
344	C₂×D₄×C₁₉	—	2	1	no	—
345	C₂×D₄×C₁₉	—	2	1	no	—
346	C₂×D₄×C₁₉	—	2	2	no	—
347	C₂×D₄×C₁₉	—	2	2	no	—
348	C₂×D₄×C₁₉	—	2	2	no	—
349	C₂×D₄×C₁₉	—	2	2	no	—
350	C₂×D₄×C₁₉	—	2	2	no	—
351	C₂×D₄×C₁₉	—	2	1	no	—
352	C₂×D₄×C₁₉	—	4	1	no	—
353	C₂×D₄×C₁₉	—	4	2	no	—
354	C₂×D₄×C₁₉	—	4	2	no	—
355	C₂×D₄×C₁₉	—	4	2	no	—
356	C₂×D₄×C₁₉	—	4	2	no	—
357	C₂×D₄×C₁₉	—	4	2	no	—
358	C₂×D₄×C₁₉	—	8	2	no	—
359	C₂×D₄×C₁₉	—	8	2	no	—
360	C₂×D₄×C₁₉	—	8	2	no	—
361	C₂×D₄×C₁₉	—	8	2	no	—
362	C₂×D₄×C₁₉	—	8	4	no	—
363	C₂×D₄×C₁₉	—	8	4	no	—
364	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
367	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
368	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
369	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
370	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
371	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₁₉	—	2	1	no	—
373	C₂²×C₄×C₁₉	—	2	1	no	—
374	C₂²×C₄×C₁₉	—	2	1	no	—
375	C₂²×C₄×C₁₉	—	2	1	no	—
376	C₂²×C₄×C₁₉	—	2	1	no	—
377	C₂²×C₄×C₁₉	—	2	2	no	—
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	1	no	—
383	C₂²×C₄×C₁₉	—	2	2	no	—
384	C₂²×C₄×C₁₉	—	8	2	no	—
385	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
389	SD₁₆×C₁₉	—	2	2	no	—
390	SD₁₆×C₁₉	—	4	1	no	—
391	SD₁₆×C₁₉	—	4	2	no	—
392	D₈×C₁₉	—	2	2	no	—
393	D₈×C₁₉	—	2	4	no	—
394	D₈×C₁₉	—	2	4	no	—
395	D₈×C₁₉	—	4	2	no	—
396	D₈×C₁₉	—	4	2	no	—
397	D₈×C₁₉	—	4	2	no	—
398	D₈×C₁₉	—	4	2	no	—
399	D₈×C₁₉	—	4	2	no	—
400	D₈×C₁₉	—	4	1	no	—
401	D₈×C₁₉	—	4	2	no	—
402	D₈×C₁₉	—	4	2	no	—
403	M₁₆×C₁₉	—	4	2	no	—
404	C₂×C₈×C₁₉	—	4	2	no	—
405	C₂×C₈×C₁₉	—	4	2	no	—
406	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
407	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
409	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₁₉	—	2	1	no	—
413	C₄⋊C₄×C₁₉	—	2	2	no	—
414	C₄⋊C₄×C₁₉	—	2	1	no	—
415	C₄⋊C₄×C₁₉	—	2	1	no	—
416	C₄⋊C₄×C₁₉	—	2	1	no	—
417	C₄⋊C₄×C₁₉	—	2	1	no	—
418	C₄⋊C₄×C₁₉	—	2	2	no	—
419	C₄⋊C₄×C₁₉	—	2	1	no	—
420	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
425	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
426	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
431	C₂²⋊C₄×C₁₉	—	2	2	no	—
432	C₂²⋊C₄×C₁₉	—	2	1	no	—
433	C₂²⋊C₄×C₁₉	—	2	1	no	—
434	C₂²⋊C₄×C₁₉	—	2	2	no	—
435	C₂²⋊C₄×C₁₉	—	2	1	no	—
436	C₂²⋊C₄×C₁₉	—	2	2	no	—
437	C₂²⋊C₄×C₁₉	—	2	1	no	—
438	C₂²⋊C₄×C₁₉	—	2	2	no	—
439	C₂²⋊C₄×C₁₉	—	2	1	no	—
440	C₂²⋊C₄×C₁₉	—	2	2	no	—
441	C₂²⋊C₄×C₁₉	—	2	2	no	—
442	C₂²⋊C₄×C₁₉	—	2	1	no	—
443	C₂²⋊C₄×C₁₉	—	2	1	no	—
444	C₂²⋊C₄×C₁₉	—	2	2	no	—
445	C₂²⋊C₄×C₁₉	—	2	1	no	—
446	C₂²⋊C₄×C₁₉	—	2	2	no	—
447	C₂²⋊C₄×C₁₉	—	2	2	no	—
448	C₂²⋊C₄×C₁₉	—	2	2	no	—
449	C₂²⋊C₄×C₁₉	—	2	2	no	—
450	C₂²⋊C₄×C₁₉	—	2	1	no	—
451	C₂²⋊C₄×C₁₉	—	2	2	no	—
452	C₂²⋊C₄×C₁₉	—	2	2	no	—
453	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
455	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
456	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
458	C₄²×C₁₉	—	2	2	no	—
459	C₄²×C₁₉	—	2	1	no	—
460	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
461	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
462	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
463	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
464	C₄²×C₁₉	C₂⁴	1	2	yes	—
465	#62051	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
466	C₂³×C₁₉	—	2	1	no	—
467	C₂³×C₁₉	—	2	1	no	—
468	C₂³×C₁₉	—	2	2	no	—
469	C₂³×C₁₉	—	2	1	no	—
470	C₂³×C₁₉	—	2	2	no	—
471	C₂³×C₁₉	—	2	2	no	—
472	C₂³×C₁₉	—	4	2	no	—
473	C₂³×C₁₉	—	4	4	no	—
474	C₂³×C₁₉	—	4	2	no	—
475	C₂³×C₁₉	—	4	4	no	—
476	C₂³×C₁₉	—	8	1	no	—
477	C₂³×C₁₉	—	8	2	no	—
478	C₂³×C₁₉	—	8	2	no	—
479	C₂³×C₁₉	—	8	2	no	—
480	C₂³×C₁₉	—	8	2	no	—
481	C₂³×C₁₉	—	8	2	no	—
482	C₂³×C₁₉	—	8	2	no	—
483	C₂³×C₁₉	—	8	2	no	—
484	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
485	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
486	Q₈×C₁₉	—	2	2	no	—
487	Q₈×C₁₉	—	2	1	no	—
488	Q₈×C₁₉	—	2	1	no	—
489	Q₈×C₁₉	—	8	1	no	—
490	D₄×C₁₉	—	2	4	no	—
491	D₄×C₁₉	—	2	2	no	—
492	D₄×C₁₉	—	2	1	no	—
493	D₄×C₁₉	—	2	2	no	—
494	D₄×C₁₉	—	2	2	no	—
495	D₄×C₁₉	—	2	1	no	—
496	D₄×C₁₉	—	2	2	no	—
497	D₄×C₁₉	—	2	1	no	—
498	D₄×C₁₉	—	2	2	no	—
499	D₄×C₁₉	—	2	1	no	—
500	D₄×C₁₉	—	2	1	no	—
501	D₄×C₁₉	—	2	2	no	—
502	D₄×C₁₉	—	2	2	no	—
503	D₄×C₁₉	—	4	4	no	—
504	D₄×C₁₉	—	4	2	no	—
505	D₄×C₁₉	—	4	2	no	—
506	D₄×C₁₉	—	4	4	no	—
507	D₄×C₁₉	—	4	2	no	—
508	D₄×C₁₉	—	4	2	no	—
509	D₄×C₁₉	—	4	2	no	—
510	D₄×C₁₉	—	8	2	no	—
511	D₄×C₁₉	—	8	2	no	—
512	D₄×C₁₉	—	8	2	no	—
513	D₄×C₁₉	—	8	2	no	—
514	D₄×C₁₉	—	8	1	no	—
515	D₄×C₁₉	—	8	1	no	—
516	D₄×C₁₉	—	8	2	no	—
517	D₄×C₁₉	—	8	2	no	—
518	D₄×C₁₉	—	8	1	no	—
519	D₄×C₁₉	—	8	2	no	—
520	D₄×C₁₉	—	8	2	no	—
521	D₄×C₁₉	—	8	2	no	—
522	D₄×C₁₉	—	8	2	no	—
523	D₄×C₁₉	—	8	2	no	—
524	D₄×C₁₉	—	8	2	no	—
525	D₄×C₁₉	—	8	2	no	—
526	D₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
527	C₂×C₄×C₁₉	—	2	2	no	—
528	C₂×C₄×C₁₉	—	2	2	no	—
529	C₂×C₄×C₁₉	—	2	1	no	—
530	C₂×C₄×C₁₉	—	2	2	no	—
531	C₂×C₄×C₁₉	—	2	1	no	—
532	C₂×C₄×C₁₉	—	2	2	no	—
533	C₂×C₄×C₁₉	—	2	1	no	—
534	C₂×C₄×C₁₉	—	2	1	no	—
535	C₂×C₄×C₁₉	—	2	1	no	—
536	C₂×C₄×C₁₉	—	2	2	no	—
537	C₂×C₄×C₁₉	—	2	1	no	—
538	C₂×C₄×C₁₉	—	2	1	no	—
539	C₂×C₄×C₁₉	—	4	2	no	—
540	C₂×C₄×C₁₉	—	4	2	no	—
541	C₂×C₄×C₁₉	—	4	2	no	—
542	C₂×C₄×C₁₉	—	8	1	no	—
543	C₂×C₄×C₁₉	—	8	1	no	—
544	C₂×C₄×C₁₉	—	8	2	no	—
545	C₂×C₄×C₁₉	—	8	2	no	—
546	C₂×C₄×C₁₉	—	8	2	no	—
547	C₂×C₄×C₁₉	—	8	2	no	—
548	C₂×C₄×C₁₉	—	8	2	no	—
549	C₂×C₄×C₁₉	—	8	2	no	—
550	C₂×C₄×C₁₉	—	8	1	no	—
551	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
560	C₈×C₁₉	—	2	1	no	—
561	C₈×C₁₉	—	2	2	no	—
562	C₈×C₁₉	—	2	2	no	—
563	C₈×C₁₉	—	2	1	no	—
564	C₈×C₁₉	—	2	1	no	—
565	C₈×C₁₉	—	2	1	no	—
566	#3543	C₂×C₁₉	1	1	yes	characteristic, complemented
567	#3519	C₂×C₁₉	1	1	yes	characteristic, complemented
568	#3399	C₂×C₁₉	1	1	yes	characteristic, complemented
569	#3391	C₂×C₁₉	1	1	yes	characteristic, complemented
570	#3366	C₂×C₁₉	1	1	yes	characteristic, complemented
571	#3361	C₂×C₁₉	1	1	yes	characteristic, complemented
572	#3325	C₂×C₁₉	1	1	yes	characteristic, complemented
573	#3318	C₂×C₁₉	1	2	yes	complemented
574	#3305	C₂×C₁₉	1	1	yes	characteristic, complemented
575	#3297	C₂×C₁₉	1	2	yes	complemented
576	D₄×D₈	C₂×C₁₉	1	2	yes	complemented
577	D₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
578	#3274	C₂×C₁₉	1	1	yes	characteristic, complemented
579	#3264	C₂×C₁₉	1	2	yes	complemented
580	#3259	C₂×C₁₉	1	2	yes	complemented
581	#3247	C₂×C₁₉	1	1	yes	characteristic, complemented
582	#3220	C₂×C₁₉	1	2	yes	complemented
583	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
584	#3122	C₂×C₁₉	1	2	yes	complemented
585	#3105	C₂×C₁₉	1	1	yes	characteristic, complemented
586	#3041	C₂×C₁₉	1	2	yes	complemented
587	C₂×#459	C₂×C₁₉	1	1	yes	characteristic, complemented
588	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
589	C₂²×C₁₉	—	2	1	no	—
590	C₂²×C₁₉	—	2	1	no	—
591	C₂²×C₁₉	—	2	2	no	—
592	C₂²×C₁₉	—	2	2	no	—
593	C₂²×C₁₉	—	2	2	no	—
594	C₂²×C₁₉	—	2	2	no	—
595	C₂²×C₁₉	—	4	1	no	—
596	C₂²×C₁₉	—	4	1	no	—
597	C₂²×C₁₉	—	4	2	no	—
598	C₂²×C₁₉	—	4	1	no	—
599	C₂²×C₁₉	—	4	2	no	—
600	C₂²×C₁₉	—	4	1	no	—
601	C₂²×C₁₉	—	4	2	no	—
602	C₂²×C₁₉	—	4	1	no	—
603	C₂²×C₁₉	—	4	1	no	—
604	C₂²×C₁₉	—	4	2	no	—
605	C₂²×C₁₉	—	4	2	no	—
606	C₂²×C₁₉	—	4	2	no	—
607	C₂²×C₁₉	—	4	2	no	—
608	C₂²×C₁₉	—	4	1	no	—
609	C₂²×C₁₉	—	4	2	no	—
610	C₂²×C₁₉	—	4	1	no	—
611	C₂²×C₁₉	—	4	2	no	—
612	C₂²×C₁₉	—	8	4	no	—
613	C₂²×C₁₉	—	16	4	no	—
614	C₂²×C₁₉	—	16	4	no	—
615	C₂²×C₁₉	—	16	4	no	—
616	C₂²×C₁₉	#576	1	2	yes	—
617	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₁₉	—	2	2	no	—
619	C₄×C₁₉	—	2	1	no	—
620	C₄×C₁₉	—	2	1	no	—
621	C₄×C₁₉	—	2	1	no	—
622	C₄×C₁₉	—	2	1	no	—
623	C₄×C₁₉	—	2	2	no	—
624	C₄×C₁₉	—	2	2	no	—
625	C₄×C₁₉	—	4	1	no	—
626	C₄×C₁₉	—	4	1	no	—
627	C₄×C₁₉	—	4	1	no	—
628	C₄×C₁₉	—	4	1	no	—
629	C₄×C₁₉	—	4	1	no	—
630	C₄×C₁₉	—	4	2	no	—
631	C₄×C₁₉	#576	1	2	yes	—
632	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
633	C₄×C₁₉	#585	1	1	yes	characteristic
634	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
635	C₂²×D₈	C₂²×C₁₉	1	2	yes	complemented
636	C₂²×D₈	C₂²×C₁₉	1	2	yes	complemented
637	#560	—	2	2	no	—
638	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
639	#555	C₂²×C₁₉	1	1	yes	characteristic, complemented
640	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
641	#553	—	2	1	no	—
642	#553	C₂²×C₁₉	1	2	yes	complemented
643	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
644	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
646	#546	—	2	1	no	—
647	#546	—	2	2	no	—
648	#546	—	2	1	no	—
649	#546	C₂²×C₁₉	1	2	yes	complemented
650	D₄²	—	2	1	no	—
651	D₄²	C₂²×C₁₉	1	2	yes	complemented
652	D₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
653	D₄²	C₂²×C₁₉	1	2	yes	complemented
654	D₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
655	#540	—	2	1	no	—
656	#540	C₂²×C₁₉	1	2	yes	complemented
657	#540	C₂²×C₁₉	1	2	yes	complemented
658	#538	—	2	2	no	—
659	#535	—	2	1	no	—
660	#535	C₂²×C₁₉	1	2	yes	complemented
661	#534	—	2	2	no	—
662	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
663	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
664	#529	C₂²×C₁₉	1	1	yes	characteristic
665	#529	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	#525	—	2	1	no	—
667	C₂×#121	—	2	1	no	—
668	#518	C₂²×C₁₉	1	2	yes	complemented
669	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	#496	C₂²×C₁₉	1	2	yes	complemented
671	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
672	#493	C₂²×C₁₉	1	2	yes	complemented
673	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
674	#490	C₂²×C₁₉	1	2	yes	complemented
675	#488	C₂²×C₁₉	1	2	yes	complemented
676	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
677	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
678	#484	C₂²×C₁₉	1	1	yes	characteristic, complemented
679	#482	C₂²×C₁₉	1	2	yes	complemented
680	#482	C₂²×C₁₉	1	2	yes	complemented
681	#481	C₂²×C₁₉	1	1	yes	characteristic, complemented
682	#478	C₂²×C₁₉	1	1	yes	characteristic, complemented
683	#478	C₂²×C₁₉	1	1	yes	characteristic, complemented
684	#478	C₂²×C₁₉	1	2	yes	complemented
685	#478	C₂²×C₁₉	1	2	yes	complemented
686	#478	C₂²×C₁₉	1	2	yes	complemented
687	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
688	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
689	#469	C₂²×C₁₉	1	2	yes	complemented
690	#469	C₂²×C₁₉	1	2	yes	complemented
691	#466	C₂²×C₁₉	1	2	yes	complemented
692	#466	C₂²×C₁₉	1	2	yes	complemented
693	#466	C₂²×C₁₉	1	2	yes	complemented
694	#465	C₂²×C₁₉	1	2	yes	complemented
695	#463	C₂²×C₁₉	1	1	yes	characteristic, complemented
696	#463	C₂²×C₁₉	1	1	yes	characteristic, complemented
697	#463	C₂²×C₁₉	1	2	yes	complemented
698	#463	C₂²×C₁₉	1	2	yes	complemented
699	#463	C₂²×C₁₉	1	2	yes	complemented
700	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
701	#459	C₂²×C₁₉	1	1	yes	characteristic
702	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
703	#459	C₂²×C₁₉	1	2	yes	complemented
704	#459	C₂²×C₁₉	1	2	yes	complemented
705	#459	C₂²×C₁₉	1	2	yes	complemented
706	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#459	C₂²×C₁₉	1	2	yes	complemented
708	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
709	#459	C₂²×C₁₉	1	2	yes	complemented
710	#459	C₂²×C₁₉	1	2	yes	complemented
711	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
712	#459	C₂²×C₁₉	1	2	yes	complemented
713	#459	C₂²×C₁₉	1	2	yes	complemented
714	#450	C₂²×C₁₉	1	1	yes	characteristic, complemented
715	#449	C₂²×C₁₉	1	2	yes	complemented
716	#449	C₂²×C₁₉	1	2	yes	complemented
717	#447	C₂²×C₁₉	1	1	yes	characteristic
718	#447	C₂²×C₁₉	1	2	yes	complemented
719	#447	C₂²×C₁₉	1	2	yes	complemented
720	#447	C₂²×C₁₉	1	2	yes	complemented
721	#447	C₂²×C₁₉	1	2	yes	complemented
722	#447	C₂²×C₁₉	1	2	yes	complemented
723	#447	C₂²×C₁₉	1	2	yes	complemented
724	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
725	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
726	#442	C₂²×C₁₉	1	2	yes	complemented
727	#442	C₂²×C₁₉	1	2	yes	complemented
728	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
729	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
730	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
731	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
732	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
733	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
734	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
735	#435	C₂²×C₁₉	1	2	yes	complemented
736	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
737	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
738	#433	C₂²×C₁₉	1	2	yes	complemented
739	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
740	#424	C₂²×C₁₉	1	2	yes	complemented
741	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
742	#418	C₂²×C₁₉	1	2	yes	complemented
743	#416	C₂²×C₁₉	1	2	yes	complemented
744	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
745	C₂×C₁₉	—	2	2	no	—
746	C₂×C₁₉	—	4	2	no	—
747	C₂×C₁₉	—	4	2	no	—
748	C₂×C₁₉	—	8	1	no	—
749	C₂×C₁₉	—	8	2	no	—
750	C₂×C₁₉	—	8	2	no	—
751	C₂×C₁₉	—	8	1	no	—
752	C₂×C₁₉	—	8	2	no	—
753	C₂×C₁₉	#3488	1	1	yes	characteristic
754	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
755	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
756	C₂×#41	—	2	1	no	—
757	C₂×#41	—	2	1	no	—
758	C₂×#41	—	2	1	no	—
759	C₂×#41	C₂³×C₁₉	1	2	yes	—
760	C₂²×D₄	—	2	1	no	—
761	C₂²×D₄	—	2	2	no	—
762	C₂²×D₄	—	2	2	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	—	2	1	no	—
766	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
767	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
768	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
769	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
770	C₂³×C₄	—	2	1	no	—
771	AGL(1,ℤ/8)	—	4	4	no	—
772	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
773	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
775	C₂×D₈	—	4	4	no	—
776	C₂×D₈	—	4	4	no	—
777	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
778	C₂×D₈	C₂³×C₁₉	1	2	yes	—
779	C₂×D₈	C₂³×C₁₉	1	2	yes	—
780	C₂×D₈	C₂³×C₁₉	1	2	yes	—
781	C₂×D₈	C₂³×C₁₉	1	2	yes	—
782	C₂×D₈	C₂³×C₁₉	1	2	yes	—
783	C₂×D₈	C₂³×C₁₉	1	2	yes	—
784	C₂×D₈	C₂³×C₁₉	1	2	yes	—
785	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
786	C₂×D₈	C₂³×C₁₉	1	2	yes	—
787	C₂×D₈	C₂³×C₁₉	1	2	yes	—
788	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
789	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
790	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
791	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
792	#127	—	2	1	no	—
793	#127	—	2	1	no	—
794	#127	—	2	1	no	—
795	#127	C₂³×C₁₉	1	2	yes	—
796	#127	C₂³×C₁₉	1	1	yes	characteristic
797	#127	C₂³×C₁₉	1	1	yes	characteristic
798	#127	C₂³×C₁₉	1	1	yes	characteristic
799	#127	C₂³×C₁₉	1	2	yes	—
800	#127	C₂³×C₁₉	1	2	yes	—
801	#126	—	2	2	no	—
802	#126	—	2	1	no	—
803	#126	D₄×C₁₉	1	2	yes	—
804	#125	D₄×C₁₉	1	1	yes	characteristic
805	#125	C₂³×C₁₉	1	1	yes	characteristic
806	#125	C₂³×C₁₉	1	2	yes	—
807	#124	—	2	1	no	—
808	#124	—	2	2	no	—
809	#124	—	2	1	no	—
810	#124	D₄×C₁₉	1	1	yes	characteristic
811	#124	C₂³×C₁₉	1	1	yes	characteristic
812	#124	C₂³×C₁₉	1	2	yes	—
813	#123	—	2	1	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	D₄×C₁₉	1	2	yes	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
825	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
826	#121	—	2	2	no	—
827	#121	—	2	1	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	1	no	—
837	#121	—	2	1	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	D₄×C₁₉	1	1	yes	characteristic
846	#121	C₂³×C₁₉	1	1	yes	characteristic
847	#121	C₂³×C₁₉	1	2	yes	—
848	#121	C₂³×C₁₉	1	2	yes	—
849	#121	C₂³×C₁₉	1	2	yes	—
850	#121	C₂³×C₁₉	1	2	yes	—
851	#121	C₂³×C₁₉	1	2	yes	—
852	#120	—	2	2	no	—
853	#120	—	2	2	no	—
854	#120	—	2	2	no	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₁₉	1	2	yes	—
877	C₄×D₄	C₂³×C₁₉	1	2	yes	—
878	C₄×D₄	C₂³×C₁₉	1	2	yes	—
879	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
880	C₄×D₄	C₂³×C₁₉	1	2	yes	—
881	C₄×D₄	C₂³×C₁₉	1	2	yes	—
882	C₄×D₄	C₂³×C₁₉	1	2	yes	—
883	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
884	#117	—	2	1	no	—
885	#117	—	2	1	no	—
886	#117	C₂³×C₁₉	1	2	yes	—
887	#117	C₂³×C₁₉	1	2	yes	—
888	C₂×C₄⋊C₄	—	2	1	no	—
889	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
890	C₂×C₂²⋊C₄	—	2	1	no	—
891	C₂×C₂²⋊C₄	—	2	2	no	—
892	C₂×C₂²⋊C₄	—	2	2	no	—
893	C₂×C₂²⋊C₄	—	2	2	no	—
894	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
895	#107	C₂³×C₁₉	1	1	yes	characteristic
896	#107	C₂³×C₁₉	1	2	yes	—
897	#107	C₂³×C₁₉	1	1	yes	characteristic
898	#106	C₂³×C₁₉	1	1	yes	characteristic
899	#106	C₂³×C₁₉	1	1	yes	characteristic
900	#106	C₂³×C₁₉	1	2	yes	—
901	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
902	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
903	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
904	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
905	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
906	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
907	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
908	#103	C₂³×C₁₉	1	1	yes	characteristic
909	#103	C₂³×C₁₉	1	2	yes	—
910	#103	C₂³×C₁₉	1	1	yes	characteristic
911	#102	C₂³×C₁₉	1	2	yes	—
912	#102	C₂³×C₁₉	1	2	yes	—
913	#102	C₂³×C₁₉	1	2	yes	—
914	#102	C₂³×C₁₉	1	2	yes	—
915	#102	C₂³×C₁₉	1	2	yes	—
916	#102	C₂³×C₁₉	1	1	yes	characteristic
917	#102	C₂³×C₁₉	1	2	yes	—
918	#102	C₂³×C₁₉	1	2	yes	—
919	#102	C₂³×C₁₉	1	1	yes	characteristic
920	#102	C₂³×C₁₉	1	1	yes	characteristic
921	#102	C₂³×C₁₉	1	2	yes	—
922	#102	C₂³×C₁₉	1	1	yes	characteristic
923	#102	C₂³×C₁₉	1	2	yes	—
924	#102	C₂³×C₁₉	1	1	yes	characteristic
925	#102	C₂³×C₁₉	1	1	yes	characteristic
926	#102	C₂³×C₁₉	1	2	yes	—
927	#102	C₂³×C₁₉	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
932	#97	C₂³×C₁₉	1	2	yes	—
933	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
934	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
935	C₄×C₈	C₂³×C₁₉	1	2	yes	—
936	C₁₉	#62051	1	1	yes	characteristic, direct product factor, Sylow
937	C₂⁴	—	2	1	no	—
938	C₂⁴	—	2	2	no	—
939	C₂⁴	—	2	2	no	—
940	C₂⁴	—	2	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	8	2	no	—
944	#41	—	8	2	no	—
945	#41	—	8	2	no	—
946	C₂×Q₈	—	2	1	no	—
947	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
948	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	4	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	4	1	no	—
975	C₂×D₄	—	4	2	no	—
976	C₂×D₄	—	4	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	2	no	—
979	C₂×D₄	—	4	2	no	—
980	C₂×D₄	—	8	2	no	—
981	C₂×D₄	—	8	2	no	—
982	C₂×D₄	—	8	2	no	—
983	C₂×D₄	—	8	2	no	—
984	C₂×D₄	—	8	4	no	—
985	C₂×D₄	—	8	4	no	—
986	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
987	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
989	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
990	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
991	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
993	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	8	2	no	—
1007	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	4	1	no	—
1013	SD₁₆	—	4	2	no	—
1014	D₈	—	2	2	no	—
1015	D₈	—	2	4	no	—
1016	D₈	—	2	4	no	—
1017	D₈	—	4	2	no	—
1018	D₈	—	4	2	no	—
1019	D₈	—	4	2	no	—
1020	D₈	—	4	2	no	—
1021	D₈	—	4	2	no	—
1022	D₈	—	4	1	no	—
1023	D₈	—	4	2	no	—
1024	D₈	—	4	2	no	—
1025	M₁₆	—	4	2	no	—
1026	C₂×C₈	—	4	2	no	—
1027	C₂×C₈	—	4	2	no	—
1028	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1033	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1043	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1044	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1045	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1046	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1047	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1078	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1083	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1085	C₄²	C₂⁴×C₁₉	1	2	yes	—
1086	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	4	4	no	—
1095	C₂³	—	4	2	no	—
1096	C₂³	—	4	4	no	—
1097	C₂³	—	8	1	no	—
1098	C₂³	—	8	2	no	—
1099	C₂³	—	8	2	no	—
1100	C₂³	—	8	2	no	—
1101	C₂³	—	8	2	no	—
1102	C₂³	—	8	2	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1106	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1107	Q₈	—	2	2	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	8	1	no	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	4	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	D₄	—	8	2	no	—
1135	D₄	—	8	1	no	—
1136	D₄	—	8	1	no	—
1137	D₄	—	8	2	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	1	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	2	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	8	1	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	2	no	—
1166	C₂×C₄	—	8	2	no	—
1167	C₂×C₄	—	8	2	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	8	2	no	—
1170	C₂×C₄	—	8	2	no	—
1171	C₂×C₄	—	8	1	no	—
1172	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1173	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1174	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1178	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1180	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1181	C₈	—	2	1	no	—
1182	C₈	—	2	2	no	—
1183	C₈	—	2	2	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	1	no	—
1186	C₈	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	2	no	—
1204	C₂²	—	4	2	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	8	4	no	—
1211	C₂²	—	16	4	no	—
1212	C₂²	—	16	4	no	—
1213	C₂²	—	16	4	no	—
1214	C₂²	C₁₉×#576	1	2	yes	—
1215	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1216	C₄	—	2	2	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	2	1	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	2	no	—
1229	C₄	C₁₉×#576	1	2	yes	—
1230	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1231	C₄	C₁₉×#585	1	1	yes	characteristic
1232	C₂	—	2	2	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	—	8	1	no	—
1237	C₂	—	8	2	no	—
1238	C₂	—	8	2	no	—
1239	C₂	—	8	2	no	—
1240	C₂	C₁₉×#3488	1	1	yes	characteristic
1241	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
1242	C₂	C₂×C₁₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3543	C₂	semidirect
2. C₁₉×#3519	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3391	C₂	semidirect
5. C₁₉×#3366	C₂	semidirect
6. C₁₉×#3361	C₂	semidirect
7. C₁₉×#3325	C₂	semidirect
8. C₁₉×#3318	C₂	semidirect
9. C₁₉×#3305	C₂	semidirect
10. C₁₉×#3297	C₂	semidirect
11. D₄×D₈×C₁₉	C₂	semidirect
12. D₄×D₈×C₁₉	C₂	semidirect
13. C₁₉×#3274	C₂	semidirect
14. C₁₉×#3264	C₂	semidirect
15. C₁₉×#3259	C₂	semidirect
16. C₁₉×#3247	C₂	semidirect
17. C₁₉×#3220	C₂	semidirect
18. C₁₉×#3205	C₂	semidirect
19. C₁₉×#3122	C₂	semidirect
20. C₁₉×#3105	C₂	semidirect
21. C₁₉×#3041	C₂	semidirect
22. C₂×C₁₉×#459	C₂	semidirect
23. C₁₉×#2994	C₂	semidirect
24. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂²×D₈×C₁₉	C₂²	semidirect
26. C₂²×D₈×C₁₉	C₂²	semidirect
28. C₁₉×#559	C₂²	semidirect
29. C₁₉×#555	C₂²	semidirect
30. C₁₉×#554	C₂²	semidirect
32. C₁₉×#553	C₂²	semidirect
33. C₁₉×#550	C₂²	semidirect
34. C₁₉×#550	C₂²	semidirect
35. C₁₉×#550	C₂²	semidirect
39. C₁₉×#546	C₂²	semidirect
41. D₄²×C₁₉	C₂²	semidirect
42. D₄²×C₁₉	C₂²	semidirect
43. D₄²×C₁₉	C₂²	semidirect
44. D₄²×C₁₉	C₂²	semidirect
46. C₁₉×#540	C₂²	semidirect
47. C₁₉×#540	C₂²	semidirect
50. C₁₉×#535	C₂²	semidirect
52. C₁₉×#532	C₂²	semidirect
53. C₂×C₁₉×#127	C₂²	semidirect
55. C₁₉×#529	C₂²	semidirect
58. C₁₉×#518	C₂²	semidirect
59. C₂×C₄×D₄×C₁₉	C₂²	semidirect
60. C₁₉×#496	C₂²	semidirect
61. C₁₉×#493	C₂²	semidirect
62. C₁₉×#493	C₂²	semidirect
63. C₁₉×#493	C₂²	semidirect
64. C₁₉×#490	C₂²	semidirect
65. C₁₉×#488	C₂²	semidirect
66. C₁₉×#486	C₂²	semidirect
67. C₁₉×#486	C₂²	semidirect
68. C₁₉×#484	C₂²	semidirect
69. C₁₉×#482	C₂²	semidirect
70. C₁₉×#482	C₂²	semidirect
71. C₁₉×#481	C₂²	semidirect
72. C₁₉×#478	C₂²	semidirect
73. C₁₉×#478	C₂²	semidirect
74. C₁₉×#478	C₂²	semidirect
75. C₁₉×#478	C₂²	semidirect
76. C₁₉×#478	C₂²	semidirect
77. C₁₉×#477	C₂²	semidirect
78. C₁₉×#476	C₂²	semidirect
79. C₁₉×#469	C₂²	semidirect
80. C₁₉×#469	C₂²	semidirect
81. C₁₉×#466	C₂²	semidirect
82. C₁₉×#466	C₂²	semidirect
83. C₁₉×#466	C₂²	semidirect
84. C₁₉×#465	C₂²	semidirect
85. C₁₉×#463	C₂²	semidirect
86. C₁₉×#463	C₂²	semidirect
87. C₁₉×#463	C₂²	semidirect
88. C₁₉×#463	C₂²	semidirect
89. C₁₉×#463	C₂²	semidirect
90. C₁₉×#460	C₂²	semidirect
92. C₁₉×#459	C₂²	semidirect
93. C₁₉×#459	C₂²	semidirect
94. C₁₉×#459	C₂²	semidirect
95. C₁₉×#459	C₂²	semidirect
96. C₁₉×#459	C₂²	semidirect
97. C₁₉×#459	C₂²	semidirect
98. C₁₉×#459	C₂²	semidirect
99. C₁₉×#459	C₂²	semidirect
100. C₁₉×#459	C₂²	semidirect
101. C₁₉×#459	C₂²	semidirect
102. C₁₉×#459	C₂²	semidirect
103. C₁₉×#459	C₂²	semidirect
104. C₁₉×#450	C₂²	semidirect
105. C₁₉×#449	C₂²	semidirect
106. C₁₉×#449	C₂²	semidirect
108. C₁₉×#447	C₂²	semidirect
109. C₁₉×#447	C₂²	semidirect
110. C₁₉×#447	C₂²	semidirect
111. C₁₉×#447	C₂²	semidirect
112. C₁₉×#447	C₂²	semidirect
113. C₁₉×#447	C₂²	semidirect
114. C₁₉×#446	C₂²	semidirect
115. C₈×Q₈×C₁₉	C₂²	semidirect
116. C₁₉×#442	C₂²	semidirect
117. C₁₉×#442	C₂²	semidirect
118. C₄×SD₁₆×C₁₉	C₂²	semidirect
119. C₄×SD₁₆×C₁₉	C₂²	semidirect
120. C₄×D₈×C₁₉	C₂²	semidirect
121. C₄×D₈×C₁₉	C₂²	semidirect
122. C₄×D₈×C₁₉	C₂²	semidirect
123. C₄×D₈×C₁₉	C₂²	semidirect
124. C₁₉×#436	C₂²	semidirect
125. C₁₉×#435	C₂²	semidirect
126. C₈×D₄×C₁₉	C₂²	semidirect
127. C₈×D₄×C₁₉	C₂²	semidirect
128. C₁₉×#433	C₂²	semidirect
129. C₁₉×#431	C₂²	semidirect
130. C₁₉×#424	C₂²	semidirect
131. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
132. C₁₉×#418	C₂²	semidirect
133. C₁₉×#416	C₂²	semidirect
134. C₂×C₁₉×#102	C₂²	semidirect
465. #62051	C₁₉	direct (N × H)
566. #3543	C₂×C₁₉	semidirect
567. #3519	C₂×C₁₉	semidirect
568. #3399	C₂×C₁₉	semidirect
569. #3391	C₂×C₁₉	semidirect
570. #3366	C₂×C₁₉	semidirect
571. #3361	C₂×C₁₉	semidirect
572. #3325	C₂×C₁₉	semidirect
573. #3318	C₂×C₁₉	semidirect
574. #3305	C₂×C₁₉	semidirect
575. #3297	C₂×C₁₉	semidirect
576. D₄×D₈	C₂×C₁₉	semidirect
577. D₄×D₈	C₂×C₁₉	semidirect
578. #3274	C₂×C₁₉	semidirect
579. #3264	C₂×C₁₉	semidirect
580. #3259	C₂×C₁₉	semidirect
581. #3247	C₂×C₁₉	semidirect
582. #3220	C₂×C₁₉	semidirect
583. #3205	C₂×C₁₉	semidirect
584. #3122	C₂×C₁₉	semidirect
585. #3105	C₂×C₁₉	semidirect
586. #3041	C₂×C₁₉	semidirect
587. C₂×#459	C₂×C₁₉	semidirect
588. #2994	C₂×C₁₉	semidirect
634. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
635. C₂²×D₈	C₂²×C₁₉	semidirect
636. C₂²×D₈	C₂²×C₁₉	semidirect
638. #559	C₂²×C₁₉	semidirect
639. #555	C₂²×C₁₉	semidirect
640. #554	C₂²×C₁₉	semidirect
642. #553	C₂²×C₁₉	semidirect
643. #550	C₂²×C₁₉	semidirect
644. #550	C₂²×C₁₉	semidirect
645. #550	C₂²×C₁₉	semidirect
649. #546	C₂²×C₁₉	semidirect
651. D₄²	C₂²×C₁₉	semidirect
652. D₄²	C₂²×C₁₉	semidirect
653. D₄²	C₂²×C₁₉	semidirect
654. D₄²	C₂²×C₁₉	semidirect
656. #540	C₂²×C₁₉	semidirect
657. #540	C₂²×C₁₉	semidirect
660. #535	C₂²×C₁₉	semidirect
662. #532	C₂²×C₁₉	semidirect
663. C₂×#127	C₂²×C₁₉	semidirect
665. #529	C₂²×C₁₉	semidirect
668. #518	C₂²×C₁₉	semidirect
669. C₂×C₄×D₄	C₂²×C₁₉	semidirect
670. #496	C₂²×C₁₉	semidirect
671. #493	C₂²×C₁₉	semidirect
672. #493	C₂²×C₁₉	semidirect
673. #493	C₂²×C₁₉	semidirect
674. #490	C₂²×C₁₉	semidirect
675. #488	C₂²×C₁₉	semidirect
676. #486	C₂²×C₁₉	semidirect
677. #486	C₂²×C₁₉	semidirect
678. #484	C₂²×C₁₉	semidirect
679. #482	C₂²×C₁₉	semidirect
680. #482	C₂²×C₁₉	semidirect
681. #481	C₂²×C₁₉	semidirect
682. #478	C₂²×C₁₉	semidirect
683. #478	C₂²×C₁₉	semidirect
684. #478	C₂²×C₁₉	semidirect
685. #478	C₂²×C₁₉	semidirect
686. #478	C₂²×C₁₉	semidirect
687. #477	C₂²×C₁₉	semidirect
688. #476	C₂²×C₁₉	semidirect
689. #469	C₂²×C₁₉	semidirect
690. #469	C₂²×C₁₉	semidirect
691. #466	C₂²×C₁₉	semidirect
692. #466	C₂²×C₁₉	semidirect
693. #466	C₂²×C₁₉	semidirect
694. #465	C₂²×C₁₉	semidirect
695. #463	C₂²×C₁₉	semidirect
696. #463	C₂²×C₁₉	semidirect
697. #463	C₂²×C₁₉	semidirect
698. #463	C₂²×C₁₉	semidirect
699. #463	C₂²×C₁₉	semidirect
700. #460	C₂²×C₁₉	semidirect
702. #459	C₂²×C₁₉	semidirect
703. #459	C₂²×C₁₉	semidirect
704. #459	C₂²×C₁₉	semidirect
705. #459	C₂²×C₁₉	semidirect
706. #459	C₂²×C₁₉	semidirect
707. #459	C₂²×C₁₉	semidirect
708. #459	C₂²×C₁₉	semidirect
709. #459	C₂²×C₁₉	semidirect
710. #459	C₂²×C₁₉	semidirect
711. #459	C₂²×C₁₉	semidirect
712. #459	C₂²×C₁₉	semidirect
713. #459	C₂²×C₁₉	semidirect
714. #450	C₂²×C₁₉	semidirect
715. #449	C₂²×C₁₉	semidirect
716. #449	C₂²×C₁₉	semidirect
718. #447	C₂²×C₁₉	semidirect
719. #447	C₂²×C₁₉	semidirect
720. #447	C₂²×C₁₉	semidirect
721. #447	C₂²×C₁₉	semidirect
722. #447	C₂²×C₁₉	semidirect
723. #447	C₂²×C₁₉	semidirect
724. #446	C₂²×C₁₉	semidirect
725. C₈×Q₈	C₂²×C₁₉	semidirect
726. #442	C₂²×C₁₉	semidirect
727. #442	C₂²×C₁₉	semidirect
728. C₄×SD₁₆	C₂²×C₁₉	semidirect
729. C₄×SD₁₆	C₂²×C₁₉	semidirect
730. C₄×D₈	C₂²×C₁₉	semidirect
731. C₄×D₈	C₂²×C₁₉	semidirect
732. C₄×D₈	C₂²×C₁₉	semidirect
733. C₄×D₈	C₂²×C₁₉	semidirect
734. #436	C₂²×C₁₉	semidirect
735. #435	C₂²×C₁₉	semidirect
736. C₈×D₄	C₂²×C₁₉	semidirect
737. C₈×D₄	C₂²×C₁₉	semidirect
738. #433	C₂²×C₁₉	semidirect
739. #431	C₂²×C₁₉	semidirect
740. #424	C₂²×C₁₉	semidirect
741. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
742. #418	C₂²×C₁₉	semidirect
743. #416	C₂²×C₁₉	semidirect
744. C₂×#102	C₂²×C₁₉	semidirect
936. C₁₉	#62051	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×#3543	2
C₁₉×#3519	2
C₁₉×#3399	2
C₁₉×#3391	2
C₁₉×#3366	2
C₁₉×#3361	2
C₁₉×#3325	2
C₁₉×#3318	2
C₁₉×#3305	2
C₁₉×#3297	2
D₄×D₈×C₁₉	2
C₁₉×#3274	2
C₁₉×#3264	2
C₁₉×#3259	2
C₁₉×#3247	2
C₁₉×#3220	2
C₁₉×#3205	2
C₁₉×#3122	2
C₁₉×#3105	2
C₁₉×#3041	2
C₂×C₁₉×#459	2
C₁₉×#2994	2
#62051	19

Subgroups — C19×#62051 #18068010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62051 #18068010