Subgroups — C₁₉×#62355 #18068314

Order 4864.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3345	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3333	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3307	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3306	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3267	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3204	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3198	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3062	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3060	C₂	1	2	yes	maximal, complemented
23	C₁₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
27	C₁₉×#562	—	2	2	no	—
28	C₁₉×#560	—	2	2	no	—
29	C₁₉×#556	C₂²	1	1	yes	characteristic
30	C₁₉×#554	—	2	1	no	—
31	C₁₉×#554	C₂²	1	1	yes	characteristic
32	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#553	C₂²	1	2	yes	—
34	C₁₉×#550	—	2	1	no	—
35	C₁₉×#550	—	2	1	no	—
36	C₁₉×#550	C₂²	1	1	yes	characteristic
37	C₁₉×#550	C₂²	1	1	yes	characteristic
38	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#547	C₂²	1	1	yes	characteristic
40	C₁₉×#547	C₂²	1	2	yes	complemented
41	C₁₉×#547	C₂²	1	2	yes	complemented
42	C₁₉×#546	—	2	1	no	—
43	C₁₉×#546	C₂²	1	2	yes	—
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#542	—	2	1	no	—
46	C₁₉×#540	—	2	1	no	—
47	C₁₉×#540	—	2	1	no	—
48	C₁₉×#538	—	2	2	no	—
49	C₁₉×#537	—	2	2	no	—
50	C₁₉×#537	C₂²	1	2	yes	—
51	C₁₉×#537	C₂²	1	2	yes	complemented
52	C₁₉×#537	C₂²	1	2	yes	complemented
53	C₁₉×#535	—	2	1	no	—
54	C₁₉×#535	C₂²	1	2	yes	—
55	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#532	C₂²	1	1	yes	characteristic
57	C₁₉×#532	C₂²	1	1	yes	characteristic
58	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#529	C₂²	1	1	yes	characteristic
60	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#497	C₂²	1	1	yes	characteristic
63	C₁₉×#493	C₂²	1	1	yes	characteristic
64	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#489	C₂²	1	1	yes	characteristic
66	C₁₉×#486	C₂²	1	1	yes	characteristic
67	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#485	C₂²	1	2	yes	complemented
69	C₁₉×#483	C₂²	1	2	yes	complemented
70	C₁₉×#483	C₂²	1	2	yes	complemented
71	C₁₉×#482	C₂²	1	2	yes	complemented
72	C₁₉×#481	C₂²	1	2	yes	—
73	C₁₉×#481	C₂²	1	2	yes	—
74	C₁₉×#481	C₂²	1	2	yes	complemented
75	C₁₉×#480	C₂²	1	2	yes	complemented
76	C₁₉×#478	C₂²	1	2	yes	complemented
77	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#476	C₂²	1	1	yes	characteristic
79	C₁₉×#476	C₂²	1	2	yes	complemented
80	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
81	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
82	C₁₉×#470	C₂²	1	1	yes	characteristic, complemented
83	C₁₉×#470	C₂²	1	1	yes	characteristic, complemented
84	C₁₉×#470	C₂²	1	2	yes	complemented
85	C₁₉×#469	C₂²	1	2	yes	—
86	C₁₉×#469	C₂²	1	2	yes	—
87	C₁₉×#469	C₂²	1	2	yes	complemented
88	C₁₉×#469	C₂²	1	2	yes	complemented
89	C₁₉×#468	C₂²	1	1	yes	characteristic
90	C₁₉×#468	C₂²	1	1	yes	characteristic
91	C₁₉×#468	C₂²	1	2	yes	complemented
92	C₁₉×#466	C₂²	1	2	yes	—
93	C₁₉×#466	C₂²	1	2	yes	complemented
94	C₁₉×#465	C₂²	1	2	yes	—
95	C₁₉×#465	C₂²	1	2	yes	—
96	C₁₉×#465	C₂²	1	2	yes	complemented
97	C₁₉×#465	C₂²	1	2	yes	complemented
98	C₁₉×#465	C₂²	1	2	yes	complemented
99	C₁₉×#465	C₂²	1	2	yes	complemented
100	C₁₉×#463	C₂²	1	2	yes	—
101	C₁₉×#461	C₂²	1	2	yes	complemented
102	C₁₉×#460	C₂²	1	1	yes	characteristic
103	C₁₉×#460	C₂²	1	1	yes	characteristic
104	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
105	C₁₉×#459	C₂²	1	1	yes	characteristic
106	C₁₉×#452	C₂²	1	2	yes	complemented
107	C₁₉×#452	C₂²	1	2	yes	complemented
108	C₁₉×#450	C₂²	1	2	yes	—
109	C₁₉×#449	C₂²	1	2	yes	—
110	C₁₉×#449	C₂²	1	2	yes	—
111	C₁₉×#449	C₂²	1	2	yes	complemented
112	C₁₉×#449	C₂²	1	2	yes	complemented
113	C₁₉×#447	C₂²	1	2	yes	—
114	C₁₉×#442	C₂²	1	2	yes	complemented
115	C₁₉×#442	C₂²	1	2	yes	complemented
116	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
120	C₁₉×#436	C₂²	1	1	yes	characteristic
121	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₉×#435	C₂²	1	2	yes	complemented
123	C₁₉×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
126	C₁₉×#428	C₂²	1	2	yes	complemented
127	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
128	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
129	C₁₉×#417	C₂²	1	2	yes	complemented
130	C₁₉×#417	C₂²	1	2	yes	complemented
131	C₁₉×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₉×#102	C₂²	1	2	yes	—
133	C₁₉×#408	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	2	no	—
137	C₂×#41×C₁₉	—	2	1	no	—
138	C₂×#41×C₁₉	—	2	1	no	—
139	C₂×#41×C₁₉	C₂³	1	2	yes	—
140	C₂×#41×C₁₉	C₂³	1	2	yes	—
141	C₂×#41×C₁₉	C₂³	1	2	yes	—
142	C₂×#41×C₁₉	C₂³	1	2	yes	—
143	C₂²×D₄×C₁₉	—	2	1	no	—
144	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
145	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
146	C₁₉×#135	—	4	4	no	—
147	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
148	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
154	C₂×D₈×C₁₉	C₂³	1	2	yes	—
155	C₂×D₈×C₁₉	C₂³	1	2	yes	—
156	C₂×D₈×C₁₉	C₂³	1	2	yes	—
157	C₁₉×#131	—	4	4	no	—
158	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
163	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
164	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
165	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
166	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×#127	—	2	1	no	—
171	C₁₉×#127	—	2	2	no	—
172	C₁₉×#127	—	2	1	no	—
173	C₁₉×#127	—	2	1	no	—
174	C₁₉×#127	D₄	1	1	yes	characteristic
175	C₁₉×#127	C₂³	1	1	yes	characteristic
176	C₁₉×#127	C₂³	1	1	yes	characteristic
177	C₁₉×#126	—	2	2	no	—
178	C₁₉×#126	—	2	2	no	—
179	C₁₉×#126	—	2	1	no	—
180	C₁₉×#125	—	2	1	no	—
181	C₁₉×#125	—	2	1	no	—
182	C₁₉×#125	—	2	1	no	—
183	C₁₉×#125	C₂³	1	1	yes	characteristic
184	C₁₉×#124	—	2	2	no	—
185	C₁₉×#124	—	2	1	no	—
186	C₁₉×#124	—	2	1	no	—
187	C₁₉×#124	—	2	1	no	—
188	C₁₉×#124	D₄	1	2	yes	—
189	C₁₉×#124	C₂³	1	1	yes	characteristic
190	C₁₉×#123	—	2	1	no	—
191	C₁₉×#123	—	2	2	no	—
192	C₁₉×#123	—	2	2	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×C₂²⋊Q₈	—	2	2	no	—
199	C₁₉×C₂²⋊Q₈	—	2	2	no	—
200	C₁₉×C₂²⋊Q₈	—	2	2	no	—
201	C₁₉×C₂²⋊Q₈	—	2	1	no	—
202	C₁₉×C₂²⋊Q₈	—	2	2	no	—
203	C₁₉×C₂²⋊Q₈	—	2	1	no	—
204	C₁₉×C₂²⋊Q₈	—	2	2	no	—
205	C₁₉×C₂²⋊Q₈	—	2	2	no	—
206	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₉×#121	—	2	2	no	—
213	C₁₉×#121	—	2	2	no	—
214	C₁₉×#121	—	2	2	no	—
215	C₁₉×#121	—	2	2	no	—
216	C₁₉×#121	—	2	2	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	1	no	—
224	C₁₉×#121	—	2	1	no	—
225	C₁₉×#121	—	2	1	no	—
226	C₁₉×#121	—	2	2	no	—
227	C₁₉×#121	—	2	2	no	—
228	C₁₉×#121	—	2	2	no	—
229	C₁₉×#121	—	2	2	no	—
230	C₁₉×#121	D₄	1	2	yes	—
231	C₁₉×#121	D₄	1	1	yes	characteristic
232	C₁₉×#121	D₄	1	1	yes	characteristic
233	C₁₉×#121	C₂³	1	2	yes	—
234	C₁₉×#121	C₂³	1	2	yes	—
235	C₁₉×#121	C₂³	1	2	yes	—
236	C₁₉×#121	C₂³	1	2	yes	—
237	C₁₉×#121	C₂³	1	2	yes	—
238	C₁₉×#121	C₂³	1	2	yes	—
239	C₁₉×#121	C₂³	1	2	yes	—
240	C₁₉×#121	C₂³	1	1	yes	characteristic
241	C₁₉×#120	—	2	2	no	—
242	C₁₉×#120	—	2	2	no	—
243	C₁₉×#120	—	2	2	no	—
244	C₁₉×#120	—	2	2	no	—
245	C₄×Q₈×C₁₉	—	2	1	no	—
246	C₄×Q₈×C₁₉	—	2	1	no	—
247	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₉	—	2	1	no	—
251	C₄×D₄×C₁₉	—	2	1	no	—
252	C₄×D₄×C₁₉	—	2	1	no	—
253	C₄×D₄×C₁₉	—	2	1	no	—
254	C₄×D₄×C₁₉	—	2	1	no	—
255	C₄×D₄×C₁₉	—	2	1	no	—
256	C₄×D₄×C₁₉	—	2	2	no	—
257	C₄×D₄×C₁₉	—	2	1	no	—
258	C₄×D₄×C₁₉	—	2	1	no	—
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	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₁₉	C₂³	1	2	yes	—
265	C₁₉×#117	—	2	1	no	—
266	C₁₉×#117	—	2	1	no	—
267	C₁₉×#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
269	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	2	yes	—
279	C₁₉×#106	C₂³	1	2	yes	—
280	C₁₉×#106	C₂³	1	2	yes	—
281	C₁₉×#106	C₂³	1	2	yes	—
282	C₁₉×#106	C₂³	1	1	yes	characteristic
283	C₁₉×#106	C₂³	1	2	yes	—
284	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#103	C₂³	1	1	yes	characteristic
295	C₁₉×#103	C₂³	1	1	yes	characteristic
296	C₁₉×#102	C₂³	1	1	yes	characteristic
297	C₁₉×#102	C₂³	1	2	yes	—
298	C₁₉×#102	C₂³	1	2	yes	—
299	C₁₉×#102	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	2	yes	—
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
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	2	yes	—
308	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×#97	C₂³	1	1	yes	characteristic
312	C₁₉×#97	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
315	C₂⁴×C₁₉	—	2	2	no	—
316	#41×C₁₉	—	4	2	no	—
317	#41×C₁₉	—	4	2	no	—
318	#41×C₁₉	—	4	2	no	—
319	#41×C₁₉	—	4	2	no	—
320	#41×C₁₉	—	4	2	no	—
321	#41×C₁₉	—	4	2	no	—
322	#41×C₁₉	—	4	2	no	—
323	#41×C₁₉	—	4	2	no	—
324	#41×C₁₉	—	8	2	no	—
325	#41×C₁₉	—	8	2	no	—
326	#41×C₁₉	—	8	2	no	—
327	#41×C₁₉	—	8	4	no	—
328	C₂×Q₈×C₁₉	—	2	1	no	—
329	C₂×Q₈×C₁₉	—	2	1	no	—
330	C₂×Q₈×C₁₉	—	2	1	no	—
331	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
332	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₁₉	—	2	1	no	—
336	C₂×D₄×C₁₉	—	2	2	no	—
337	C₂×D₄×C₁₉	—	2	2	no	—
338	C₂×D₄×C₁₉	—	2	2	no	—
339	C₂×D₄×C₁₉	—	2	2	no	—
340	C₂×D₄×C₁₉	—	2	2	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	2	no	—
345	C₂×D₄×C₁₉	—	2	2	no	—
346	C₂×D₄×C₁₉	—	2	1	no	—
347	C₂×D₄×C₁₉	—	2	1	no	—
348	C₂×D₄×C₁₉	—	2	1	no	—
349	C₂×D₄×C₁₉	—	2	2	no	—
350	C₂×D₄×C₁₉	—	2	1	no	—
351	C₂×D₄×C₁₉	—	4	2	no	—
352	C₂×D₄×C₁₉	—	4	2	no	—
353	C₂×D₄×C₁₉	—	8	2	no	—
354	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
357	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
358	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
359	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
361	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
362	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₁₉	—	2	2	no	—
364	C₂²×C₄×C₁₉	—	2	2	no	—
365	C₂²×C₄×C₁₉	—	2	2	no	—
366	C₂²×C₄×C₁₉	—	2	2	no	—
367	C₂²×C₄×C₁₉	—	2	1	no	—
368	C₂²×C₄×C₁₉	—	2	2	no	—
369	C₂²×C₄×C₁₉	—	2	2	no	—
370	C₂²×C₄×C₁₉	—	2	2	no	—
371	C₂²×C₄×C₁₉	—	2	2	no	—
372	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
377	Q₁₆×C₁₉	—	2	2	no	—
378	Q₁₆×C₁₉	—	4	1	no	—
379	SD₁₆×C₁₉	—	2	2	no	—
380	SD₁₆×C₁₉	—	4	1	no	—
381	SD₁₆×C₁₉	—	4	2	no	—
382	SD₁₆×C₁₉	—	4	2	no	—
383	SD₁₆×C₁₉	—	4	2	no	—
384	D₈×C₁₉	—	2	4	no	—
385	D₈×C₁₉	—	4	2	no	—
386	D₈×C₁₉	—	4	2	no	—
387	M₁₆×C₁₉	—	2	2	no	—
388	M₁₆×C₁₉	—	2	4	no	—
389	M₁₆×C₁₉	—	4	1	no	—
390	M₁₆×C₁₉	—	4	2	no	—
391	C₂×C₈×C₁₉	—	2	4	no	—
392	C₂×C₈×C₁₉	—	4	2	no	—
393	C₂×C₈×C₁₉	—	4	2	no	—
394	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
395	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
397	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₁₉	—	2	1	no	—
401	C₄⋊C₄×C₁₉	—	2	2	no	—
402	C₄⋊C₄×C₁₉	—	2	2	no	—
403	C₄⋊C₄×C₁₉	—	2	2	no	—
404	C₄⋊C₄×C₁₉	—	2	2	no	—
405	C₄⋊C₄×C₁₉	—	2	2	no	—
406	C₄⋊C₄×C₁₉	—	2	1	no	—
407	C₄⋊C₄×C₁₉	—	2	1	no	—
408	C₄⋊C₄×C₁₉	—	2	1	no	—
409	C₄⋊C₄×C₁₉	—	2	1	no	—
410	C₄⋊C₄×C₁₉	—	2	1	no	—
411	C₄⋊C₄×C₁₉	—	2	1	no	—
412	C₄⋊C₄×C₁₉	—	2	1	no	—
413	C₄⋊C₄×C₁₉	—	2	1	no	—
414	C₄⋊C₄×C₁₉	—	2	1	no	—
415	C₄⋊C₄×C₁₉	—	2	2	no	—
416	C₄⋊C₄×C₁₉	—	2	1	no	—
417	C₄⋊C₄×C₁₉	—	2	1	no	—
418	C₄⋊C₄×C₁₉	—	2	1	no	—
419	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
428	C₂²⋊C₄×C₁₉	—	2	2	no	—
429	C₂²⋊C₄×C₁₉	—	2	1	no	—
430	C₂²⋊C₄×C₁₉	—	2	1	no	—
431	C₂²⋊C₄×C₁₉	—	2	2	no	—
432	C₂²⋊C₄×C₁₉	—	2	1	no	—
433	C₂²⋊C₄×C₁₉	—	2	2	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	1	no	—
439	C₂²⋊C₄×C₁₉	—	2	2	no	—
440	C₂²⋊C₄×C₁₉	—	2	2	no	—
441	C₂²⋊C₄×C₁₉	—	2	2	no	—
442	C₂²⋊C₄×C₁₉	—	2	2	no	—
443	C₂²⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
452	C₄²×C₁₉	—	2	1	no	—
453	C₄²×C₁₉	—	2	1	no	—
454	C₄²×C₁₉	—	2	1	no	—
455	C₄²×C₁₉	—	2	2	no	—
456	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
460	#62355	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂³×C₁₉	—	2	1	no	—
462	C₂³×C₁₉	—	2	2	no	—
463	C₂³×C₁₉	—	2	2	no	—
464	C₂³×C₁₉	—	8	2	no	—
465	C₂³×C₁₉	—	8	2	no	—
466	C₂³×C₁₉	—	8	2	no	—
467	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
468	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
469	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
470	Q₈×C₁₉	—	2	1	no	—
471	Q₈×C₁₉	—	2	1	no	—
472	Q₈×C₁₉	—	2	1	no	—
473	Q₈×C₁₉	—	2	1	no	—
474	Q₈×C₁₉	—	2	1	no	—
475	Q₈×C₁₉	—	2	1	no	—
476	Q₈×C₁₉	—	4	2	no	—
477	Q₈×C₁₉	—	4	2	no	—
478	Q₈×C₁₉	—	4	2	no	—
479	Q₈×C₁₉	—	8	1	no	—
480	D₄×C₁₉	—	2	2	no	—
481	D₄×C₁₉	—	2	2	no	—
482	D₄×C₁₉	—	2	2	no	—
483	D₄×C₁₉	—	2	2	no	—
484	D₄×C₁₉	—	2	1	no	—
485	D₄×C₁₉	—	2	2	no	—
486	D₄×C₁₉	—	2	2	no	—
487	D₄×C₁₉	—	2	1	no	—
488	D₄×C₁₉	—	4	2	no	—
489	D₄×C₁₉	—	4	2	no	—
490	D₄×C₁₉	—	4	2	no	—
491	D₄×C₁₉	—	4	2	no	—
492	D₄×C₁₉	—	4	2	no	—
493	D₄×C₁₉	—	4	2	no	—
494	D₄×C₁₉	—	8	1	no	—
495	D₄×C₁₉	—	8	2	no	—
496	D₄×C₁₉	—	8	1	no	—
497	D₄×C₁₉	—	8	1	no	—
498	D₄×C₁₉	—	8	2	no	—
499	D₄×C₁₉	—	8	2	no	—
500	D₄×C₁₉	—	8	2	no	—
501	D₄×C₁₉	—	8	2	no	—
502	D₄×C₁₉	—	8	2	no	—
503	D₄×C₁₉	—	8	2	no	—
504	D₄×C₁₉	—	8	2	no	—
505	D₄×C₁₉	—	8	2	no	—
506	D₄×C₁₉	—	8	2	no	—
507	D₄×C₁₉	—	8	2	no	—
508	C₂×C₄×C₁₉	—	2	2	no	—
509	C₂×C₄×C₁₉	—	2	2	no	—
510	C₂×C₄×C₁₉	—	2	1	no	—
511	C₂×C₄×C₁₉	—	2	2	no	—
512	C₂×C₄×C₁₉	—	2	1	no	—
513	C₂×C₄×C₁₉	—	2	2	no	—
514	C₂×C₄×C₁₉	—	2	2	no	—
515	C₂×C₄×C₁₉	—	2	1	no	—
516	C₂×C₄×C₁₉	—	2	1	no	—
517	C₂×C₄×C₁₉	—	2	2	no	—
518	C₂×C₄×C₁₉	—	2	1	no	—
519	C₂×C₄×C₁₉	—	2	1	no	—
520	C₂×C₄×C₁₉	—	2	1	no	—
521	C₂×C₄×C₁₉	—	2	1	no	—
522	C₂×C₄×C₁₉	—	2	1	no	—
523	C₂×C₄×C₁₉	—	2	2	no	—
524	C₂×C₄×C₁₉	—	4	1	no	—
525	C₂×C₄×C₁₉	—	4	4	no	—
526	C₂×C₄×C₁₉	—	4	2	no	—
527	C₂×C₄×C₁₉	—	8	2	no	—
528	C₂×C₄×C₁₉	—	8	2	no	—
529	C₂×C₄×C₁₉	—	8	2	no	—
530	C₂×C₄×C₁₉	—	8	2	no	—
531	C₂×C₄×C₁₉	—	8	2	no	—
532	C₂×C₄×C₁₉	—	8	2	no	—
533	C₂×C₄×C₁₉	—	8	2	no	—
534	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
542	C₈×C₁₉	—	2	2	no	—
543	C₈×C₁₉	—	2	1	no	—
544	C₈×C₁₉	—	2	2	no	—
545	C₈×C₁₉	—	2	1	no	—
546	C₈×C₁₉	—	2	1	no	—
547	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
548	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
549	#3546	C₂×C₁₉	1	1	yes	characteristic, complemented
550	#3356	C₂×C₁₉	1	1	yes	characteristic, complemented
551	#3345	C₂×C₁₉	1	2	yes	complemented
552	#3335	C₂×C₁₉	1	1	yes	characteristic, complemented
553	#3333	C₂×C₁₉	1	1	yes	characteristic, complemented
554	#3332	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3307	C₂×C₁₉	1	2	yes	complemented
556	#3306	C₂×C₁₉	1	2	yes	complemented
557	#3304	C₂×C₁₉	1	1	yes	characteristic, complemented
558	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
559	#3287	C₂×C₁₉	1	1	yes	characteristic, complemented
560	#3274	C₂×C₁₉	1	1	yes	characteristic, complemented
561	#3267	C₂×C₁₉	1	2	yes	complemented
562	#3247	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
564	#3204	C₂×C₁₉	1	2	yes	complemented
565	#3198	C₂×C₁₉	1	2	yes	complemented
566	#3184	C₂×C₁₉	1	1	yes	characteristic, complemented
567	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
568	#3062	C₂×C₁₉	1	2	yes	complemented
569	#3060	C₂×C₁₉	1	2	yes	complemented
570	#2935	C₂×C₁₉	1	1	yes	characteristic, complemented
571	C₂²×C₁₉	—	2	1	no	—
572	C₂²×C₁₉	—	2	2	no	—
573	C₂²×C₁₉	—	2	2	no	—
574	C₂²×C₁₉	—	2	1	no	—
575	C₂²×C₁₉	—	2	2	no	—
576	C₂²×C₁₉	—	2	2	no	—
577	C₂²×C₁₉	—	2	1	no	—
578	C₂²×C₁₉	—	2	2	no	—
579	C₂²×C₁₉	—	2	2	no	—
580	C₂²×C₁₉	—	4	2	no	—
581	C₂²×C₁₉	—	4	2	no	—
582	C₂²×C₁₉	—	4	1	no	—
583	C₂²×C₁₉	—	4	2	no	—
584	C₂²×C₁₉	—	4	2	no	—
585	C₂²×C₁₉	—	4	1	no	—
586	C₂²×C₁₉	—	4	1	no	—
587	C₂²×C₁₉	—	4	2	no	—
588	C₂²×C₁₉	—	4	2	no	—
589	C₂²×C₁₉	—	16	4	no	—
590	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
591	C₄×C₁₉	—	2	1	no	—
592	C₄×C₁₉	—	2	1	no	—
593	C₄×C₁₉	—	2	2	no	—
594	C₄×C₁₉	—	2	2	no	—
595	C₄×C₁₉	—	2	1	no	—
596	C₄×C₁₉	—	2	1	no	—
597	C₄×C₁₉	—	4	2	no	—
598	C₄×C₁₉	—	4	1	no	—
599	C₄×C₁₉	—	4	1	no	—
600	C₄×C₁₉	—	4	1	no	—
601	C₄×C₁₉	—	4	1	no	—
602	C₄×C₁₉	—	4	1	no	—
603	C₄×C₁₉	—	4	1	no	—
604	C₄×C₁₉	—	4	1	no	—
605	C₄×C₁₉	—	4	2	no	—
606	C₄×C₁₉	#577	1	2	yes	—
607	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₄×C₁₉	#585	1	1	yes	characteristic
609	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
610	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
611	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
612	#562	—	2	2	no	—
613	#560	—	2	2	no	—
614	#556	C₂²×C₁₉	1	1	yes	characteristic
615	#554	—	2	1	no	—
616	#554	C₂²×C₁₉	1	1	yes	characteristic
617	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
618	#553	C₂²×C₁₉	1	2	yes	—
619	#550	—	2	1	no	—
620	#550	—	2	1	no	—
621	#550	C₂²×C₁₉	1	1	yes	characteristic
622	#550	C₂²×C₁₉	1	1	yes	characteristic
623	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
624	#547	C₂²×C₁₉	1	1	yes	characteristic
625	#547	C₂²×C₁₉	1	2	yes	complemented
626	#547	C₂²×C₁₉	1	2	yes	complemented
627	#546	—	2	1	no	—
628	#546	C₂²×C₁₉	1	2	yes	—
629	D₄²	C₂²×C₁₉	1	1	yes	characteristic
630	#542	—	2	1	no	—
631	#540	—	2	1	no	—
632	#540	—	2	1	no	—
633	#538	—	2	2	no	—
634	#537	—	2	2	no	—
635	#537	C₂²×C₁₉	1	2	yes	—
636	#537	C₂²×C₁₉	1	2	yes	complemented
637	#537	C₂²×C₁₉	1	2	yes	complemented
638	#535	—	2	1	no	—
639	#535	C₂²×C₁₉	1	2	yes	—
640	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
641	#532	C₂²×C₁₉	1	1	yes	characteristic
642	#532	C₂²×C₁₉	1	1	yes	characteristic
643	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
644	#529	C₂²×C₁₉	1	1	yes	characteristic
645	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
646	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
647	#497	C₂²×C₁₉	1	1	yes	characteristic
648	#493	C₂²×C₁₉	1	1	yes	characteristic
649	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
650	#489	C₂²×C₁₉	1	1	yes	characteristic
651	#486	C₂²×C₁₉	1	1	yes	characteristic
652	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
653	#485	C₂²×C₁₉	1	2	yes	complemented
654	#483	C₂²×C₁₉	1	2	yes	complemented
655	#483	C₂²×C₁₉	1	2	yes	complemented
656	#482	C₂²×C₁₉	1	2	yes	complemented
657	#481	C₂²×C₁₉	1	2	yes	—
658	#481	C₂²×C₁₉	1	2	yes	—
659	#481	C₂²×C₁₉	1	2	yes	complemented
660	#480	C₂²×C₁₉	1	2	yes	complemented
661	#478	C₂²×C₁₉	1	2	yes	complemented
662	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
663	#476	C₂²×C₁₉	1	1	yes	characteristic
664	#476	C₂²×C₁₉	1	2	yes	complemented
665	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	#470	C₂²×C₁₉	1	2	yes	complemented
668	#470	C₂²×C₁₉	1	1	yes	characteristic, complemented
669	#470	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	#469	C₂²×C₁₉	1	2	yes	—
671	#469	C₂²×C₁₉	1	2	yes	—
672	#469	C₂²×C₁₉	1	2	yes	complemented
673	#469	C₂²×C₁₉	1	2	yes	complemented
674	#468	C₂²×C₁₉	1	1	yes	characteristic
675	#468	C₂²×C₁₉	1	1	yes	characteristic
676	#468	C₂²×C₁₉	1	2	yes	complemented
677	#466	C₂²×C₁₉	1	2	yes	—
678	#466	C₂²×C₁₉	1	2	yes	complemented
679	#465	C₂²×C₁₉	1	2	yes	—
680	#465	C₂²×C₁₉	1	2	yes	—
681	#465	C₂²×C₁₉	1	2	yes	complemented
682	#465	C₂²×C₁₉	1	2	yes	complemented
683	#465	C₂²×C₁₉	1	2	yes	complemented
684	#465	C₂²×C₁₉	1	2	yes	complemented
685	#463	C₂²×C₁₉	1	2	yes	—
686	#461	C₂²×C₁₉	1	2	yes	complemented
687	#460	C₂²×C₁₉	1	1	yes	characteristic
688	#460	C₂²×C₁₉	1	1	yes	characteristic
689	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
690	#459	C₂²×C₁₉	1	1	yes	characteristic
691	#452	C₂²×C₁₉	1	2	yes	complemented
692	#452	C₂²×C₁₉	1	2	yes	complemented
693	#450	C₂²×C₁₉	1	2	yes	—
694	#449	C₂²×C₁₉	1	2	yes	—
695	#449	C₂²×C₁₉	1	2	yes	—
696	#449	C₂²×C₁₉	1	2	yes	complemented
697	#449	C₂²×C₁₉	1	2	yes	complemented
698	#447	C₂²×C₁₉	1	2	yes	—
699	#442	C₂²×C₁₉	1	2	yes	complemented
700	#442	C₂²×C₁₉	1	2	yes	complemented
701	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
702	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
703	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
704	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
705	#436	C₂²×C₁₉	1	1	yes	characteristic
706	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#435	C₂²×C₁₉	1	2	yes	complemented
708	#435	C₂²×C₁₉	1	2	yes	complemented
709	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
710	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
711	#428	C₂²×C₁₉	1	2	yes	complemented
712	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
713	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
714	#417	C₂²×C₁₉	1	2	yes	complemented
715	#417	C₂²×C₁₉	1	2	yes	complemented
716	#416	C₂²×C₁₉	1	2	yes	complemented
717	C₂×#102	C₂²×C₁₉	1	2	yes	—
718	#408	C₂²×C₁₉	1	2	yes	complemented
719	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
720	C₂×C₁₉	—	4	1	no	—
721	C₂×C₁₉	—	4	2	no	—
722	C₂×C₁₉	—	4	2	no	—
723	C₂×C₁₉	—	8	2	no	—
724	C₂×C₁₉	—	8	2	no	—
725	C₂×C₁₉	—	8	1	no	—
726	C₂×C₁₉	#3496	1	1	yes	characteristic
727	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
728	C₂×C₁₉	#3585	1	1	yes	characteristic
729	C₂×#41	—	2	1	no	—
730	C₂×#41	—	2	2	no	—
731	C₂×#41	—	2	1	no	—
732	C₂×#41	—	2	1	no	—
733	C₂×#41	C₂³×C₁₉	1	2	yes	—
734	C₂×#41	C₂³×C₁₉	1	2	yes	—
735	C₂×#41	C₂³×C₁₉	1	2	yes	—
736	C₂×#41	C₂³×C₁₉	1	2	yes	—
737	C₂²×D₄	—	2	1	no	—
738	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
739	AGL(1,ℤ/8)	—	4	4	no	—
740	#135	—	4	4	no	—
741	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
742	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
748	C₂×D₈	C₂³×C₁₉	1	2	yes	—
749	C₂×D₈	C₂³×C₁₉	1	2	yes	—
750	C₂×D₈	C₂³×C₁₉	1	2	yes	—
751	#131	—	4	4	no	—
752	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
753	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
754	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
755	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
757	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
758	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
759	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
760	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
761	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
762	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
764	#127	—	2	1	no	—
765	#127	—	2	2	no	—
766	#127	—	2	1	no	—
767	#127	—	2	1	no	—
768	#127	D₄×C₁₉	1	1	yes	characteristic
769	#127	C₂³×C₁₉	1	1	yes	characteristic
770	#127	C₂³×C₁₉	1	1	yes	characteristic
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	—	2	1	no	—
774	#125	—	2	1	no	—
775	#125	—	2	1	no	—
776	#125	—	2	1	no	—
777	#125	C₂³×C₁₉	1	1	yes	characteristic
778	#124	—	2	2	no	—
779	#124	—	2	1	no	—
780	#124	—	2	1	no	—
781	#124	—	2	1	no	—
782	#124	D₄×C₁₉	1	2	yes	—
783	#124	C₂³×C₁₉	1	1	yes	characteristic
784	#123	—	2	1	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
801	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
802	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
803	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	1	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	D₄×C₁₉	1	2	yes	—
825	#121	D₄×C₁₉	1	1	yes	characteristic
826	#121	D₄×C₁₉	1	1	yes	characteristic
827	#121	C₂³×C₁₉	1	1	yes	characteristic
828	#121	C₂³×C₁₉	1	2	yes	—
829	#121	C₂³×C₁₉	1	2	yes	—
830	#121	C₂³×C₁₉	1	2	yes	—
831	#121	C₂³×C₁₉	1	2	yes	—
832	#121	C₂³×C₁₉	1	2	yes	—
833	#121	C₂³×C₁₉	1	2	yes	—
834	#121	C₂³×C₁₉	1	2	yes	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	#120	—	2	2	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	2	1	no	—
841	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
842	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
843	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₁₉	1	2	yes	—
855	C₄×D₄	C₂³×C₁₉	1	2	yes	—
856	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₁₉	1	2	yes	—
858	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
859	#117	—	2	1	no	—
860	#117	—	2	1	no	—
861	#117	C₂³×C₁₉	1	2	yes	—
862	C₂×C₄⋊C₄	—	2	2	no	—
863	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
864	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
865	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
868	#107	C₂³×C₁₉	1	1	yes	characteristic
869	#107	C₂³×C₁₉	1	2	yes	—
870	#107	C₂³×C₁₉	1	1	yes	characteristic
871	#106	C₂³×C₁₉	1	1	yes	characteristic
872	#106	C₂³×C₁₉	1	2	yes	—
873	#106	C₂³×C₁₉	1	2	yes	—
874	#106	C₂³×C₁₉	1	2	yes	—
875	#106	C₂³×C₁₉	1	2	yes	—
876	#106	C₂³×C₁₉	1	1	yes	characteristic
877	#106	C₂³×C₁₉	1	2	yes	—
878	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
879	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
880	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
881	#103	C₂³×C₁₉	1	1	yes	characteristic
882	#103	C₂³×C₁₉	1	2	yes	—
883	#103	C₂³×C₁₉	1	1	yes	characteristic
884	#103	C₂³×C₁₉	1	1	yes	characteristic
885	#103	C₂³×C₁₉	1	2	yes	—
886	#103	C₂³×C₁₉	1	2	yes	—
887	#103	C₂³×C₁₉	1	1	yes	characteristic
888	#103	C₂³×C₁₉	1	1	yes	characteristic
889	#103	C₂³×C₁₉	1	1	yes	characteristic
890	#102	C₂³×C₁₉	1	1	yes	characteristic
891	#102	C₂³×C₁₉	1	2	yes	—
892	#102	C₂³×C₁₉	1	2	yes	—
893	#102	C₂³×C₁₉	1	2	yes	—
894	#102	C₂³×C₁₉	1	2	yes	—
895	#102	C₂³×C₁₉	1	2	yes	—
896	#102	C₂³×C₁₉	1	2	yes	—
897	#102	C₂³×C₁₉	1	2	yes	—
898	#102	C₂³×C₁₉	1	1	yes	characteristic
899	#102	C₂³×C₁₉	1	2	yes	—
900	#102	C₂³×C₁₉	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
905	#97	C₂³×C₁₉	1	1	yes	characteristic
906	#97	C₂³×C₁₉	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
908	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
909	C₁₉	#62355	1	1	yes	characteristic, direct product factor, Sylow
910	C₂⁴	—	2	2	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	2	no	—
917	#41	—	4	2	no	—
918	#41	—	4	2	no	—
919	#41	—	8	2	no	—
920	#41	—	8	2	no	—
921	#41	—	8	2	no	—
922	#41	—	8	4	no	—
923	C₂×Q₈	—	2	1	no	—
924	C₂×Q₈	—	2	1	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
929	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	4	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	8	2	no	—
949	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
950	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
951	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
952	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
953	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
954	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
955	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
956	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
957	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
968	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
969	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
970	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
971	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
972	Q₁₆	—	2	2	no	—
973	Q₁₆	—	4	1	no	—
974	SD₁₆	—	2	2	no	—
975	SD₁₆	—	4	1	no	—
976	SD₁₆	—	4	2	no	—
977	SD₁₆	—	4	2	no	—
978	SD₁₆	—	4	2	no	—
979	D₈	—	2	4	no	—
980	D₈	—	4	2	no	—
981	D₈	—	4	2	no	—
982	M₁₆	—	2	2	no	—
983	M₁₆	—	2	4	no	—
984	M₁₆	—	4	1	no	—
985	M₁₆	—	4	2	no	—
986	C₂×C₈	—	2	4	no	—
987	C₂×C₈	—	4	2	no	—
988	C₂×C₈	—	4	2	no	—
989	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
990	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
991	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
992	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
993	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
994	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1016	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1022	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1052	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	8	2	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1062	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1063	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	4	2	no	—
1071	Q₈	—	4	2	no	—
1072	Q₈	—	4	2	no	—
1073	Q₈	—	8	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	4	2	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	1	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	1	no	—
1101	D₄	—	8	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	—	8	2	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1131	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1132	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1135	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1136	C₈	—	2	2	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	2	1	no	—
1140	C₈	—	2	1	no	—
1141	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	2	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	16	4	no	—
1161	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	2	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	2	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	1	no	—
1177	C₄	C₁₉×#577	1	2	yes	—
1178	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1179	C₄	C₁₉×#585	1	1	yes	characteristic
1180	C₂	—	4	2	no	—
1181	C₂	—	4	1	no	—
1182	C₂	—	4	2	no	—
1183	C₂	—	8	1	no	—
1184	C₂	—	8	2	no	—
1185	C₂	—	8	2	no	—
1186	C₂	C₁₉×#3496	1	1	yes	characteristic
1187	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1188	C₂	C₁₉×#3585	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3548	C₂	semidirect
2. C₁₉×#3546	C₂	semidirect
3. C₁₉×#3356	C₂	semidirect
4. C₁₉×#3345	C₂	semidirect
5. C₁₉×#3335	C₂	semidirect
6. C₁₉×#3333	C₂	semidirect
7. C₁₉×#3332	C₂	semidirect
8. C₁₉×#3307	C₂	semidirect
9. C₁₉×#3306	C₂	semidirect
10. C₁₉×#3304	C₂	semidirect
11. C₁₉×#3295	C₂	semidirect
12. C₁₉×#3287	C₂	semidirect
13. C₁₉×#3274	C₂	semidirect
14. C₁₉×#3267	C₂	semidirect
15. C₁₉×#3247	C₂	semidirect
16. C₁₉×#3246	C₂	semidirect
17. C₁₉×#3204	C₂	semidirect
18. C₁₉×#3198	C₂	semidirect
19. C₁₉×#3184	C₂	semidirect
20. C₁₉×#3172	C₂	semidirect
21. C₁₉×#3062	C₂	semidirect
22. C₁₉×#3060	C₂	semidirect
23. C₁₉×#2935	C₂	semidirect
25. C₂×C₁₉×#135	C₂²	semidirect
26. C₂×C₁₉×#131	C₂²	semidirect
32. C₁₉×#554	C₂²	semidirect
38. C₁₉×#550	C₂²	semidirect
40. C₁₉×#547	C₂²	semidirect
41. C₁₉×#547	C₂²	semidirect
51. C₁₉×#537	C₂²	semidirect
52. C₁₉×#537	C₂²	semidirect
55. C₁₉×#533	C₂²	semidirect
58. C₁₉×#532	C₂²	semidirect
60. C₁₉×#501	C₂²	semidirect
61. C₁₉×#498	C₂²	semidirect
64. C₁₉×#491	C₂²	semidirect
67. C₁₉×#486	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
69. C₁₉×#483	C₂²	semidirect
70. C₁₉×#483	C₂²	semidirect
71. C₁₉×#482	C₂²	semidirect
74. C₁₉×#481	C₂²	semidirect
75. C₁₉×#480	C₂²	semidirect
76. C₁₉×#478	C₂²	semidirect
77. C₁₉×#477	C₂²	semidirect
79. C₁₉×#476	C₂²	semidirect
80. C₁₉×#475	C₂²	semidirect
81. C₁₉×#475	C₂²	semidirect
82. C₁₉×#470	C₂²	semidirect
83. C₁₉×#470	C₂²	semidirect
84. C₁₉×#470	C₂²	semidirect
87. C₁₉×#469	C₂²	semidirect
88. C₁₉×#469	C₂²	semidirect
91. C₁₉×#468	C₂²	semidirect
93. C₁₉×#466	C₂²	semidirect
96. C₁₉×#465	C₂²	semidirect
97. C₁₉×#465	C₂²	semidirect
98. C₁₉×#465	C₂²	semidirect
99. C₁₉×#465	C₂²	semidirect
101. C₁₉×#461	C₂²	semidirect
104. C₁₉×#460	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
107. C₁₉×#452	C₂²	semidirect
111. C₁₉×#449	C₂²	semidirect
112. C₁₉×#449	C₂²	semidirect
114. C₁₉×#442	C₂²	semidirect
115. C₁₉×#442	C₂²	semidirect
116. C₄×Q₁₆×C₁₉	C₂²	semidirect
117. C₄×Q₁₆×C₁₉	C₂²	semidirect
121. C₁₉×#436	C₂²	semidirect
122. C₁₉×#435	C₂²	semidirect
123. C₁₉×#435	C₂²	semidirect
125. C₈×D₄×C₁₉	C₂²	semidirect
126. C₁₉×#428	C₂²	semidirect
127. C₂×C₁₉×#106	C₂²	semidirect
128. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
129. C₁₉×#417	C₂²	semidirect
130. C₁₉×#417	C₂²	semidirect
131. C₁₉×#416	C₂²	semidirect
133. C₁₉×#408	C₂²	semidirect
134. C₄×M₁₆×C₁₉	C₂²	semidirect
460. #62355	C₁₉	direct (N × H)
548. #3548	C₂×C₁₉	semidirect
549. #3546	C₂×C₁₉	semidirect
550. #3356	C₂×C₁₉	semidirect
551. #3345	C₂×C₁₉	semidirect
552. #3335	C₂×C₁₉	semidirect
553. #3333	C₂×C₁₉	semidirect
554. #3332	C₂×C₁₉	semidirect
555. #3307	C₂×C₁₉	semidirect
556. #3306	C₂×C₁₉	semidirect
557. #3304	C₂×C₁₉	semidirect
558. #3295	C₂×C₁₉	semidirect
559. #3287	C₂×C₁₉	semidirect
560. #3274	C₂×C₁₉	semidirect
561. #3267	C₂×C₁₉	semidirect
562. #3247	C₂×C₁₉	semidirect
563. #3246	C₂×C₁₉	semidirect
564. #3204	C₂×C₁₉	semidirect
565. #3198	C₂×C₁₉	semidirect
566. #3184	C₂×C₁₉	semidirect
567. #3172	C₂×C₁₉	semidirect
568. #3062	C₂×C₁₉	semidirect
569. #3060	C₂×C₁₉	semidirect
570. #2935	C₂×C₁₉	semidirect
610. C₂×#135	C₂²×C₁₉	semidirect
611. C₂×#131	C₂²×C₁₉	semidirect
617. #554	C₂²×C₁₉	semidirect
623. #550	C₂²×C₁₉	semidirect
625. #547	C₂²×C₁₉	semidirect
626. #547	C₂²×C₁₉	semidirect
636. #537	C₂²×C₁₉	semidirect
637. #537	C₂²×C₁₉	semidirect
640. #533	C₂²×C₁₉	semidirect
643. #532	C₂²×C₁₉	semidirect
645. #501	C₂²×C₁₉	semidirect
646. #498	C₂²×C₁₉	semidirect
649. #491	C₂²×C₁₉	semidirect
652. #486	C₂²×C₁₉	semidirect
653. #485	C₂²×C₁₉	semidirect
654. #483	C₂²×C₁₉	semidirect
655. #483	C₂²×C₁₉	semidirect
656. #482	C₂²×C₁₉	semidirect
659. #481	C₂²×C₁₉	semidirect
660. #480	C₂²×C₁₉	semidirect
661. #478	C₂²×C₁₉	semidirect
662. #477	C₂²×C₁₉	semidirect
664. #476	C₂²×C₁₉	semidirect
665. #475	C₂²×C₁₉	semidirect
666. #475	C₂²×C₁₉	semidirect
667. #470	C₂²×C₁₉	semidirect
668. #470	C₂²×C₁₉	semidirect
669. #470	C₂²×C₁₉	semidirect
672. #469	C₂²×C₁₉	semidirect
673. #469	C₂²×C₁₉	semidirect
676. #468	C₂²×C₁₉	semidirect
678. #466	C₂²×C₁₉	semidirect
681. #465	C₂²×C₁₉	semidirect
682. #465	C₂²×C₁₉	semidirect
683. #465	C₂²×C₁₉	semidirect
684. #465	C₂²×C₁₉	semidirect
686. #461	C₂²×C₁₉	semidirect
689. #460	C₂²×C₁₉	semidirect
691. #452	C₂²×C₁₉	semidirect
692. #452	C₂²×C₁₉	semidirect
696. #449	C₂²×C₁₉	semidirect
697. #449	C₂²×C₁₉	semidirect
699. #442	C₂²×C₁₉	semidirect
700. #442	C₂²×C₁₉	semidirect
701. C₄×Q₁₆	C₂²×C₁₉	semidirect
702. C₄×Q₁₆	C₂²×C₁₉	semidirect
706. #436	C₂²×C₁₉	semidirect
707. #435	C₂²×C₁₉	semidirect
708. #435	C₂²×C₁₉	semidirect
710. C₈×D₄	C₂²×C₁₉	semidirect
711. #428	C₂²×C₁₉	semidirect
712. C₂×#106	C₂²×C₁₉	semidirect
713. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
714. #417	C₂²×C₁₉	semidirect
715. #417	C₂²×C₁₉	semidirect
716. #416	C₂²×C₁₉	semidirect
718. #408	C₂²×C₁₉	semidirect
719. C₄×M₁₆	C₂²×C₁₉	semidirect
909. C₁₉	#62355	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×#3548	2
C₁₉×#3546	2
C₁₉×#3356	2
C₁₉×#3345	2
C₁₉×#3335	2
C₁₉×#3333	2
C₁₉×#3332	2
C₁₉×#3307	2
C₁₉×#3306	2
C₁₉×#3304	2
C₁₉×#3295	2
C₁₉×#3287	2
C₁₉×#3274	2
C₁₉×#3267	2
C₁₉×#3247	2
C₁₉×#3246	2
C₁₉×#3204	2
C₁₉×#3198	2
C₁₉×#3184	2
C₁₉×#3172	2
C₁₉×#3062	2
C₁₉×#3060	2
C₁₉×#2935	2
#62355	19

Subgroups — C19×#62355 #18068314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62355 #18068314