Subgroups — C₁₉×#62052 #18068011

Order 4864.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3320	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3301	C₂	1	2	yes	maximal, complemented
11	D₄×SD₁₆×C₁₉	C₂	1	2	yes	maximal, 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×#3260	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3221	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3123	C₂	1	2	yes	maximal, complemented
20	C₁₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3042	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₉×#461	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	—
25	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#563	—	2	2	no	—
28	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#555	C₂²	1	1	yes	characteristic
31	C₁₉×#554	—	2	1	no	—
32	C₁₉×#554	C₂²	1	1	yes	characteristic
33	C₁₉×#553	—	2	1	no	—
34	C₁₉×#553	—	2	1	no	—
35	C₁₉×#553	C₂²	1	2	yes	—
36	C₁₉×#550	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₁₉	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	C₁₉×#546	—	2	1	no	—
42	C₁₉×#546	—	2	2	no	—
43	D₄²×C₁₉	C₂²	1	2	yes	—
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#544	—	2	1	no	—
46	C₁₉×#542	—	2	1	no	—
47	C₁₉×#541	C₂²	1	2	yes	complemented
48	C₁₉×#540	C₂²	1	2	yes	—
49	C₁₉×#539	—	2	2	no	—
50	C₁₉×#538	—	2	2	no	—
51	C₁₉×#536	C₂²	1	2	yes	complemented
52	C₁₉×#532	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×C₄⋊Q₈	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	—
59	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₁₉×#496	C₂²	1	2	yes	complemented
61	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#492	C₂²	1	2	yes	complemented
64	C₁₉×#491	C₂²	1	2	yes	complemented
65	C₁₉×#488	C₂²	1	2	yes	complemented
66	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#485	C₂²	1	2	yes	complemented
69	C₁₉×#485	C₂²	1	2	yes	complemented
70	C₁₉×#484	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#481	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#479	C₂²	1	2	yes	complemented
73	C₁₉×#479	C₂²	1	2	yes	complemented
74	C₁₉×#478	C₂²	1	1	yes	characteristic
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×#468	C₂²	1	2	yes	complemented
80	C₁₉×#468	C₂²	1	2	yes	complemented
81	C₁₉×#466	C₂²	1	2	yes	complemented
82	C₁₉×#465	C₂²	1	2	yes	complemented
83	C₁₉×#465	C₂²	1	2	yes	complemented
84	C₁₉×#465	C₂²	1	2	yes	complemented
85	C₁₉×#463	C₂²	1	2	yes	—
86	C₁₉×#463	C₂²	1	1	yes	characteristic
87	C₁₉×#463	C₂²	1	1	yes	characteristic, complemented
88	C₁₉×#463	C₂²	1	2	yes	complemented
89	C₁₉×#463	C₂²	1	2	yes	complemented
90	C₁₉×#461	C₂²	1	1	yes	characteristic
91	C₁₉×#461	C₂²	1	1	yes	characteristic
92	C₁₉×#461	C₂²	1	2	yes	—
93	C₁₉×#461	C₂²	1	2	yes	—
94	C₁₉×#461	C₂²	1	2	yes	complemented
95	C₁₉×#461	C₂²	1	2	yes	complemented
96	C₁₉×#461	C₂²	1	2	yes	complemented
97	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
98	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
99	C₁₉×#461	C₂²	1	2	yes	complemented
100	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
101	C₁₉×#460	C₂²	1	2	yes	complemented
102	C₁₉×#460	C₂²	1	2	yes	complemented
103	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
104	C₁₉×#450	C₂²	1	2	yes	—
105	C₁₉×#450	C₂²	1	2	yes	—
106	C₁₉×#450	C₂²	1	1	yes	characteristic
107	C₁₉×#449	C₂²	1	2	yes	complemented
108	C₁₉×#449	C₂²	1	2	yes	complemented
109	C₁₉×#448	C₂²	1	2	yes	complemented
110	C₁₉×#448	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	1	yes	characteristic
114	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
116	C₁₉×#440	C₂²	1	2	yes	—
117	C₁₉×#440	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
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×#419	C₂²	1	2	yes	complemented
133	C₁₉×#416	C₂²	1	2	yes	complemented
134	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	1	no	—
137	C₂×#41×C₁₉	C₂³	1	2	yes	—
138	C₂²×Q₈×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	2	no	—
142	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₉	—	2	1	no	—
145	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
146	C₂×SD₁₆×C₁₉	—	4	4	no	—
147	C₂×SD₁₆×C₁₉	—	4	4	no	—
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	1	yes	characteristic
152	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
159	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₁₉	C₂³	1	2	yes	—
162	C₂×M₁₆×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	1	no	—
166	C₁₉×C₄⋊Q₈	—	2	2	no	—
167	C₁₉×C₄⋊Q₈	—	2	1	no	—
168	C₁₉×C₄⋊Q₈	—	2	1	no	—
169	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	C₁₉×#127	C₂³	1	1	yes	characteristic
175	C₁₉×#127	C₂³	1	2	yes	—
176	C₁₉×#126	—	2	2	no	—
177	C₁₉×#126	—	2	2	no	—
178	C₁₉×#126	—	2	2	no	—
179	C₁₉×#126	—	2	2	no	—
180	C₁₉×#126	—	2	1	no	—
181	C₁₉×#126	D₄	1	2	yes	—
182	C₁₉×#125	—	2	2	no	—
183	C₁₉×#125	—	2	2	no	—
184	C₁₉×#125	—	2	2	no	—
185	C₁₉×#125	—	2	1	no	—
186	C₁₉×#125	D₄	1	1	yes	characteristic
187	C₁₉×#125	C₂³	1	1	yes	characteristic
188	C₁₉×#125	C₂³	1	2	yes	—
189	C₁₉×#124	—	2	2	no	—
190	C₁₉×#124	—	2	2	no	—
191	C₁₉×#124	—	2	1	no	—
192	C₁₉×#124	D₄	1	1	yes	characteristic
193	C₁₉×#124	C₂³	1	1	yes	characteristic
194	C₁₉×#124	C₂³	1	2	yes	—
195	C₁₉×#123	—	2	1	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	—	2	2	no	—
201	C₁₉×#123	—	2	2	no	—
202	C₁₉×#123	D₄	1	2	yes	—
203	C₁₉×C₂²⋊Q₈	—	2	1	no	—
204	C₁₉×C₂²⋊Q₈	—	2	1	no	—
205	C₁₉×C₂²⋊Q₈	—	2	2	no	—
206	C₁₉×C₂²⋊Q₈	—	2	2	no	—
207	C₁₉×C₂²⋊Q₈	—	2	2	no	—
208	C₁₉×C₂²⋊Q₈	—	2	2	no	—
209	C₁₉×C₂²⋊Q₈	—	2	2	no	—
210	C₁₉×C₂²⋊Q₈	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	—	2	2	no	—
212	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
213	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
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	2	no	—
224	C₁₉×#121	—	2	2	no	—
225	C₁₉×#121	—	2	2	no	—
226	C₁₉×#121	—	2	2	no	—
227	C₁₉×#121	D₄	1	1	yes	characteristic
228	C₁₉×#121	C₂³	1	1	yes	characteristic
229	C₁₉×#121	C₂³	1	2	yes	—
230	C₁₉×#121	C₂³	1	2	yes	—
231	C₁₉×#121	C₂³	1	2	yes	—
232	C₁₉×#120	—	2	2	no	—
233	C₁₉×#120	—	2	2	no	—
234	C₁₉×#120	—	2	2	no	—
235	C₄×Q₈×C₁₉	—	2	1	no	—
236	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₉	—	2	2	no	—
241	C₄×D₄×C₁₉	—	2	1	no	—
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	2	no	—
246	C₄×D₄×C₁₉	—	2	2	no	—
247	C₄×D₄×C₁₉	—	2	1	no	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	1	no	—
250	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₉	C₂³	1	2	yes	—
254	C₄×D₄×C₁₉	C₂³	1	2	yes	—
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	2	yes	—
259	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	—	2	1	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	C₂³	1	2	yes	—
264	C₁₉×#117	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
267	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₁₉	—	2	1	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	1	yes	characteristic
276	C₁₉×#107	C₂³	1	2	yes	—
277	C₁₉×#106	C₂³	1	2	yes	—
278	C₁₉×#106	C₂³	1	1	yes	characteristic
279	C₁₉×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
288	C₁₉×#103	C₂³	1	2	yes	—
289	C₁₉×#103	C₂³	1	2	yes	—
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×#103	C₂³	1	2	yes	—
295	C₁₉×#103	C₂³	1	2	yes	—
296	C₁₉×#103	C₂³	1	1	yes	characteristic
297	C₁₉×#103	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	1	yes	characteristic
302	C₁₉×#102	C₂³	1	1	yes	characteristic
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	#41×C₁₉	—	4	2	no	—
318	#41×C₁₉	—	4	2	no	—
319	#41×C₁₉	—	8	2	no	—
320	#41×C₁₉	—	8	2	no	—
321	C₂×Q₈×C₁₉	—	2	2	no	—
322	C₂×Q₈×C₁₉	—	2	1	no	—
323	C₂×Q₈×C₁₉	—	2	2	no	—
324	C₂×Q₈×C₁₉	—	4	2	no	—
325	C₂×Q₈×C₁₉	—	4	2	no	—
326	C₂×Q₈×C₁₉	—	4	2	no	—
327	C₂×Q₈×C₁₉	—	4	2	no	—
328	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
332	C₂×D₄×C₁₉	—	2	2	no	—
333	C₂×D₄×C₁₉	—	2	4	no	—
334	C₂×D₄×C₁₉	—	2	1	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	2	no	—
339	C₂×D₄×C₁₉	—	2	2	no	—
340	C₂×D₄×C₁₉	—	2	1	no	—
341	C₂×D₄×C₁₉	—	2	1	no	—
342	C₂×D₄×C₁₉	—	2	2	no	—
343	C₂×D₄×C₁₉	—	2	1	no	—
344	C₂×D₄×C₁₉	—	2	2	no	—
345	C₂×D₄×C₁₉	—	4	1	no	—
346	C₂×D₄×C₁₉	—	4	2	no	—
347	C₂×D₄×C₁₉	—	8	2	no	—
348	C₂×D₄×C₁₉	—	8	4	no	—
349	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
352	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₁₉	—	2	1	no	—
356	C₂²×C₄×C₁₉	—	2	2	no	—
357	C₂²×C₄×C₁₉	—	2	2	no	—
358	C₂²×C₄×C₁₉	—	2	1	no	—
359	C₂²×C₄×C₁₉	—	2	1	no	—
360	C₂²×C₄×C₁₉	—	2	1	no	—
361	C₂²×C₄×C₁₉	—	2	1	no	—
362	C₂²×C₄×C₁₉	—	2	2	no	—
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	1	no	—
367	C₂²×C₄×C₁₉	—	8	2	no	—
368	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
372	SD₁₆×C₁₉	—	2	2	no	—
373	SD₁₆×C₁₉	—	2	4	no	—
374	SD₁₆×C₁₉	—	2	4	no	—
375	SD₁₆×C₁₉	—	4	2	no	—
376	SD₁₆×C₁₉	—	4	2	no	—
377	SD₁₆×C₁₉	—	4	2	no	—
378	SD₁₆×C₁₉	—	4	2	no	—
379	SD₁₆×C₁₉	—	4	2	no	—
380	SD₁₆×C₁₉	—	4	1	no	—
381	SD₁₆×C₁₉	—	4	2	no	—
382	SD₁₆×C₁₉	—	4	2	no	—
383	D₈×C₁₉	—	2	2	no	—
384	D₈×C₁₉	—	4	1	no	—
385	D₈×C₁₉	—	4	2	no	—
386	M₁₆×C₁₉	—	4	2	no	—
387	C₂×C₈×C₁₉	—	4	2	no	—
388	C₂×C₈×C₁₉	—	4	2	no	—
389	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
390	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
392	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₁₉	—	2	1	no	—
396	C₄⋊C₄×C₁₉	—	2	1	no	—
397	C₄⋊C₄×C₁₉	—	2	1	no	—
398	C₄⋊C₄×C₁₉	—	2	2	no	—
399	C₄⋊C₄×C₁₉	—	2	1	no	—
400	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
409	C₄⋊C₄×C₁₉	—	2	2	no	—
410	C₄⋊C₄×C₁₉	—	2	1	no	—
411	C₄⋊C₄×C₁₉	—	2	2	no	—
412	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₁₉	C₂⁴	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	C₂²⋊C₄×C₁₉	—	2	2	no	—
427	C₂²⋊C₄×C₁₉	—	2	1	no	—
428	C₂²⋊C₄×C₁₉	—	2	2	no	—
429	C₂²⋊C₄×C₁₉	—	2	2	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	1	no	—
435	C₂²⋊C₄×C₁₉	—	2	2	no	—
436	C₂²⋊C₄×C₁₉	—	2	1	no	—
437	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
442	C₂²⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
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	1	no	—
453	C₄²×C₁₉	—	2	2	no	—
454	C₄²×C₁₉	—	2	2	no	—
455	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
458	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₁₉	C₂⁴	1	2	yes	—
460	#62052	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂³×C₁₉	—	2	1	no	—
462	C₂³×C₁₉	—	2	1	no	—
463	C₂³×C₁₉	—	2	1	no	—
464	C₂³×C₁₉	—	2	2	no	—
465	C₂³×C₁₉	—	4	2	no	—
466	C₂³×C₁₉	—	4	4	no	—
467	C₂³×C₁₉	—	4	2	no	—
468	C₂³×C₁₉	—	8	1	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	1	yes	characteristic
473	Q₈×C₁₉	—	2	2	no	—
474	Q₈×C₁₉	—	2	1	no	—
475	Q₈×C₁₉	—	2	2	no	—
476	Q₈×C₁₉	—	2	2	no	—
477	Q₈×C₁₉	—	2	2	no	—
478	Q₈×C₁₉	—	2	1	no	—
479	Q₈×C₁₉	—	2	2	no	—
480	Q₈×C₁₉	—	8	2	no	—
481	Q₈×C₁₉	—	8	2	no	—
482	Q₈×C₁₉	—	8	1	no	—
483	D₄×C₁₉	—	2	4	no	—
484	D₄×C₁₉	—	2	2	no	—
485	D₄×C₁₉	—	2	1	no	—
486	D₄×C₁₉	—	2	2	no	—
487	D₄×C₁₉	—	2	1	no	—
488	D₄×C₁₉	—	2	1	no	—
489	D₄×C₁₉	—	2	1	no	—
490	D₄×C₁₉	—	2	1	no	—
491	D₄×C₁₉	—	2	2	no	—
492	D₄×C₁₉	—	4	4	no	—
493	D₄×C₁₉	—	4	2	no	—
494	D₄×C₁₉	—	4	2	no	—
495	D₄×C₁₉	—	4	4	no	—
496	D₄×C₁₉	—	4	2	no	—
497	D₄×C₁₉	—	8	2	no	—
498	D₄×C₁₉	—	8	1	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	H(5,𝔽₂)	1	2	yes	—
504	C₂×C₄×C₁₉	—	2	2	no	—
505	C₂×C₄×C₁₉	—	2	2	no	—
506	C₂×C₄×C₁₉	—	2	1	no	—
507	C₂×C₄×C₁₉	—	2	2	no	—
508	C₂×C₄×C₁₉	—	2	1	no	—
509	C₂×C₄×C₁₉	—	2	2	no	—
510	C₂×C₄×C₁₉	—	2	1	no	—
511	C₂×C₄×C₁₉	—	2	1	no	—
512	C₂×C₄×C₁₉	—	2	1	no	—
513	C₂×C₄×C₁₉	—	2	2	no	—
514	C₂×C₄×C₁₉	—	2	1	no	—
515	C₂×C₄×C₁₉	—	2	2	no	—
516	C₂×C₄×C₁₉	—	2	2	no	—
517	C₂×C₄×C₁₉	—	2	1	no	—
518	C₂×C₄×C₁₉	—	4	2	no	—
519	C₂×C₄×C₁₉	—	4	2	no	—
520	C₂×C₄×C₁₉	—	4	2	no	—
521	C₂×C₄×C₁₉	—	8	1	no	—
522	C₂×C₄×C₁₉	—	8	1	no	—
523	C₂×C₄×C₁₉	—	8	2	no	—
524	C₂×C₄×C₁₉	—	8	2	no	—
525	C₂×C₄×C₁₉	—	8	2	no	—
526	C₂×C₄×C₁₉	—	8	2	no	—
527	C₂×C₄×C₁₉	—	8	1	no	—
528	C₂×C₄×C₁₉	—	8	2	no	—
529	C₂×C₄×C₁₉	—	8	2	no	—
530	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
539	C₈×C₁₉	—	2	1	no	—
540	C₈×C₁₉	—	2	2	no	—
541	C₈×C₁₉	—	2	2	no	—
542	C₈×C₁₉	—	2	1	no	—
543	C₈×C₁₉	—	2	1	no	—
544	C₈×C₁₉	—	2	1	no	—
545	#3552	C₂×C₁₉	1	1	yes	characteristic, complemented
546	#3519	C₂×C₁₉	1	1	yes	characteristic, complemented
547	#3397	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
549	#3372	C₂×C₁₉	1	1	yes	characteristic, complemented
550	#3360	C₂×C₁₉	1	1	yes	characteristic, complemented
551	#3329	C₂×C₁₉	1	1	yes	characteristic, complemented
552	#3320	C₂×C₁₉	1	2	yes	complemented
553	#3303	C₂×C₁₉	1	1	yes	characteristic, complemented
554	#3301	C₂×C₁₉	1	2	yes	complemented
555	D₄×SD₁₆	C₂×C₁₉	1	2	yes	complemented
556	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#3272	C₂×C₁₉	1	1	yes	characteristic, complemented
558	#3265	C₂×C₁₉	1	2	yes	complemented
559	#3260	C₂×C₁₉	1	2	yes	complemented
560	#3247	C₂×C₁₉	1	1	yes	characteristic, complemented
561	#3221	C₂×C₁₉	1	2	yes	complemented
562	#3206	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#3123	C₂×C₁₉	1	2	yes	complemented
564	#3105	C₂×C₁₉	1	1	yes	characteristic, complemented
565	#3042	C₂×C₁₉	1	2	yes	complemented
566	C₂×#461	C₂×C₁₉	1	1	yes	characteristic, complemented
567	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
568	C₂²×C₁₉	—	2	1	no	—
569	C₂²×C₁₉	—	2	1	no	—
570	C₂²×C₁₉	—	2	2	no	—
571	C₂²×C₁₉	—	2	2	no	—
572	C₂²×C₁₉	—	2	2	no	—
573	C₂²×C₁₉	—	2	2	no	—
574	C₂²×C₁₉	—	4	1	no	—
575	C₂²×C₁₉	—	4	1	no	—
576	C₂²×C₁₉	—	4	1	no	—
577	C₂²×C₁₉	—	4	1	no	—
578	C₂²×C₁₉	—	4	2	no	—
579	C₂²×C₁₉	—	4	1	no	—
580	C₂²×C₁₉	—	4	1	no	—
581	C₂²×C₁₉	—	4	2	no	—
582	C₂²×C₁₉	—	4	2	no	—
583	C₂²×C₁₉	—	4	1	no	—
584	C₂²×C₁₉	—	4	1	no	—
585	C₂²×C₁₉	—	8	4	no	—
586	C₂²×C₁₉	—	16	4	no	—
587	C₂²×C₁₉	#577	1	2	yes	—
588	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₁₉	—	2	2	no	—
590	C₄×C₁₉	—	2	1	no	—
591	C₄×C₁₉	—	2	1	no	—
592	C₄×C₁₉	—	2	1	no	—
593	C₄×C₁₉	—	2	1	no	—
594	C₄×C₁₉	—	2	2	no	—
595	C₄×C₁₉	—	2	2	no	—
596	C₄×C₁₉	—	4	2	no	—
597	C₄×C₁₉	—	4	1	no	—
598	C₄×C₁₉	—	4	2	no	—
599	C₄×C₁₉	—	4	1	no	—
600	C₄×C₁₉	—	4	1	no	—
601	C₄×C₁₉	—	4	1	no	—
602	C₄×C₁₉	—	4	2	no	—
603	C₄×C₁₉	—	4	1	no	—
604	C₄×C₁₉	#577	1	2	yes	—
605	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	C₄×C₁₉	#585	1	1	yes	characteristic
607	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
608	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
609	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
610	#563	—	2	2	no	—
611	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
612	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
613	#555	C₂²×C₁₉	1	1	yes	characteristic
614	#554	—	2	1	no	—
615	#554	C₂²×C₁₉	1	1	yes	characteristic
616	#553	—	2	1	no	—
617	#553	—	2	1	no	—
618	#553	C₂²×C₁₉	1	2	yes	—
619	#550	C₂²×C₁₉	1	1	yes	characteristic
620	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
621	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
622	#548	C₂²×C₁₉	1	2	yes	complemented
623	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
624	#546	—	2	1	no	—
625	#546	—	2	2	no	—
626	D₄²	C₂²×C₁₉	1	2	yes	—
627	D₄²	C₂²×C₁₉	1	1	yes	characteristic
628	#544	—	2	1	no	—
629	#542	—	2	1	no	—
630	#541	C₂²×C₁₉	1	2	yes	complemented
631	#540	C₂²×C₁₉	1	2	yes	—
632	#539	—	2	2	no	—
633	#538	—	2	2	no	—
634	#536	C₂²×C₁₉	1	2	yes	complemented
635	#532	C₂²×C₁₉	1	1	yes	characteristic
636	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
637	#529	C₂²×C₁₉	1	1	yes	characteristic
638	#529	C₂²×C₁₉	1	1	yes	characteristic, complemented
639	#525	—	2	1	no	—
640	C₂×#121	—	2	1	no	—
641	#518	C₂²×C₁₉	1	2	yes	—
642	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
643	#496	C₂²×C₁₉	1	2	yes	complemented
644	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	#492	C₂²×C₁₉	1	2	yes	complemented
646	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
647	#491	C₂²×C₁₉	1	2	yes	complemented
648	#488	C₂²×C₁₉	1	2	yes	complemented
649	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
650	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
651	#485	C₂²×C₁₉	1	2	yes	complemented
652	#485	C₂²×C₁₉	1	2	yes	complemented
653	#484	C₂²×C₁₉	1	1	yes	characteristic, complemented
654	#481	C₂²×C₁₉	1	1	yes	characteristic, complemented
655	#479	C₂²×C₁₉	1	2	yes	complemented
656	#479	C₂²×C₁₉	1	2	yes	complemented
657	#478	C₂²×C₁₉	1	1	yes	characteristic
658	#478	C₂²×C₁₉	1	1	yes	characteristic, complemented
659	#478	C₂²×C₁₉	1	2	yes	complemented
660	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
661	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
662	#468	C₂²×C₁₉	1	2	yes	complemented
663	#468	C₂²×C₁₉	1	2	yes	complemented
664	#466	C₂²×C₁₉	1	2	yes	complemented
665	#465	C₂²×C₁₉	1	2	yes	complemented
666	#465	C₂²×C₁₉	1	2	yes	complemented
667	#465	C₂²×C₁₉	1	2	yes	complemented
668	#463	C₂²×C₁₉	1	2	yes	—
669	#463	C₂²×C₁₉	1	1	yes	characteristic
670	#463	C₂²×C₁₉	1	1	yes	characteristic, complemented
671	#463	C₂²×C₁₉	1	2	yes	complemented
672	#463	C₂²×C₁₉	1	2	yes	complemented
673	#461	C₂²×C₁₉	1	1	yes	characteristic
674	#461	C₂²×C₁₉	1	1	yes	characteristic
675	#461	C₂²×C₁₉	1	2	yes	—
676	#461	C₂²×C₁₉	1	2	yes	—
677	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
678	#461	C₂²×C₁₉	1	2	yes	complemented
679	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
680	#461	C₂²×C₁₉	1	2	yes	complemented
681	#461	C₂²×C₁₉	1	2	yes	complemented
682	#461	C₂²×C₁₉	1	2	yes	complemented
683	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
684	#460	C₂²×C₁₉	1	2	yes	complemented
685	#460	C₂²×C₁₉	1	2	yes	complemented
686	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
687	#450	C₂²×C₁₉	1	1	yes	characteristic
688	#450	C₂²×C₁₉	1	2	yes	—
689	#450	C₂²×C₁₉	1	2	yes	—
690	#449	C₂²×C₁₉	1	2	yes	complemented
691	#449	C₂²×C₁₉	1	2	yes	complemented
692	#448	C₂²×C₁₉	1	2	yes	complemented
693	#448	C₂²×C₁₉	1	2	yes	complemented
694	#448	C₂²×C₁₉	1	2	yes	complemented
695	#448	C₂²×C₁₉	1	2	yes	complemented
696	#447	C₂²×C₁₉	1	1	yes	characteristic
697	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
698	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
699	#440	C₂²×C₁₉	1	2	yes	—
700	#440	C₂²×C₁₉	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
702	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
705	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
706	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
708	#435	C₂²×C₁₉	1	2	yes	complemented
709	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
710	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
711	#433	C₂²×C₁₉	1	2	yes	complemented
712	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
713	#424	C₂²×C₁₉	1	2	yes	complemented
714	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
715	#419	C₂²×C₁₉	1	2	yes	complemented
716	#416	C₂²×C₁₉	1	2	yes	complemented
717	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
718	C₂×C₁₉	—	2	2	no	—
719	C₂×C₁₉	—	4	2	no	—
720	C₂×C₁₉	—	4	2	no	—
721	C₂×C₁₉	—	8	1	no	—
722	C₂×C₁₉	—	8	1	no	—
723	C₂×C₁₉	—	8	2	no	—
724	C₂×C₁₉	#3488	1	1	yes	characteristic
725	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
726	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
727	C₂×#41	—	2	1	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	C₂³×C₁₉	1	2	yes	—
730	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
731	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
732	C₂²×D₄	—	2	1	no	—
733	C₂²×D₄	—	2	2	no	—
734	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
735	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
736	C₂³×C₄	—	2	1	no	—
737	AGL(1,ℤ/8)	—	4	4	no	—
738	C₂×SD₁₆	—	4	4	no	—
739	C₂×SD₁₆	—	4	4	no	—
740	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
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	2	yes	—
748	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
751	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
752	C₂×D₈	C₂³×C₁₉	1	2	yes	—
753	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
754	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
755	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
756	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
757	C₄⋊Q₈	—	2	1	no	—
758	C₄⋊Q₈	—	2	2	no	—
759	C₄⋊Q₈	—	2	1	no	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
762	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
765	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
766	#127	C₂³×C₁₉	1	1	yes	characteristic
767	#127	C₂³×C₁₉	1	2	yes	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	1	no	—
773	#126	D₄×C₁₉	1	2	yes	—
774	#125	—	2	2	no	—
775	#125	—	2	2	no	—
776	#125	—	2	2	no	—
777	#125	—	2	1	no	—
778	#125	D₄×C₁₉	1	1	yes	characteristic
779	#125	C₂³×C₁₉	1	1	yes	characteristic
780	#125	C₂³×C₁₉	1	2	yes	—
781	#124	—	2	2	no	—
782	#124	—	2	2	no	—
783	#124	—	2	1	no	—
784	#124	D₄×C₁₉	1	1	yes	characteristic
785	#124	C₂³×C₁₉	1	1	yes	characteristic
786	#124	C₂³×C₁₉	1	2	yes	—
787	#123	—	2	1	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	D₄×C₁₉	1	2	yes	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
805	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
808	#121	—	2	2	no	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	D₄×C₁₉	1	1	yes	characteristic
820	#121	C₂³×C₁₉	1	1	yes	characteristic
821	#121	C₂³×C₁₉	1	2	yes	—
822	#121	C₂³×C₁₉	1	2	yes	—
823	#121	C₂³×C₁₉	1	2	yes	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	C₄×Q₈	—	2	1	no	—
828	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
829	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
830	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
831	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₁₉	1	2	yes	—
847	C₄×D₄	C₂³×C₁₉	1	2	yes	—
848	C₄×D₄	C₂³×C₁₉	1	2	yes	—
849	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₁₉	1	2	yes	—
852	#117	—	2	1	no	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	C₂³×C₁₉	1	2	yes	—
856	#117	C₂³×C₁₉	1	2	yes	—
857	C₂×C₄⋊C₄	—	2	1	no	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
862	C₂×C₂²⋊C₄	—	2	1	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
866	#107	C₂³×C₁₉	1	1	yes	characteristic
867	#107	C₂³×C₁₉	1	1	yes	characteristic
868	#107	C₂³×C₁₉	1	2	yes	—
869	#106	C₂³×C₁₉	1	2	yes	—
870	#106	C₂³×C₁₉	1	1	yes	characteristic
871	#106	C₂³×C₁₉	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
873	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
877	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
878	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
879	#103	C₂³×C₁₉	1	2	yes	—
880	#103	C₂³×C₁₉	1	2	yes	—
881	#103	C₂³×C₁₉	1	2	yes	—
882	#103	C₂³×C₁₉	1	2	yes	—
883	#103	C₂³×C₁₉	1	2	yes	—
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	2	yes	—
888	#103	C₂³×C₁₉	1	1	yes	characteristic
889	#103	C₂³×C₁₉	1	2	yes	—
890	#102	C₂³×C₁₉	1	1	yes	characteristic
891	#102	C₂³×C₁₉	1	2	yes	—
892	#102	C₂³×C₁₉	1	1	yes	characteristic
893	#102	C₂³×C₁₉	1	1	yes	characteristic
894	#102	C₂³×C₁₉	1	1	yes	characteristic
895	#102	C₂³×C₁₉	1	1	yes	characteristic
896	#102	C₂³×C₁₉	1	1	yes	characteristic
897	#102	C₂³×C₁₉	1	2	yes	—
898	#102	C₂³×C₁₉	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
900	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
903	#97	C₂³×C₁₉	1	2	yes	—
904	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
905	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₁₉	1	2	yes	—
907	C₁₉	#62052	1	1	yes	characteristic, direct product factor, Sylow
908	C₂⁴	—	2	1	no	—
909	C₂⁴	—	2	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	8	2	no	—
913	#41	—	8	2	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	—	2	1	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	4	2	no	—
918	C₂×Q₈	—	4	2	no	—
919	C₂×Q₈	—	4	2	no	—
920	C₂×Q₈	—	4	2	no	—
921	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
923	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
924	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	4	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	4	1	no	—
939	C₂×D₄	—	4	2	no	—
940	C₂×D₄	—	8	2	no	—
941	C₂×D₄	—	8	4	no	—
942	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
946	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	8	2	no	—
961	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
962	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
965	SD₁₆	—	2	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	1	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	D₈	—	2	2	no	—
977	D₈	—	4	1	no	—
978	D₈	—	4	2	no	—
979	M₁₆	—	4	2	no	—
980	C₂×C₈	—	4	2	no	—
981	C₂×C₈	—	4	2	no	—
982	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
986	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1012	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	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	1	no	—
1030	C₂²⋊C₄	—	2	2	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	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1042	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	2	no	—
1048	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1050	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₁₉	1	2	yes	—
1052	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	4	2	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	4	2	no	—
1060	C₂³	—	8	1	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1064	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1065	Q₈	—	2	2	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	8	2	no	—
1073	Q₈	—	8	2	no	—
1074	Q₈	—	8	1	no	—
1075	D₄	—	2	4	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	8	2	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	C₁₉×H(5,𝔽₂)	1	2	yes	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	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	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	8	1	no	—
1114	C₂×C₄	—	8	1	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	1	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1129	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1130	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	8	4	no	—
1155	C₂²	—	16	4	no	—
1156	C₂²	C₁₉×#577	1	2	yes	—
1157	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₁₉×#577	1	2	yes	—
1174	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1175	C₄	C₁₉×#585	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	4	2	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	C₁₉×#3488	1	1	yes	characteristic
1183	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1184	C₂	C₂×C₁₉×#577	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×#3552	C₂	semidirect
2. C₁₉×#3519	C₂	semidirect
3. C₁₉×#3397	C₂	semidirect
4. C₁₉×#3392	C₂	semidirect
5. C₁₉×#3372	C₂	semidirect
6. C₁₉×#3360	C₂	semidirect
7. C₁₉×#3329	C₂	semidirect
8. C₁₉×#3320	C₂	semidirect
9. C₁₉×#3303	C₂	semidirect
10. C₁₉×#3301	C₂	semidirect
11. D₄×SD₁₆×C₁₉	C₂	semidirect
12. D₄×SD₁₆×C₁₉	C₂	semidirect
13. C₁₉×#3272	C₂	semidirect
14. C₁₉×#3265	C₂	semidirect
15. C₁₉×#3260	C₂	semidirect
16. C₁₉×#3247	C₂	semidirect
17. C₁₉×#3221	C₂	semidirect
18. C₁₉×#3206	C₂	semidirect
19. C₁₉×#3123	C₂	semidirect
20. C₁₉×#3105	C₂	semidirect
21. C₁₉×#3042	C₂	semidirect
22. C₂×C₁₉×#461	C₂	semidirect
23. C₁₉×#2994	C₂	semidirect
28. C₁₉×#557	C₂²	semidirect
29. C₁₉×#556	C₂²	semidirect
37. D₄×Q₈×C₁₉	C₂²	semidirect
38. D₄×Q₈×C₁₉	C₂²	semidirect
39. C₁₉×#548	C₂²	semidirect
40. C₁₉×#547	C₂²	semidirect
47. C₁₉×#541	C₂²	semidirect
51. C₁₉×#536	C₂²	semidirect
53. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
55. C₁₉×#529	C₂²	semidirect
60. C₁₉×#496	C₂²	semidirect
61. C₁₉×#492	C₂²	semidirect
62. C₁₉×#492	C₂²	semidirect
63. C₁₉×#492	C₂²	semidirect
64. C₁₉×#491	C₂²	semidirect
65. C₁₉×#488	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
67. C₁₉×#487	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
69. C₁₉×#485	C₂²	semidirect
70. C₁₉×#484	C₂²	semidirect
71. C₁₉×#481	C₂²	semidirect
72. C₁₉×#479	C₂²	semidirect
73. C₁₉×#479	C₂²	semidirect
75. C₁₉×#478	C₂²	semidirect
76. C₁₉×#478	C₂²	semidirect
77. C₁₉×#477	C₂²	semidirect
78. C₁₉×#476	C₂²	semidirect
79. C₁₉×#468	C₂²	semidirect
80. C₁₉×#468	C₂²	semidirect
81. C₁₉×#466	C₂²	semidirect
82. C₁₉×#465	C₂²	semidirect
83. C₁₉×#465	C₂²	semidirect
84. C₁₉×#465	C₂²	semidirect
87. C₁₉×#463	C₂²	semidirect
88. C₁₉×#463	C₂²	semidirect
89. C₁₉×#463	C₂²	semidirect
94. C₁₉×#461	C₂²	semidirect
95. C₁₉×#461	C₂²	semidirect
96. C₁₉×#461	C₂²	semidirect
97. C₁₉×#461	C₂²	semidirect
98. C₁₉×#461	C₂²	semidirect
99. C₁₉×#461	C₂²	semidirect
100. C₁₉×#460	C₂²	semidirect
101. C₁₉×#460	C₂²	semidirect
102. C₁₉×#460	C₂²	semidirect
103. C₁₉×#459	C₂²	semidirect
107. C₁₉×#449	C₂²	semidirect
108. C₁₉×#449	C₂²	semidirect
109. C₁₉×#448	C₂²	semidirect
110. C₁₉×#448	C₂²	semidirect
111. C₁₉×#448	C₂²	semidirect
112. C₁₉×#448	C₂²	semidirect
114. C₁₉×#446	C₂²	semidirect
115. C₈×Q₈×C₁₉	C₂²	semidirect
117. C₁₉×#440	C₂²	semidirect
120. C₄×SD₁₆×C₁₉	C₂²	semidirect
121. C₄×SD₁₆×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×#419	C₂²	semidirect
133. C₁₉×#416	C₂²	semidirect
134. C₂×C₁₉×#103	C₂²	semidirect
460. #62052	C₁₉	direct (N × H)
545. #3552	C₂×C₁₉	semidirect
546. #3519	C₂×C₁₉	semidirect
547. #3397	C₂×C₁₉	semidirect
548. #3392	C₂×C₁₉	semidirect
549. #3372	C₂×C₁₉	semidirect
550. #3360	C₂×C₁₉	semidirect
551. #3329	C₂×C₁₉	semidirect
552. #3320	C₂×C₁₉	semidirect
553. #3303	C₂×C₁₉	semidirect
554. #3301	C₂×C₁₉	semidirect
555. D₄×SD₁₆	C₂×C₁₉	semidirect
556. D₄×SD₁₆	C₂×C₁₉	semidirect
557. #3272	C₂×C₁₉	semidirect
558. #3265	C₂×C₁₉	semidirect
559. #3260	C₂×C₁₉	semidirect
560. #3247	C₂×C₁₉	semidirect
561. #3221	C₂×C₁₉	semidirect
562. #3206	C₂×C₁₉	semidirect
563. #3123	C₂×C₁₉	semidirect
564. #3105	C₂×C₁₉	semidirect
565. #3042	C₂×C₁₉	semidirect
566. C₂×#461	C₂×C₁₉	semidirect
567. #2994	C₂×C₁₉	semidirect
611. #557	C₂²×C₁₉	semidirect
612. #556	C₂²×C₁₉	semidirect
620. D₄×Q₈	C₂²×C₁₉	semidirect
621. D₄×Q₈	C₂²×C₁₉	semidirect
622. #548	C₂²×C₁₉	semidirect
623. #547	C₂²×C₁₉	semidirect
630. #541	C₂²×C₁₉	semidirect
634. #536	C₂²×C₁₉	semidirect
636. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
638. #529	C₂²×C₁₉	semidirect
643. #496	C₂²×C₁₉	semidirect
644. #492	C₂²×C₁₉	semidirect
645. #492	C₂²×C₁₉	semidirect
646. #492	C₂²×C₁₉	semidirect
647. #491	C₂²×C₁₉	semidirect
648. #488	C₂²×C₁₉	semidirect
649. #487	C₂²×C₁₉	semidirect
650. #487	C₂²×C₁₉	semidirect
651. #485	C₂²×C₁₉	semidirect
652. #485	C₂²×C₁₉	semidirect
653. #484	C₂²×C₁₉	semidirect
654. #481	C₂²×C₁₉	semidirect
655. #479	C₂²×C₁₉	semidirect
656. #479	C₂²×C₁₉	semidirect
658. #478	C₂²×C₁₉	semidirect
659. #478	C₂²×C₁₉	semidirect
660. #477	C₂²×C₁₉	semidirect
661. #476	C₂²×C₁₉	semidirect
662. #468	C₂²×C₁₉	semidirect
663. #468	C₂²×C₁₉	semidirect
664. #466	C₂²×C₁₉	semidirect
665. #465	C₂²×C₁₉	semidirect
666. #465	C₂²×C₁₉	semidirect
667. #465	C₂²×C₁₉	semidirect
670. #463	C₂²×C₁₉	semidirect
671. #463	C₂²×C₁₉	semidirect
672. #463	C₂²×C₁₉	semidirect
677. #461	C₂²×C₁₉	semidirect
678. #461	C₂²×C₁₉	semidirect
679. #461	C₂²×C₁₉	semidirect
680. #461	C₂²×C₁₉	semidirect
681. #461	C₂²×C₁₉	semidirect
682. #461	C₂²×C₁₉	semidirect
683. #460	C₂²×C₁₉	semidirect
684. #460	C₂²×C₁₉	semidirect
685. #460	C₂²×C₁₉	semidirect
686. #459	C₂²×C₁₉	semidirect
690. #449	C₂²×C₁₉	semidirect
691. #449	C₂²×C₁₉	semidirect
692. #448	C₂²×C₁₉	semidirect
693. #448	C₂²×C₁₉	semidirect
694. #448	C₂²×C₁₉	semidirect
695. #448	C₂²×C₁₉	semidirect
697. #446	C₂²×C₁₉	semidirect
698. C₈×Q₈	C₂²×C₁₉	semidirect
700. #440	C₂²×C₁₉	semidirect
703. C₄×SD₁₆	C₂²×C₁₉	semidirect
704. C₄×SD₁₆	C₂²×C₁₉	semidirect
706. C₄×D₈	C₂²×C₁₉	semidirect
707. #436	C₂²×C₁₉	semidirect
708. #435	C₂²×C₁₉	semidirect
709. C₈×D₄	C₂²×C₁₉	semidirect
710. C₈×D₄	C₂²×C₁₉	semidirect
711. #433	C₂²×C₁₉	semidirect
712. #431	C₂²×C₁₉	semidirect
713. #424	C₂²×C₁₉	semidirect
714. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
715. #419	C₂²×C₁₉	semidirect
716. #416	C₂²×C₁₉	semidirect
717. C₂×#103	C₂²×C₁₉	semidirect
907. C₁₉	#62052	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×#3552	2
C₁₉×#3519	2
C₁₉×#3397	2
C₁₉×#3392	2
C₁₉×#3372	2
C₁₉×#3360	2
C₁₉×#3329	2
C₁₉×#3320	2
C₁₉×#3303	2
C₁₉×#3301	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3272	2
C₁₉×#3265	2
C₁₉×#3260	2
C₁₉×#3247	2
C₁₉×#3221	2
C₁₉×#3206	2
C₁₉×#3123	2
C₁₉×#3105	2
C₁₉×#3042	2
C₂×C₁₉×#461	2
C₁₉×#2994	2
#62052	19

Subgroups — C19×#62052 #18068011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62052 #18068011