Subgroups — C₁₉×#62346 #18068305

Order 4864.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3348	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3321	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3310	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3265	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×#3200	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3198	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3062	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3057	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	complemented
25	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
27	C₁₉×#562	—	2	2	no	—
28	C₁₉×H(3,𝔽₄)	—	2	2	no	—
29	C₁₉×#555	—	2	1	no	—
30	C₁₉×#555	—	2	1	no	—
31	C₁₉×#555	C₂²	1	1	yes	characteristic
32	C₁₉×#555	C₂²	1	2	yes	—
33	C₁₉×#555	C₂²	1	1	yes	characteristic
34	C₁₉×#555	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#553	—	2	1	no	—
37	C₁₉×#552	C₂²	1	2	yes	complemented
38	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#548	C₂²	1	2	yes	complemented
40	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
41	D₄²×C₁₉	—	2	1	no	—
42	D₄²×C₁₉	C₂²	1	2	yes	—
43	D₄²×C₁₉	C₂²	1	1	yes	characteristic
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#544	—	2	1	no	—
46	C₁₉×#542	—	2	2	no	—
47	C₁₉×#540	—	2	1	no	—
48	C₁₉×#537	C₂²	1	2	yes	complemented
49	C₁₉×#536	C₂²	1	2	yes	complemented
50	C₁₉×#535	—	2	1	no	—
51	C₁₉×#535	—	2	1	no	—
52	C₁₉×#535	—	2	2	no	—
53	C₁₉×#535	C₂²	1	2	yes	—
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
59	C₁₉×#529	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#496	C₂²	1	1	yes	characteristic
63	C₁₉×#492	C₂²	1	1	yes	characteristic
64	C₁₉×#490	C₂²	1	1	yes	characteristic
65	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#486	C₂²	1	1	yes	characteristic
68	C₁₉×#485	C₂²	1	2	yes	complemented
69	C₁₉×#485	C₂²	1	2	yes	complemented
70	C₁₉×#485	C₂²	1	2	yes	complemented
71	C₁₉×#482	C₂²	1	2	yes	complemented
72	C₁₉×#482	C₂²	1	2	yes	complemented
73	C₁₉×#482	C₂²	1	2	yes	complemented
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, complemented
79	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
81	C₁₉×#475	C₂²	1	2	yes	complemented
82	C₁₉×#469	C₂²	1	1	yes	characteristic, complemented
83	C₁₉×#469	C₂²	1	1	yes	characteristic, complemented
84	C₁₉×#469	C₂²	1	2	yes	complemented
85	C₁₉×#468	C₂²	1	1	yes	characteristic, complemented
86	C₁₉×#468	C₂²	1	1	yes	characteristic, complemented
87	C₁₉×#468	C₂²	1	2	yes	complemented
88	C₁₉×#468	C₂²	1	2	yes	complemented
89	C₁₉×#468	C₂²	1	2	yes	complemented
90	C₁₉×#468	C₂²	1	2	yes	complemented
91	C₁₉×#468	C₂²	1	2	yes	complemented
92	C₁₉×#466	C₂²	1	2	yes	complemented
93	C₁₉×#466	C₂²	1	2	yes	complemented
94	C₁₉×#465	C₂²	1	2	yes	complemented
95	C₁₉×#465	C₂²	1	2	yes	complemented
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	complemented
101	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
102	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
103	C₁₉×#460	C₂²	1	2	yes	—
104	C₁₉×#460	C₂²	1	1	yes	characteristic
105	C₁₉×#459	C₂²	1	1	yes	characteristic
106	C₁₉×#450	C₂²	1	2	yes	complemented
107	C₁₉×#450	C₂²	1	2	yes	complemented
108	C₁₉×#450	C₂²	1	2	yes	complemented
109	C₁₉×#449	C₂²	1	2	yes	complemented
110	C₁₉×#449	C₂²	1	2	yes	complemented
111	C₁₉×#448	C₂²	1	2	yes	complemented
112	C₁₉×#448	C₂²	1	2	yes	complemented
113	C₁₉×#447	C₂²	1	2	yes	complemented
114	C₁₉×#440	C₂²	1	2	yes	complemented
115	C₁₉×#440	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
120	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
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, complemented
125	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
126	C₁₉×#428	C₂²	1	2	yes	complemented
127	C₁₉×#427	C₂²	1	2	yes	complemented
128	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
129	C₁₉×#419	C₂²	1	2	yes	complemented
130	C₁₉×#418	C₂²	1	2	yes	complemented
131	C₁₉×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
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	1	no	—
137	C₂×#41×C₁₉	C₂³	1	2	yes	—
138	C₂×#41×C₁₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₁₉	—	2	1	no	—
141	C₂²×D₄×C₁₉	—	2	1	no	—
142	C₂²×D₄×C₁₉	—	2	2	no	—
143	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
145	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
146	C₂×SD₁₆×C₁₉	—	4	4	no	—
147	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
155	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
166	C₁₉×C₄⋊Q₈	—	2	1	no	—
167	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
168	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₉×#127	—	2	2	no	—
173	C₁₉×#127	—	2	2	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	1	no	—
179	C₁₉×#125	—	2	2	no	—
180	C₁₉×#125	—	2	1	no	—
181	C₁₉×#125	—	2	1	no	—
182	C₁₉×#125	C₂³	1	1	yes	characteristic
183	C₁₉×#124	—	2	2	no	—
184	C₁₉×#124	—	2	2	no	—
185	C₁₉×#124	—	2	2	no	—
186	C₁₉×#124	—	2	2	no	—
187	C₁₉×#124	—	2	2	no	—
188	C₁₉×#124	—	2	2	no	—
189	C₁₉×#124	—	2	2	no	—
190	C₁₉×#124	—	2	2	no	—
191	C₁₉×#124	—	2	2	no	—
192	C₁₉×#124	—	2	1	no	—
193	C₁₉×#124	—	2	1	no	—
194	C₁₉×#124	D₄	1	2	yes	—
195	C₁₉×#124	C₂³	1	1	yes	characteristic
196	C₁₉×#123	—	2	2	no	—
197	C₁₉×#123	—	2	2	no	—
198	C₁₉×#123	—	2	2	no	—
199	C₁₉×#123	—	2	1	no	—
200	C₁₉×#123	—	2	2	no	—
201	C₁₉×C₂²⋊Q₈	—	2	2	no	—
202	C₁₉×C₂²⋊Q₈	—	2	1	no	—
203	C₁₉×C₂²⋊Q₈	—	2	2	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	2	yes	—
211	C₁₉×#121	—	2	1	no	—
212	C₁₉×#121	—	2	1	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	1	no	—
218	C₁₉×#121	—	2	2	no	—
219	C₁₉×#121	—	2	1	no	—
220	C₁₉×#121	—	2	1	no	—
221	C₁₉×#121	—	2	1	no	—
222	C₁₉×#121	—	2	1	no	—
223	C₁₉×#121	—	2	1	no	—
224	C₁₉×#121	—	2	2	no	—
225	C₁₉×#121	D₄	1	1	yes	characteristic
226	C₁₉×#121	D₄	1	1	yes	characteristic
227	C₁₉×#121	D₄	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×#121	C₂³	1	2	yes	—
232	C₁₉×#121	C₂³	1	2	yes	—
233	C₁₉×#121	C₂³	1	1	yes	characteristic
234	C₁₉×#121	C₂³	1	1	yes	characteristic
235	C₁₉×#121	C₂³	1	2	yes	—
236	C₁₉×#121	C₂³	1	1	yes	characteristic
237	C₁₉×#120	—	2	2	no	—
238	C₁₉×#120	—	2	2	no	—
239	C₁₉×#120	—	2	2	no	—
240	C₁₉×#120	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
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	—	2	2	no	—
252	C₄×D₄×C₁₉	—	2	1	no	—
253	C₄×D₄×C₁₉	—	2	1	no	—
254	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×#117	—	2	1	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	—	2	1	no	—
264	C₁₉×#117	—	2	2	no	—
265	C₁₉×#117	—	2	1	no	—
266	C₁₉×#117	—	2	2	no	—
267	C₁₉×#117	—	2	1	no	—
268	C₁₉×#117	C₂³	1	2	yes	—
269	C₁₉×#117	C₂³	1	2	yes	—
270	C₁₉×#117	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	2	yes	—
277	C₁₉×#107	C₂³	1	1	yes	characteristic
278	C₁₉×#107	C₂³	1	2	yes	—
279	C₁₉×#106	C₂³	1	2	yes	—
280	C₁₉×#106	C₂³	1	2	yes	—
281	C₁₉×#106	C₂³	1	1	yes	characteristic
282	C₁₉×#106	C₂³	1	2	yes	—
283	C₁₉×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
288	C₁₉×#103	C₂³	1	2	yes	—
289	C₁₉×#103	C₂³	1	1	yes	characteristic
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	1	yes	characteristic
293	C₁₉×#103	C₂³	1	2	yes	—
294	C₁₉×#102	C₂³	1	1	yes	characteristic
295	C₁₉×#102	C₂³	1	2	yes	—
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	2	yes	—
300	C₁₉×#102	C₂³	1	1	yes	characteristic
301	C₁₉×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₂⁴×C₁₉	—	2	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	—	8	2	no	—
322	#41×C₁₉	—	8	2	no	—
323	C₂×Q₈×C₁₉	—	2	1	no	—
324	C₂×Q₈×C₁₉	—	2	2	no	—
325	C₂×Q₈×C₁₉	—	2	1	no	—
326	C₂×Q₈×C₁₉	—	2	1	no	—
327	C₂×Q₈×C₁₉	—	4	2	no	—
328	C₂×Q₈×C₁₉	—	4	2	no	—
329	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
330	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
332	C₂×D₄×C₁₉	—	2	1	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	2	no	—
338	C₂×D₄×C₁₉	—	2	1	no	—
339	C₂×D₄×C₁₉	—	2	1	no	—
340	C₂×D₄×C₁₉	—	2	2	no	—
341	C₂×D₄×C₁₉	—	2	2	no	—
342	C₂×D₄×C₁₉	—	2	1	no	—
343	C₂×D₄×C₁₉	—	2	1	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	—	4	2	no	—
349	C₂×D₄×C₁₉	—	4	2	no	—
350	C₂×D₄×C₁₉	—	4	2	no	—
351	C₂×D₄×C₁₉	—	4	2	no	—
352	C₂×D₄×C₁₉	—	8	2	no	—
353	C₂×D₄×C₁₉	—	8	2	no	—
354	C₂×D₄×C₁₉	—	8	4	no	—
355	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
361	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
364	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
370	C₂²×C₄×C₁₉	—	2	1	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	SD₁₆×C₁₉	—	2	2	no	—
378	SD₁₆×C₁₉	—	2	4	no	—
379	SD₁₆×C₁₉	—	4	2	no	—
380	SD₁₆×C₁₉	—	4	2	no	—
381	SD₁₆×C₁₉	—	4	1	no	—
382	SD₁₆×C₁₉	—	4	2	no	—
383	SD₁₆×C₁₉	—	4	2	no	—
384	D₈×C₁₉	—	2	2	no	—
385	D₈×C₁₉	—	4	1	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	1	no	—
404	C₄⋊C₄×C₁₉	—	2	1	no	—
405	C₄⋊C₄×C₁₉	—	2	1	no	—
406	C₄⋊C₄×C₁₉	—	2	1	no	—
407	C₄⋊C₄×C₁₉	—	2	2	no	—
408	C₄⋊C₄×C₁₉	—	2	1	no	—
409	C₄⋊C₄×C₁₉	—	2	1	no	—
410	C₄⋊C₄×C₁₉	—	2	2	no	—
411	C₄⋊C₄×C₁₉	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₁₉	—	2	2	no	—
425	C₂²⋊C₄×C₁₉	—	2	2	no	—
426	C₂²⋊C₄×C₁₉	—	2	2	no	—
427	C₂²⋊C₄×C₁₉	—	2	2	no	—
428	C₂²⋊C₄×C₁₉	—	2	2	no	—
429	C₂²⋊C₄×C₁₉	—	2	2	no	—
430	C₂²⋊C₄×C₁₉	—	2	2	no	—
431	C₂²⋊C₄×C₁₉	—	2	1	no	—
432	C₂²⋊C₄×C₁₉	—	2	2	no	—
433	C₂²⋊C₄×C₁₉	—	2	2	no	—
434	C₂²⋊C₄×C₁₉	—	2	2	no	—
435	C₂²⋊C₄×C₁₉	—	2	2	no	—
436	C₂²⋊C₄×C₁₉	—	2	1	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	1	no	—
441	C₂²⋊C₄×C₁₉	—	2	1	no	—
442	C₂²⋊C₄×C₁₉	—	2	2	no	—
443	C₂²⋊C₄×C₁₉	—	2	2	no	—
444	C₂²⋊C₄×C₁₉	—	2	1	no	—
445	C₂²⋊C₄×C₁₉	—	2	1	no	—
446	C₂²⋊C₄×C₁₉	—	2	1	no	—
447	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
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	C₄²×C₁₉	—	2	2	no	—
452	C₄²×C₁₉	—	2	2	no	—
453	C₄²×C₁₉	—	2	2	no	—
454	C₄²×C₁₉	—	2	2	no	—
455	C₄²×C₁₉	—	2	1	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	#62346	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	1	no	—
464	C₂³×C₁₉	—	2	1	no	—
465	C₂³×C₁₉	—	8	2	no	—
466	C₂³×C₁₉	—	8	2	no	—
467	C₂³×C₁₉	—	8	2	no	—
468	C₂³×C₁₉	—	8	2	no	—
469	C₂³×C₁₉	—	8	2	no	—
470	C₂³×C₁₉	—	8	2	no	—
471	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
472	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
473	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₁₉	—	2	1	no	—
475	Q₈×C₁₉	—	2	2	no	—
476	Q₈×C₁₉	—	2	1	no	—
477	Q₈×C₁₉	—	2	2	no	—
478	Q₈×C₁₉	—	4	2	no	—
479	Q₈×C₁₉	—	8	1	no	—
480	Q₈×C₁₉	—	8	2	no	—
481	Q₈×C₁₉	—	8	1	no	—
482	Q₈×C₁₉	—	8	1	no	—
483	D₄×C₁₉	—	2	2	no	—
484	D₄×C₁₉	—	2	2	no	—
485	D₄×C₁₉	—	2	1	no	—
486	D₄×C₁₉	—	2	1	no	—
487	D₄×C₁₉	—	2	2	no	—
488	D₄×C₁₉	—	2	1	no	—
489	D₄×C₁₉	—	2	1	no	—
490	D₄×C₁₉	—	2	1	no	—
491	D₄×C₁₉	—	2	1	no	—
492	D₄×C₁₉	—	2	2	no	—
493	D₄×C₁₉	—	4	2	no	—
494	D₄×C₁₉	—	4	2	no	—
495	D₄×C₁₉	—	4	2	no	—
496	D₄×C₁₉	—	4	2	no	—
497	D₄×C₁₉	—	4	2	no	—
498	D₄×C₁₉	—	4	2	no	—
499	D₄×C₁₉	—	8	2	no	—
500	D₄×C₁₉	—	8	2	no	—
501	D₄×C₁₉	—	8	1	no	—
502	D₄×C₁₉	—	8	1	no	—
503	D₄×C₁₉	—	8	1	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	D₄×C₁₉	—	8	2	no	—
509	D₄×C₁₉	—	8	2	no	—
510	D₄×C₁₉	—	8	2	no	—
511	D₄×C₁₉	—	8	1	no	—
512	D₄×C₁₉	—	8	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	2	no	—
517	C₂×C₄×C₁₉	—	2	1	no	—
518	C₂×C₄×C₁₉	—	2	2	no	—
519	C₂×C₄×C₁₉	—	2	2	no	—
520	C₂×C₄×C₁₉	—	2	1	no	—
521	C₂×C₄×C₁₉	—	2	2	no	—
522	C₂×C₄×C₁₉	—	2	1	no	—
523	C₂×C₄×C₁₉	—	2	1	no	—
524	C₂×C₄×C₁₉	—	2	2	no	—
525	C₂×C₄×C₁₉	—	2	1	no	—
526	C₂×C₄×C₁₉	—	2	1	no	—
527	C₂×C₄×C₁₉	—	2	2	no	—
528	C₂×C₄×C₁₉	—	4	1	no	—
529	C₂×C₄×C₁₉	—	4	4	no	—
530	C₂×C₄×C₁₉	—	4	2	no	—
531	C₂×C₄×C₁₉	—	4	2	no	—
532	C₂×C₄×C₁₉	—	4	2	no	—
533	C₂×C₄×C₁₉	—	8	2	no	—
534	C₂×C₄×C₁₉	—	8	2	no	—
535	C₂×C₄×C₁₉	—	8	2	no	—
536	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
544	C₈×C₁₉	—	2	2	no	—
545	C₈×C₁₉	—	2	1	no	—
546	C₈×C₁₉	—	2	2	no	—
547	C₈×C₁₉	—	2	1	no	—
548	C₈×C₁₉	—	2	1	no	—
549	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
550	#3549	C₂×C₁₉	1	1	yes	characteristic, complemented
551	#3547	C₂×C₁₉	1	1	yes	characteristic, complemented
552	#3357	C₂×C₁₉	1	1	yes	characteristic, complemented
553	#3348	C₂×C₁₉	1	2	yes	complemented
554	#3341	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3329	C₂×C₁₉	1	1	yes	characteristic, complemented
556	#3325	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#3321	C₂×C₁₉	1	2	yes	complemented
558	#3310	C₂×C₁₉	1	2	yes	complemented
559	#3303	C₂×C₁₉	1	1	yes	characteristic, complemented
560	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
561	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
562	#3272	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#3265	C₂×C₁₉	1	2	yes	complemented
564	#3247	C₂×C₁₉	1	1	yes	characteristic, complemented
565	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
566	#3200	C₂×C₁₉	1	2	yes	complemented
567	#3198	C₂×C₁₉	1	2	yes	complemented
568	#3182	C₂×C₁₉	1	1	yes	characteristic, complemented
569	#3171	C₂×C₁₉	1	1	yes	characteristic, complemented
570	#3062	C₂×C₁₉	1	2	yes	complemented
571	#3057	C₂×C₁₉	1	2	yes	complemented
572	#2935	C₂×C₁₉	1	1	yes	characteristic, complemented
573	C₂²×C₁₉	—	2	1	no	—
574	C₂²×C₁₉	—	2	2	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	1	no	—
580	C₂²×C₁₉	—	2	2	no	—
581	C₂²×C₁₉	—	2	2	no	—
582	C₂²×C₁₉	—	4	2	no	—
583	C₂²×C₁₉	—	4	1	no	—
584	C₂²×C₁₉	—	4	1	no	—
585	C₂²×C₁₉	—	4	1	no	—
586	C₂²×C₁₉	—	4	1	no	—
587	C₂²×C₁₉	—	4	1	no	—
588	C₂²×C₁₉	—	4	2	no	—
589	C₂²×C₁₉	—	4	1	no	—
590	C₂²×C₁₉	—	4	1	no	—
591	C₂²×C₁₉	—	4	1	no	—
592	C₂²×C₁₉	—	4	1	no	—
593	C₂²×C₁₉	—	4	2	no	—
594	C₂²×C₁₉	—	16	4	no	—
595	C₂²×C₁₉	—	16	4	no	—
596	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₁₉	—	2	1	no	—
598	C₄×C₁₉	—	2	1	no	—
599	C₄×C₁₉	—	2	2	no	—
600	C₄×C₁₉	—	2	1	no	—
601	C₄×C₁₉	—	2	2	no	—
602	C₄×C₁₉	—	2	1	no	—
603	C₄×C₁₉	—	4	2	no	—
604	C₄×C₁₉	—	4	1	no	—
605	C₄×C₁₉	—	4	2	no	—
606	C₄×C₁₉	—	4	2	no	—
607	C₄×C₁₉	—	4	1	no	—
608	C₄×C₁₉	—	4	1	no	—
609	C₄×C₁₉	—	4	1	no	—
610	C₄×C₁₉	—	4	1	no	—
611	C₄×C₁₉	#577	1	2	yes	—
612	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
613	C₄×C₁₉	#585	1	1	yes	characteristic
614	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
615	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
616	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
617	#562	—	2	2	no	—
618	H(3,𝔽₄)	—	2	2	no	—
619	#555	—	2	1	no	—
620	#555	—	2	1	no	—
621	#555	C₂²×C₁₉	1	1	yes	characteristic
622	#555	C₂²×C₁₉	1	2	yes	—
623	#555	C₂²×C₁₉	1	1	yes	characteristic
624	#555	C₂²×C₁₉	1	1	yes	characteristic, complemented
625	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
626	#553	—	2	1	no	—
627	#552	C₂²×C₁₉	1	2	yes	complemented
628	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
629	#548	C₂²×C₁₉	1	2	yes	complemented
630	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
631	D₄²	—	2	1	no	—
632	D₄²	C₂²×C₁₉	1	2	yes	—
633	D₄²	C₂²×C₁₉	1	1	yes	characteristic
634	D₄²	C₂²×C₁₉	1	1	yes	characteristic
635	#544	—	2	1	no	—
636	#542	—	2	2	no	—
637	#540	—	2	1	no	—
638	#537	C₂²×C₁₉	1	2	yes	complemented
639	#536	C₂²×C₁₉	1	2	yes	complemented
640	#535	—	2	1	no	—
641	#535	—	2	1	no	—
642	#535	—	2	2	no	—
643	#535	C₂²×C₁₉	1	2	yes	—
644	#535	C₂²×C₁₉	1	2	yes	—
645	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
646	#532	C₂²×C₁₉	1	1	yes	characteristic
647	#532	C₂²×C₁₉	1	1	yes	characteristic
648	#532	C₂²×C₁₉	1	1	yes	characteristic
649	#529	C₂²×C₁₉	1	1	yes	characteristic, complemented
650	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
651	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
652	#496	C₂²×C₁₉	1	1	yes	characteristic
653	#492	C₂²×C₁₉	1	1	yes	characteristic
654	#490	C₂²×C₁₉	1	1	yes	characteristic
655	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
656	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#486	C₂²×C₁₉	1	1	yes	characteristic
658	#485	C₂²×C₁₉	1	2	yes	complemented
659	#485	C₂²×C₁₉	1	2	yes	complemented
660	#485	C₂²×C₁₉	1	2	yes	complemented
661	#482	C₂²×C₁₉	1	2	yes	complemented
662	#482	C₂²×C₁₉	1	2	yes	complemented
663	#482	C₂²×C₁₉	1	2	yes	complemented
664	#481	C₂²×C₁₉	1	2	yes	complemented
665	#480	C₂²×C₁₉	1	2	yes	complemented
666	#478	C₂²×C₁₉	1	2	yes	complemented
667	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
669	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
671	#475	C₂²×C₁₉	1	2	yes	complemented
672	#469	C₂²×C₁₉	1	1	yes	characteristic, complemented
673	#469	C₂²×C₁₉	1	1	yes	characteristic, complemented
674	#469	C₂²×C₁₉	1	2	yes	complemented
675	#468	C₂²×C₁₉	1	2	yes	complemented
676	#468	C₂²×C₁₉	1	2	yes	complemented
677	#468	C₂²×C₁₉	1	2	yes	complemented
678	#468	C₂²×C₁₉	1	1	yes	characteristic, complemented
679	#468	C₂²×C₁₉	1	1	yes	characteristic, complemented
680	#468	C₂²×C₁₉	1	2	yes	complemented
681	#468	C₂²×C₁₉	1	2	yes	complemented
682	#466	C₂²×C₁₉	1	2	yes	complemented
683	#466	C₂²×C₁₉	1	2	yes	complemented
684	#465	C₂²×C₁₉	1	2	yes	complemented
685	#465	C₂²×C₁₉	1	2	yes	complemented
686	#465	C₂²×C₁₉	1	2	yes	complemented
687	#465	C₂²×C₁₉	1	2	yes	complemented
688	#465	C₂²×C₁₉	1	2	yes	complemented
689	#465	C₂²×C₁₉	1	2	yes	complemented
690	#463	C₂²×C₁₉	1	2	yes	complemented
691	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
692	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
693	#460	C₂²×C₁₉	1	2	yes	—
694	#460	C₂²×C₁₉	1	1	yes	characteristic
695	#459	C₂²×C₁₉	1	1	yes	characteristic
696	#450	C₂²×C₁₉	1	2	yes	complemented
697	#450	C₂²×C₁₉	1	2	yes	complemented
698	#450	C₂²×C₁₉	1	2	yes	complemented
699	#449	C₂²×C₁₉	1	2	yes	complemented
700	#449	C₂²×C₁₉	1	2	yes	complemented
701	#448	C₂²×C₁₉	1	2	yes	complemented
702	#448	C₂²×C₁₉	1	2	yes	complemented
703	#447	C₂²×C₁₉	1	2	yes	complemented
704	#440	C₂²×C₁₉	1	2	yes	complemented
705	#440	C₂²×C₁₉	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
708	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
709	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
710	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
711	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
712	#435	C₂²×C₁₉	1	2	yes	complemented
713	#435	C₂²×C₁₉	1	2	yes	complemented
714	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
715	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
716	#428	C₂²×C₁₉	1	2	yes	complemented
717	#427	C₂²×C₁₉	1	2	yes	complemented
718	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
719	#419	C₂²×C₁₉	1	2	yes	complemented
720	#418	C₂²×C₁₉	1	2	yes	complemented
721	#416	C₂²×C₁₉	1	2	yes	complemented
722	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
723	#408	C₂²×C₁₉	1	2	yes	complemented
724	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
725	C₂×C₁₉	—	4	1	no	—
726	C₂×C₁₉	—	4	2	no	—
727	C₂×C₁₉	—	4	2	no	—
728	C₂×C₁₉	—	8	1	no	—
729	C₂×C₁₉	—	8	2	no	—
730	C₂×C₁₉	—	8	1	no	—
731	C₂×C₁₉	—	8	1	no	—
732	C₂×C₁₉	#3496	1	1	yes	characteristic
733	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
734	C₂×C₁₉	#3585	1	1	yes	characteristic
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	C₂³×C₁₉	1	2	yes	—
738	C₂×#41	C₂³×C₁₉	1	2	yes	—
739	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
740	C₂²×D₄	—	2	1	no	—
741	C₂²×D₄	—	2	1	no	—
742	C₂²×D₄	—	2	2	no	—
743	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
744	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
745	AGL(1,ℤ/8)	—	4	4	no	—
746	C₂×SD₁₆	—	4	4	no	—
747	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
748	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
753	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
754	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
755	C₂×D₈	C₂³×C₁₉	1	2	yes	—
756	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
757	#131	—	4	4	no	—
758	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
759	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
760	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
761	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
762	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
763	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
764	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
765	C₄⋊Q₈	—	2	2	no	—
766	C₄⋊Q₈	—	2	1	no	—
767	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
768	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
772	#127	—	2	2	no	—
773	#127	—	2	2	no	—
774	#127	D₄×C₁₉	1	1	yes	characteristic
775	#127	C₂³×C₁₉	1	1	yes	characteristic
776	#127	C₂³×C₁₉	1	1	yes	characteristic
777	#126	—	2	2	no	—
778	#126	—	2	1	no	—
779	#125	—	2	2	no	—
780	#125	—	2	1	no	—
781	#125	—	2	1	no	—
782	#125	C₂³×C₁₉	1	1	yes	characteristic
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	—	2	2	no	—
786	#124	—	2	2	no	—
787	#124	—	2	2	no	—
788	#124	—	2	2	no	—
789	#124	—	2	2	no	—
790	#124	—	2	2	no	—
791	#124	—	2	2	no	—
792	#124	—	2	1	no	—
793	#124	—	2	1	no	—
794	#124	D₄×C₁₉	1	2	yes	—
795	#124	C₂³×C₁₉	1	1	yes	characteristic
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	1	no	—
800	#123	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	1	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
808	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
809	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
810	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
811	#121	—	2	1	no	—
812	#121	—	2	1	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	2	no	—
819	#121	—	2	1	no	—
820	#121	—	2	1	no	—
821	#121	—	2	1	no	—
822	#121	—	2	1	no	—
823	#121	—	2	1	no	—
824	#121	—	2	2	no	—
825	#121	D₄×C₁₉	1	1	yes	characteristic
826	#121	D₄×C₁₉	1	1	yes	characteristic
827	#121	D₄×C₁₉	1	2	yes	—
828	#121	C₂³×C₁₉	1	1	yes	characteristic
829	#121	C₂³×C₁₉	1	1	yes	characteristic
830	#121	C₂³×C₁₉	1	1	yes	characteristic
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	#121	C₂³×C₁₉	1	2	yes	—
836	#121	C₂³×C₁₉	1	2	yes	—
837	#120	—	2	2	no	—
838	#120	—	2	2	no	—
839	#120	—	2	2	no	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	C₄×Q₈	—	2	1	no	—
846	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
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	C₄×D₄	C₂³×C₁₉	1	2	yes	—
860	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
861	#117	—	2	1	no	—
862	#117	—	2	1	no	—
863	#117	—	2	1	no	—
864	#117	—	2	2	no	—
865	#117	—	2	1	no	—
866	#117	—	2	2	no	—
867	#117	—	2	1	no	—
868	#117	C₂³×C₁₉	1	2	yes	—
869	#117	C₂³×C₁₉	1	2	yes	—
870	#117	C₂³×C₁₉	1	2	yes	—
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
873	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
874	#107	C₂³×C₁₉	1	1	yes	characteristic
875	#107	C₂³×C₁₉	1	2	yes	—
876	#107	C₂³×C₁₉	1	2	yes	—
877	#107	C₂³×C₁₉	1	1	yes	characteristic
878	#107	C₂³×C₁₉	1	2	yes	—
879	#106	C₂³×C₁₉	1	2	yes	—
880	#106	C₂³×C₁₉	1	2	yes	—
881	#106	C₂³×C₁₉	1	1	yes	characteristic
882	#106	C₂³×C₁₉	1	2	yes	—
883	#106	C₂³×C₁₉	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
886	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
887	#103	C₂³×C₁₉	1	2	yes	—
888	#103	C₂³×C₁₉	1	2	yes	—
889	#103	C₂³×C₁₉	1	1	yes	characteristic
890	#103	C₂³×C₁₉	1	2	yes	—
891	#103	C₂³×C₁₉	1	2	yes	—
892	#103	C₂³×C₁₉	1	1	yes	characteristic
893	#103	C₂³×C₁₉	1	2	yes	—
894	#102	C₂³×C₁₉	1	1	yes	characteristic
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	1	yes	characteristic
901	#102	C₂³×C₁₉	1	2	yes	—
902	#102	C₂³×C₁₉	1	2	yes	—
903	#102	C₂³×C₁₉	1	1	yes	characteristic
904	#102	C₂³×C₁₉	1	1	yes	characteristic
905	#102	C₂³×C₁₉	1	1	yes	characteristic
906	#102	C₂³×C₁₉	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
910	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
911	#97	C₂³×C₁₉	1	1	yes	characteristic
912	#97	C₂³×C₁₉	1	1	yes	characteristic
913	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
915	C₁₉	#62346	1	1	yes	characteristic, direct product factor, Sylow
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	2	no	—
918	#41	—	4	2	no	—
919	#41	—	4	2	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	8	2	no	—
923	#41	—	8	2	no	—
924	C₂×Q₈	—	2	1	no	—
925	C₂×Q₈	—	2	2	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	4	2	no	—
929	C₂×Q₈	—	4	2	no	—
930	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
931	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
932	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
933	C₂×D₄	—	2	1	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	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	4	2	no	—
950	C₂×D₄	—	4	2	no	—
951	C₂×D₄	—	4	2	no	—
952	C₂×D₄	—	4	2	no	—
953	C₂×D₄	—	8	2	no	—
954	C₂×D₄	—	8	2	no	—
955	C₂×D₄	—	8	4	no	—
956	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
957	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
958	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
959	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
960	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
961	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
962	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
963	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
964	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
965	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
975	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
976	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
977	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
978	SD₁₆	—	2	2	no	—
979	SD₁₆	—	2	4	no	—
980	SD₁₆	—	4	2	no	—
981	SD₁₆	—	4	2	no	—
982	SD₁₆	—	4	1	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	D₈	—	2	2	no	—
986	D₈	—	4	1	no	—
987	D₈	—	4	2	no	—
988	M₁₆	—	2	2	no	—
989	M₁₆	—	2	4	no	—
990	M₁₆	—	4	1	no	—
991	M₁₆	—	4	2	no	—
992	C₂×C₈	—	2	4	no	—
993	C₂×C₈	—	4	2	no	—
994	C₂×C₈	—	4	2	no	—
995	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
999	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1000	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	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	2	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1017	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1018	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1023	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1024	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1049	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1050	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1052	C₄²	—	2	2	no	—
1053	C₄²	—	2	2	no	—
1054	C₄²	—	2	2	no	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1058	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1059	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	8	2	no	—
1066	C₂³	—	8	2	no	—
1067	C₂³	—	8	2	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1072	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1073	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1074	Q₈	—	2	1	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	2	no	—
1078	Q₈	—	4	2	no	—
1079	Q₈	—	8	2	no	—
1080	Q₈	—	8	1	no	—
1081	Q₈	—	8	1	no	—
1082	Q₈	—	8	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	—	8	2	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	1	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	1	no	—
1112	D₄	—	8	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1138	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1143	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1144	C₈	—	2	2	no	—
1145	C₈	—	2	1	no	—
1146	C₈	—	2	2	no	—
1147	C₈	—	2	1	no	—
1148	C₈	—	2	1	no	—
1149	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	1	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	—	16	4	no	—
1173	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1174	C₄	—	2	2	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	C₁₉×#577	1	2	yes	—
1189	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₄	C₁₉×#585	1	1	yes	characteristic
1191	C₂	—	4	2	no	—
1192	C₂	—	4	2	no	—
1193	C₂	—	4	1	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	1	no	—
1198	C₂	C₁₉×#3496	1	1	yes	characteristic
1199	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1200	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×#3549	C₂	semidirect
2. C₁₉×#3547	C₂	semidirect
3. C₁₉×#3357	C₂	semidirect
4. C₁₉×#3348	C₂	semidirect
5. C₁₉×#3341	C₂	semidirect
6. C₁₉×#3329	C₂	semidirect
7. C₁₉×#3325	C₂	semidirect
8. C₁₉×#3321	C₂	semidirect
9. C₁₉×#3310	C₂	semidirect
10. C₁₉×#3303	C₂	semidirect
11. C₁₉×#3295	C₂	semidirect
12. D₄×SD₁₆×C₁₉	C₂	semidirect
13. C₁₉×#3272	C₂	semidirect
14. C₁₉×#3265	C₂	semidirect
15. C₁₉×#3247	C₂	semidirect
16. C₁₉×#3246	C₂	semidirect
17. C₁₉×#3200	C₂	semidirect
18. C₁₉×#3198	C₂	semidirect
19. C₁₉×#3182	C₂	semidirect
20. C₁₉×#3171	C₂	semidirect
21. C₁₉×#3062	C₂	semidirect
22. C₁₉×#3057	C₂	semidirect
23. C₁₉×#2935	C₂	semidirect
24. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂²×SD₁₆×C₁₉	C₂²	semidirect
26. C₂×C₁₉×#131	C₂²	semidirect
34. C₁₉×#555	C₂²	semidirect
35. C₁₉×#554	C₂²	semidirect
37. C₁₉×#552	C₂²	semidirect
38. D₄×Q₈×C₁₉	C₂²	semidirect
39. C₁₉×#548	C₂²	semidirect
40. C₁₉×#547	C₂²	semidirect
48. C₁₉×#537	C₂²	semidirect
49. C₁₉×#536	C₂²	semidirect
55. C₁₉×#533	C₂²	semidirect
59. C₁₉×#529	C₂²	semidirect
60. C₁₉×#501	C₂²	semidirect
61. C₁₉×#500	C₂²	semidirect
65. C₁₉×#489	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
69. C₁₉×#485	C₂²	semidirect
70. C₁₉×#485	C₂²	semidirect
71. C₁₉×#482	C₂²	semidirect
72. C₁₉×#482	C₂²	semidirect
73. C₁₉×#482	C₂²	semidirect
74. C₁₉×#481	C₂²	semidirect
75. C₁₉×#480	C₂²	semidirect
76. C₁₉×#478	C₂²	semidirect
77. C₁₉×#477	C₂²	semidirect
78. C₁₉×#476	C₂²	semidirect
79. C₁₉×#476	C₂²	semidirect
80. C₁₉×#476	C₂²	semidirect
81. C₁₉×#475	C₂²	semidirect
82. C₁₉×#469	C₂²	semidirect
83. C₁₉×#469	C₂²	semidirect
84. C₁₉×#469	C₂²	semidirect
85. C₁₉×#468	C₂²	semidirect
86. C₁₉×#468	C₂²	semidirect
87. C₁₉×#468	C₂²	semidirect
88. C₁₉×#468	C₂²	semidirect
89. C₁₉×#468	C₂²	semidirect
90. C₁₉×#468	C₂²	semidirect
91. C₁₉×#468	C₂²	semidirect
92. C₁₉×#466	C₂²	semidirect
93. C₁₉×#466	C₂²	semidirect
94. C₁₉×#465	C₂²	semidirect
95. C₁₉×#465	C₂²	semidirect
96. C₁₉×#465	C₂²	semidirect
97. C₁₉×#465	C₂²	semidirect
98. C₁₉×#465	C₂²	semidirect
99. C₁₉×#465	C₂²	semidirect
100. C₁₉×#463	C₂²	semidirect
101. C₁₉×#461	C₂²	semidirect
102. C₁₉×#461	C₂²	semidirect
106. C₁₉×#450	C₂²	semidirect
107. C₁₉×#450	C₂²	semidirect
108. C₁₉×#450	C₂²	semidirect
109. C₁₉×#449	C₂²	semidirect
110. C₁₉×#449	C₂²	semidirect
111. C₁₉×#448	C₂²	semidirect
112. C₁₉×#448	C₂²	semidirect
113. C₁₉×#447	C₂²	semidirect
114. C₁₉×#440	C₂²	semidirect
115. C₁₉×#440	C₂²	semidirect
116. C₄×SD₁₆×C₁₉	C₂²	semidirect
117. C₄×SD₁₆×C₁₉	C₂²	semidirect
118. C₄×D₈×C₁₉	C₂²	semidirect
119. C₄×D₈×C₁₉	C₂²	semidirect
120. C₁₉×#436	C₂²	semidirect
121. C₁₉×#436	C₂²	semidirect
122. C₁₉×#435	C₂²	semidirect
123. C₁₉×#435	C₂²	semidirect
124. C₈×D₄×C₁₉	C₂²	semidirect
125. C₈×D₄×C₁₉	C₂²	semidirect
126. C₁₉×#428	C₂²	semidirect
127. C₁₉×#427	C₂²	semidirect
128. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
129. C₁₉×#419	C₂²	semidirect
130. C₁₉×#418	C₂²	semidirect
131. C₁₉×#416	C₂²	semidirect
132. C₂×C₁₉×#102	C₂²	semidirect
133. C₁₉×#408	C₂²	semidirect
134. C₄×M₁₆×C₁₉	C₂²	semidirect
460. #62346	C₁₉	direct (N × H)
550. #3549	C₂×C₁₉	semidirect
551. #3547	C₂×C₁₉	semidirect
552. #3357	C₂×C₁₉	semidirect
553. #3348	C₂×C₁₉	semidirect
554. #3341	C₂×C₁₉	semidirect
555. #3329	C₂×C₁₉	semidirect
556. #3325	C₂×C₁₉	semidirect
557. #3321	C₂×C₁₉	semidirect
558. #3310	C₂×C₁₉	semidirect
559. #3303	C₂×C₁₉	semidirect
560. #3295	C₂×C₁₉	semidirect
561. D₄×SD₁₆	C₂×C₁₉	semidirect
562. #3272	C₂×C₁₉	semidirect
563. #3265	C₂×C₁₉	semidirect
564. #3247	C₂×C₁₉	semidirect
565. #3246	C₂×C₁₉	semidirect
566. #3200	C₂×C₁₉	semidirect
567. #3198	C₂×C₁₉	semidirect
568. #3182	C₂×C₁₉	semidirect
569. #3171	C₂×C₁₉	semidirect
570. #3062	C₂×C₁₉	semidirect
571. #3057	C₂×C₁₉	semidirect
572. #2935	C₂×C₁₉	semidirect
614. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
615. C₂²×SD₁₆	C₂²×C₁₉	semidirect
616. C₂×#131	C₂²×C₁₉	semidirect
624. #555	C₂²×C₁₉	semidirect
625. #554	C₂²×C₁₉	semidirect
627. #552	C₂²×C₁₉	semidirect
628. D₄×Q₈	C₂²×C₁₉	semidirect
629. #548	C₂²×C₁₉	semidirect
630. #547	C₂²×C₁₉	semidirect
638. #537	C₂²×C₁₉	semidirect
639. #536	C₂²×C₁₉	semidirect
645. #533	C₂²×C₁₉	semidirect
649. #529	C₂²×C₁₉	semidirect
650. #501	C₂²×C₁₉	semidirect
651. #500	C₂²×C₁₉	semidirect
655. #489	C₂²×C₁₉	semidirect
656. #487	C₂²×C₁₉	semidirect
658. #485	C₂²×C₁₉	semidirect
659. #485	C₂²×C₁₉	semidirect
660. #485	C₂²×C₁₉	semidirect
661. #482	C₂²×C₁₉	semidirect
662. #482	C₂²×C₁₉	semidirect
663. #482	C₂²×C₁₉	semidirect
664. #481	C₂²×C₁₉	semidirect
665. #480	C₂²×C₁₉	semidirect
666. #478	C₂²×C₁₉	semidirect
667. #477	C₂²×C₁₉	semidirect
668. #476	C₂²×C₁₉	semidirect
669. #476	C₂²×C₁₉	semidirect
670. #476	C₂²×C₁₉	semidirect
671. #475	C₂²×C₁₉	semidirect
672. #469	C₂²×C₁₉	semidirect
673. #469	C₂²×C₁₉	semidirect
674. #469	C₂²×C₁₉	semidirect
675. #468	C₂²×C₁₉	semidirect
676. #468	C₂²×C₁₉	semidirect
677. #468	C₂²×C₁₉	semidirect
678. #468	C₂²×C₁₉	semidirect
679. #468	C₂²×C₁₉	semidirect
680. #468	C₂²×C₁₉	semidirect
681. #468	C₂²×C₁₉	semidirect
682. #466	C₂²×C₁₉	semidirect
683. #466	C₂²×C₁₉	semidirect
684. #465	C₂²×C₁₉	semidirect
685. #465	C₂²×C₁₉	semidirect
686. #465	C₂²×C₁₉	semidirect
687. #465	C₂²×C₁₉	semidirect
688. #465	C₂²×C₁₉	semidirect
689. #465	C₂²×C₁₉	semidirect
690. #463	C₂²×C₁₉	semidirect
691. #461	C₂²×C₁₉	semidirect
692. #461	C₂²×C₁₉	semidirect
696. #450	C₂²×C₁₉	semidirect
697. #450	C₂²×C₁₉	semidirect
698. #450	C₂²×C₁₉	semidirect
699. #449	C₂²×C₁₉	semidirect
700. #449	C₂²×C₁₉	semidirect
701. #448	C₂²×C₁₉	semidirect
702. #448	C₂²×C₁₉	semidirect
703. #447	C₂²×C₁₉	semidirect
704. #440	C₂²×C₁₉	semidirect
705. #440	C₂²×C₁₉	semidirect
706. C₄×SD₁₆	C₂²×C₁₉	semidirect
707. C₄×SD₁₆	C₂²×C₁₉	semidirect
708. C₄×D₈	C₂²×C₁₉	semidirect
709. C₄×D₈	C₂²×C₁₉	semidirect
710. #436	C₂²×C₁₉	semidirect
711. #436	C₂²×C₁₉	semidirect
712. #435	C₂²×C₁₉	semidirect
713. #435	C₂²×C₁₉	semidirect
714. C₈×D₄	C₂²×C₁₉	semidirect
715. C₈×D₄	C₂²×C₁₉	semidirect
716. #428	C₂²×C₁₉	semidirect
717. #427	C₂²×C₁₉	semidirect
718. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
719. #419	C₂²×C₁₉	semidirect
720. #418	C₂²×C₁₉	semidirect
721. #416	C₂²×C₁₉	semidirect
722. C₂×#102	C₂²×C₁₉	semidirect
723. #408	C₂²×C₁₉	semidirect
724. C₄×M₁₆	C₂²×C₁₉	semidirect
915. C₁₉	#62346	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×#3549	2
C₁₉×#3547	2
C₁₉×#3357	2
C₁₉×#3348	2
C₁₉×#3341	2
C₁₉×#3329	2
C₁₉×#3325	2
C₁₉×#3321	2
C₁₉×#3310	2
C₁₉×#3303	2
C₁₉×#3295	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3272	2
C₁₉×#3265	2
C₁₉×#3247	2
C₁₉×#3246	2
C₁₉×#3200	2
C₁₉×#3198	2
C₁₉×#3182	2
C₁₉×#3171	2
C₁₉×#3062	2
C₁₉×#3057	2
C₁₉×#2935	2
#62346	19

Subgroups — C19×#62346 #18068305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62346 #18068305