Subgroups — C₁₉×#62055 #18068014

Order 4864.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3543	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3310	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3296	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×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3260	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3222	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3126	C₂	1	2	yes	maximal, complemented
20	C₁₉×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3043	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
27	C₁₉×#560	—	2	2	no	—
28	C₁₉×#559	C₂²	1	1	yes	characteristic
29	C₁₉×#557	—	2	1	no	—
30	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#556	—	2	1	no	—
33	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#552	—	2	2	no	—
35	C₁₉×#552	C₂²	1	2	yes	complemented
36	C₁₉×#550	C₂²	1	1	yes	characteristic
37	C₁₉×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
39	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#546	—	2	1	no	—
41	C₁₉×#546	C₂²	1	2	yes	—
42	D₄²×C₁₉	—	2	1	no	—
43	D₄²×C₁₉	C₂²	1	2	yes	—
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#541	—	2	2	no	—
46	C₁₉×#541	C₂²	1	2	yes	complemented
47	C₁₉×#540	—	2	1	no	—
48	C₁₉×#540	C₂²	1	2	yes	—
49	C₁₉×#535	—	2	1	no	—
50	C₁₉×#535	C₂²	1	2	yes	—
51	C₁₉×#534	—	2	2	no	—
52	C₁₉×#533	—	2	1	no	—
53	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
55	C₁₉×#529	—	2	1	no	—
56	C₁₉×#529	C₂²	1	1	yes	characteristic
57	C₁₉×#529	C₂²	1	1	yes	characteristic
58	C₁₉×#519	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#497	C₂²	1	2	yes	complemented
61	C₁₉×#492	C₂²	1	1	yes	characteristic
62	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#492	C₂²	1	2	yes	complemented
64	C₁₉×#490	C₂²	1	2	yes	complemented
65	C₁₉×#488	C₂²	1	2	yes	complemented
66	C₁₉×#486	C₂²	1	1	yes	characteristic
67	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#483	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#482	C₂²	1	2	yes	complemented
70	C₁₉×#482	C₂²	1	2	yes	complemented
71	C₁₉×#480	C₂²	1	1	yes	characteristic
72	C₁₉×#479	C₂²	1	2	yes	complemented
73	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
75	C₁₉×#478	C₂²	1	2	yes	complemented
76	C₁₉×#478	C₂²	1	2	yes	complemented
77	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#468	C₂²	1	2	yes	complemented
80	C₁₉×#468	C₂²	1	2	yes	complemented
81	C₁₉×#467	C₂²	1	2	yes	complemented
82	C₁₉×#465	C₂²	1	2	yes	—
83	C₁₉×#465	C₂²	1	2	yes	complemented
84	C₁₉×#465	C₂²	1	2	yes	complemented
85	C₁₉×#464	C₂²	1	1	yes	characteristic, complemented
86	C₁₉×#464	C₂²	1	2	yes	complemented
87	C₁₉×#464	C₂²	1	2	yes	complemented
88	C₁₉×#464	C₂²	1	2	yes	complemented
89	C₁₉×#464	C₂²	1	1	yes	characteristic, complemented
90	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
92	C₁₉×#461	C₂²	1	2	yes	complemented
93	C₁₉×#461	C₂²	1	2	yes	complemented
94	C₁₉×#460	C₂²	1	1	yes	characteristic
95	C₁₉×#460	C₂²	1	1	yes	characteristic
96	C₁₉×#460	C₂²	1	2	yes	complemented
97	C₁₉×#460	C₂²	1	2	yes	complemented
98	C₁₉×#460	C₂²	1	2	yes	complemented
99	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
100	C₁₉×#460	C₂²	1	2	yes	complemented
101	C₁₉×#460	C₂²	1	2	yes	complemented
102	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
103	C₁₉×#460	C₂²	1	2	yes	complemented
104	C₁₉×#452	C₂²	1	2	yes	complemented
105	C₁₉×#452	C₂²	1	2	yes	complemented
106	C₁₉×#451	C₂²	1	1	yes	characteristic, complemented
107	C₁₉×#450	C₂²	1	2	yes	complemented
108	C₁₉×#450	C₂²	1	2	yes	complemented
109	C₁₉×#450	C₂²	1	2	yes	complemented
110	C₁₉×#450	C₂²	1	2	yes	complemented
111	C₁₉×#448	C₂²	1	1	yes	characteristic
112	C₁₉×#448	C₂²	1	2	yes	complemented
113	C₁₉×#448	C₂²	1	2	yes	complemented
114	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
116	C₁₉×#440	C₂²	1	2	yes	complemented
117	C₁₉×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
123	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
124	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
125	C₁₉×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
127	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
128	C₁₉×#433	C₂²	1	2	yes	complemented
129	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
130	C₁₉×#424	C₂²	1	2	yes	complemented
131	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₁₉×#418	C₂²	1	2	yes	complemented
133	C₁₉×#416	C₂²	1	2	yes	complemented
134	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	C₂³	1	2	yes	—
137	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₉	—	2	2	no	—
140	C₂²×D₄×C₁₉	—	2	1	no	—
141	C₂²×D₄×C₁₉	—	2	1	no	—
142	C₂²×D₄×C₁₉	—	2	1	no	—
143	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
145	C₁₉×#137	—	4	4	no	—
146	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
148	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₁₉	—	4	4	no	—
150	C₂×SD₁₆×C₁₉	—	4	4	no	—
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	1	yes	characteristic
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×SD₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
161	C₂×SD₁₆×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	1	no	—
167	C₁₉×C₄⋊Q₈	—	2	2	no	—
168	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×#127	—	2	1	no	—
172	C₁₉×#127	—	2	1	no	—
173	C₁₉×#127	—	2	1	no	—
174	C₁₉×#127	C₂³	1	1	yes	characteristic
175	C₁₉×#127	C₂³	1	2	yes	—
176	C₁₉×#127	C₂³	1	1	yes	characteristic
177	C₁₉×#127	C₂³	1	2	yes	—
178	C₁₉×#126	—	2	2	no	—
179	C₁₉×#126	—	2	2	no	—
180	C₁₉×#126	—	2	2	no	—
181	C₁₉×#126	—	2	2	no	—
182	C₁₉×#126	—	2	1	no	—
183	C₁₉×#126	D₄	1	2	yes	—
184	C₁₉×#125	—	2	1	no	—
185	C₁₉×#125	—	2	2	no	—
186	C₁₉×#125	—	2	2	no	—
187	C₁₉×#125	—	2	2	no	—
188	C₁₉×#125	—	2	2	no	—
189	C₁₉×#125	—	2	2	no	—
190	C₁₉×#125	—	2	1	no	—
191	C₁₉×#125	D₄	1	1	yes	characteristic
192	C₁₉×#125	C₂³	1	2	yes	—
193	C₁₉×#125	C₂³	1	1	yes	characteristic
194	C₁₉×#124	—	2	1	no	—
195	C₁₉×#124	—	2	1	no	—
196	C₁₉×#124	D₄	1	1	yes	characteristic
197	C₁₉×#124	C₂³	1	1	yes	characteristic
198	C₁₉×#124	C₂³	1	2	yes	—
199	C₁₉×#123	—	2	2	no	—
200	C₁₉×#123	—	2	1	no	—
201	C₁₉×#123	—	2	2	no	—
202	C₁₉×#123	—	2	2	no	—
203	C₁₉×#123	—	2	2	no	—
204	C₁₉×#123	—	2	2	no	—
205	C₁₉×#123	D₄	1	2	yes	—
206	C₁₉×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
211	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₁₉×#121	—	2	2	no	—
216	C₁₉×#121	—	2	2	no	—
217	C₁₉×#121	—	2	2	no	—
218	C₁₉×#121	—	2	1	no	—
219	C₁₉×#121	—	2	1	no	—
220	C₁₉×#121	—	2	2	no	—
221	C₁₉×#121	—	2	2	no	—
222	C₁₉×#121	—	2	2	no	—
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	—	2	2	no	—
225	C₁₉×#121	D₄	1	1	yes	characteristic
226	C₁₉×#121	C₂³	1	1	yes	characteristic
227	C₁₉×#121	C₂³	1	2	yes	—
228	C₁₉×#121	C₂³	1	2	yes	—
229	C₁₉×#120	—	2	2	no	—
230	C₁₉×#120	—	2	2	no	—
231	C₁₉×#120	—	2	2	no	—
232	C₁₉×#120	—	2	2	no	—
233	C₁₉×#120	—	2	2	no	—
234	C₁₉×#120	—	2	2	no	—
235	C₄×Q₈×C₁₉	—	2	1	no	—
236	C₄×Q₈×C₁₉	—	2	2	no	—
237	C₄×Q₈×C₁₉	—	2	2	no	—
238	C₄×Q₈×C₁₉	—	2	1	no	—
239	C₄×Q₈×C₁₉	—	2	1	no	—
240	C₄×Q₈×C₁₉	—	2	1	no	—
241	C₄×Q₈×C₁₉	—	2	1	no	—
242	C₄×Q₈×C₁₉	—	2	1	no	—
243	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
246	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
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×Q₈×C₁₉	C₂³	1	2	yes	—
251	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₉	—	2	2	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	1	no	—
257	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₉	C₂³	1	2	yes	—
259	C₄×D₄×C₁₉	C₂³	1	2	yes	—
260	C₄×D₄×C₁₉	C₂³	1	2	yes	—
261	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	—	2	2	no	—
264	C₁₉×#117	—	2	2	no	—
265	C₁₉×#117	—	2	2	no	—
266	C₁₉×#117	—	2	1	no	—
267	C₁₉×#117	C₂³	1	2	yes	—
268	C₁₉×#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
272	C₂×C₄²×C₁₉	—	2	1	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	1	yes	characteristic
278	C₁₉×#106	C₂³	1	2	yes	—
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	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	1	yes	characteristic
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#103	C₂³	1	1	yes	characteristic
295	C₁₉×#103	C₂³	1	2	yes	—
296	C₁₉×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#102	C₂³	1	2	yes	—
305	C₁₉×#102	C₂³	1	1	yes	characteristic
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	2	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	C₂×Q₈×C₁₉	—	2	1	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	—	2	4	no	—
325	C₂×Q₈×C₁₉	—	4	1	no	—
326	C₂×Q₈×C₁₉	—	4	2	no	—
327	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
337	C₂×D₄×C₁₉	—	2	1	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	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	1	no	—
346	C₂×D₄×C₁₉	—	4	2	no	—
347	C₂×D₄×C₁₉	—	4	2	no	—
348	C₂×D₄×C₁₉	—	4	2	no	—
349	C₂×D₄×C₁₉	—	4	2	no	—
350	C₂×D₄×C₁₉	—	8	2	no	—
351	C₂×D₄×C₁₉	—	8	2	no	—
352	C₂×D₄×C₁₉	—	8	2	no	—
353	C₂×D₄×C₁₉	—	8	4	no	—
354	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
358	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₁₉	—	2	1	no	—
360	C₂²×C₄×C₁₉	—	2	1	no	—
361	C₂²×C₄×C₁₉	—	2	2	no	—
362	C₂²×C₄×C₁₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
370	Q₁₆×C₁₉	—	2	2	no	—
371	Q₁₆×C₁₉	—	4	1	no	—
372	Q₁₆×C₁₉	—	4	2	no	—
373	SD₁₆×C₁₉	—	2	2	no	—
374	SD₁₆×C₁₉	—	2	4	no	—
375	SD₁₆×C₁₉	—	2	4	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	SD₁₆×C₁₉	—	4	2	no	—
384	M₁₆×C₁₉	—	4	2	no	—
385	C₂×C₈×C₁₉	—	4	2	no	—
386	C₂×C₈×C₁₉	—	4	2	no	—
387	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
388	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
390	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₁₉	—	2	1	no	—
394	C₄⋊C₄×C₁₉	—	2	1	no	—
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	2	no	—
400	C₄⋊C₄×C₁₉	—	2	2	no	—
401	C₄⋊C₄×C₁₉	—	2	1	no	—
402	C₄⋊C₄×C₁₉	—	2	1	no	—
403	C₄⋊C₄×C₁₉	—	2	1	no	—
404	C₄⋊C₄×C₁₉	—	2	2	no	—
405	C₄⋊C₄×C₁₉	—	2	1	no	—
406	C₄⋊C₄×C₁₉	—	2	2	no	—
407	C₄⋊C₄×C₁₉	—	2	1	no	—
408	C₄⋊C₄×C₁₉	—	2	1	no	—
409	C₄⋊C₄×C₁₉	—	2	2	no	—
410	C₄⋊C₄×C₁₉	—	2	2	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	2	yes	—
416	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	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	2	no	—
432	C₂²⋊C₄×C₁₉	—	2	2	no	—
433	C₂²⋊C₄×C₁₉	—	2	1	no	—
434	C₂²⋊C₄×C₁₉	—	2	1	no	—
435	C₂²⋊C₄×C₁₉	—	2	1	no	—
436	C₂²⋊C₄×C₁₉	—	2	2	no	—
437	C₂²⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
446	C₄²×C₁₉	—	2	1	no	—
447	C₄²×C₁₉	—	2	1	no	—
448	C₄²×C₁₉	—	2	1	no	—
449	C₄²×C₁₉	—	2	1	no	—
450	C₄²×C₁₉	—	2	2	no	—
451	C₄²×C₁₉	—	2	2	no	—
452	C₄²×C₁₉	—	2	2	no	—
453	C₄²×C₁₉	—	2	1	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	#62055	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	—	4	4	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	C₂²×D₄	1	2	yes	—
471	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₁₉	—	2	2	no	—
473	Q₈×C₁₉	—	2	1	no	—
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	—	2	1	no	—
479	Q₈×C₁₉	—	2	1	no	—
480	Q₈×C₁₉	—	4	4	no	—
481	Q₈×C₁₉	—	4	2	no	—
482	Q₈×C₁₉	—	4	2	no	—
483	Q₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
484	D₄×C₁₉	—	2	4	no	—
485	D₄×C₁₉	—	2	2	no	—
486	D₄×C₁₉	—	2	1	no	—
487	D₄×C₁₉	—	2	2	no	—
488	D₄×C₁₉	—	2	2	no	—
489	D₄×C₁₉	—	2	1	no	—
490	D₄×C₁₉	—	2	2	no	—
491	D₄×C₁₉	—	2	2	no	—
492	D₄×C₁₉	—	4	2	no	—
493	D₄×C₁₉	—	4	2	no	—
494	D₄×C₁₉	—	4	2	no	—
495	D₄×C₁₉	—	8	2	no	—
496	D₄×C₁₉	—	8	2	no	—
497	D₄×C₁₉	—	8	2	no	—
498	D₄×C₁₉	—	8	1	no	—
499	D₄×C₁₉	—	8	2	no	—
500	D₄×C₁₉	—	8	1	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	C₂×C₄×C₁₉	—	2	2	no	—
507	C₂×C₄×C₁₉	—	2	1	no	—
508	C₂×C₄×C₁₉	—	2	2	no	—
509	C₂×C₄×C₁₉	—	2	1	no	—
510	C₂×C₄×C₁₉	—	2	2	no	—
511	C₂×C₄×C₁₉	—	2	1	no	—
512	C₂×C₄×C₁₉	—	2	2	no	—
513	C₂×C₄×C₁₉	—	2	1	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	—	4	2	no	—
522	C₂×C₄×C₁₉	—	4	4	no	—
523	C₂×C₄×C₁₉	—	4	2	no	—
524	C₂×C₄×C₁₉	—	4	2	no	—
525	C₂×C₄×C₁₉	—	8	2	no	—
526	C₂×C₄×C₁₉	—	8	2	no	—
527	C₂×C₄×C₁₉	—	8	2	no	—
528	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
537	C₈×C₁₉	—	2	1	no	—
538	C₈×C₁₉	—	2	2	no	—
539	C₈×C₁₉	—	2	2	no	—
540	C₈×C₁₉	—	2	1	no	—
541	C₈×C₁₉	—	2	1	no	—
542	C₈×C₁₉	—	2	1	no	—
543	#3543	C₂×C₁₉	1	1	yes	characteristic
544	#3523	C₂×C₁₉	1	1	yes	characteristic, complemented
545	#3400	C₂×C₁₉	1	1	yes	characteristic, complemented
546	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
547	#3368	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3365	C₂×C₁₉	1	1	yes	characteristic, complemented
549	#3324	C₂×C₁₉	1	1	yes	characteristic, complemented
550	#3310	C₂×C₁₉	1	2	yes	complemented
551	#3304	C₂×C₁₉	1	1	yes	characteristic, complemented
552	#3296	C₂×C₁₉	1	2	yes	complemented
553	D₄×SD₁₆	C₂×C₁₉	1	2	yes	complemented
554	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3278	C₂×C₁₉	1	1	yes	characteristic, complemented
556	#3266	C₂×C₁₉	1	2	yes	complemented
557	#3260	C₂×C₁₉	1	2	yes	complemented
558	#3248	C₂×C₁₉	1	1	yes	characteristic, complemented
559	#3222	C₂×C₁₉	1	2	yes	complemented
560	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
561	#3126	C₂×C₁₉	1	2	yes	complemented
562	#3108	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#3043	C₂×C₁₉	1	2	yes	complemented
564	C₂×#460	C₂×C₁₉	1	1	yes	characteristic, complemented
565	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
566	C₂²×C₁₉	—	2	1	no	—
567	C₂²×C₁₉	—	2	1	no	—
568	C₂²×C₁₉	—	2	2	no	—
569	C₂²×C₁₉	—	2	2	no	—
570	C₂²×C₁₉	—	2	2	no	—
571	C₂²×C₁₉	—	4	2	no	—
572	C₂²×C₁₉	—	4	1	no	—
573	C₂²×C₁₉	—	4	2	no	—
574	C₂²×C₁₉	—	4	1	no	—
575	C₂²×C₁₉	—	4	2	no	—
576	C₂²×C₁₉	—	4	2	no	—
577	C₂²×C₁₉	—	4	1	no	—
578	C₂²×C₁₉	—	4	2	no	—
579	C₂²×C₁₉	—	4	2	no	—
580	C₂²×C₁₉	—	16	4	no	—
581	C₂²×C₁₉	—	16	4	no	—
582	C₂²×C₁₉	#577	1	2	yes	—
583	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₁₉	—	2	2	no	—
585	C₄×C₁₉	—	2	1	no	—
586	C₄×C₁₉	—	2	2	no	—
587	C₄×C₁₉	—	2	1	no	—
588	C₄×C₁₉	—	2	1	no	—
589	C₄×C₁₉	—	2	1	no	—
590	C₄×C₁₉	—	2	2	no	—
591	C₄×C₁₉	—	2	2	no	—
592	C₄×C₁₉	—	4	1	no	—
593	C₄×C₁₉	—	4	2	no	—
594	C₄×C₁₉	—	4	1	no	—
595	C₄×C₁₉	—	4	1	no	—
596	C₄×C₁₉	—	4	1	no	—
597	C₄×C₁₉	—	4	1	no	—
598	C₄×C₁₉	—	4	1	no	—
599	C₄×C₁₉	—	4	2	no	—
600	C₄×C₁₉	#577	1	2	yes	—
601	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
602	C₄×C₁₉	#585	1	1	yes	characteristic
603	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
604	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
605	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
606	#560	—	2	2	no	—
607	#559	C₂²×C₁₉	1	1	yes	characteristic
608	#557	—	2	1	no	—
609	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
610	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
611	#556	—	2	1	no	—
612	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
613	#552	—	2	2	no	—
614	#552	C₂²×C₁₉	1	2	yes	complemented
615	#550	C₂²×C₁₉	1	1	yes	characteristic
616	#550	C₂²×C₁₉	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
618	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
619	#546	—	2	1	no	—
620	#546	C₂²×C₁₉	1	2	yes	—
621	D₄²	—	2	1	no	—
622	D₄²	C₂²×C₁₉	1	2	yes	—
623	D₄²	C₂²×C₁₉	1	1	yes	characteristic
624	#541	—	2	2	no	—
625	#541	C₂²×C₁₉	1	2	yes	complemented
626	#540	—	2	1	no	—
627	#540	C₂²×C₁₉	1	2	yes	—
628	#535	—	2	1	no	—
629	#535	C₂²×C₁₉	1	2	yes	—
630	#534	—	2	2	no	—
631	#533	—	2	1	no	—
632	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
633	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
634	#529	—	2	1	no	—
635	#529	C₂²×C₁₉	1	1	yes	characteristic
636	#529	C₂²×C₁₉	1	1	yes	characteristic
637	#519	C₂²×C₁₉	1	2	yes	complemented
638	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
639	#497	C₂²×C₁₉	1	2	yes	complemented
640	#492	C₂²×C₁₉	1	1	yes	characteristic
641	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
642	#492	C₂²×C₁₉	1	2	yes	complemented
643	#490	C₂²×C₁₉	1	2	yes	complemented
644	#488	C₂²×C₁₉	1	2	yes	complemented
645	#486	C₂²×C₁₉	1	1	yes	characteristic
646	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
647	#483	C₂²×C₁₉	1	1	yes	characteristic, complemented
648	#482	C₂²×C₁₉	1	2	yes	complemented
649	#482	C₂²×C₁₉	1	2	yes	complemented
650	#480	C₂²×C₁₉	1	1	yes	characteristic
651	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
652	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
653	#479	C₂²×C₁₉	1	2	yes	complemented
654	#478	C₂²×C₁₉	1	2	yes	complemented
655	#478	C₂²×C₁₉	1	2	yes	complemented
656	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
658	#468	C₂²×C₁₉	1	2	yes	complemented
659	#468	C₂²×C₁₉	1	2	yes	complemented
660	#467	C₂²×C₁₉	1	2	yes	complemented
661	#465	C₂²×C₁₉	1	2	yes	—
662	#465	C₂²×C₁₉	1	2	yes	complemented
663	#465	C₂²×C₁₉	1	2	yes	complemented
664	#464	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	#464	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	#464	C₂²×C₁₉	1	2	yes	complemented
667	#464	C₂²×C₁₉	1	2	yes	complemented
668	#464	C₂²×C₁₉	1	2	yes	complemented
669	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
671	#461	C₂²×C₁₉	1	2	yes	complemented
672	#461	C₂²×C₁₉	1	2	yes	complemented
673	#460	C₂²×C₁₉	1	1	yes	characteristic
674	#460	C₂²×C₁₉	1	1	yes	characteristic
675	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
676	#460	C₂²×C₁₉	1	2	yes	complemented
677	#460	C₂²×C₁₉	1	2	yes	complemented
678	#460	C₂²×C₁₉	1	2	yes	complemented
679	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
680	#460	C₂²×C₁₉	1	2	yes	complemented
681	#460	C₂²×C₁₉	1	2	yes	complemented
682	#460	C₂²×C₁₉	1	2	yes	complemented
683	#452	C₂²×C₁₉	1	2	yes	complemented
684	#452	C₂²×C₁₉	1	2	yes	complemented
685	#451	C₂²×C₁₉	1	1	yes	characteristic, complemented
686	#450	C₂²×C₁₉	1	2	yes	complemented
687	#450	C₂²×C₁₉	1	2	yes	complemented
688	#450	C₂²×C₁₉	1	2	yes	complemented
689	#450	C₂²×C₁₉	1	2	yes	complemented
690	#448	C₂²×C₁₉	1	1	yes	characteristic
691	#448	C₂²×C₁₉	1	2	yes	complemented
692	#448	C₂²×C₁₉	1	2	yes	complemented
693	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
694	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
695	#440	C₂²×C₁₉	1	2	yes	complemented
696	#440	C₂²×C₁₉	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
698	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
702	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
703	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
704	#435	C₂²×C₁₉	1	2	yes	complemented
705	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
706	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#433	C₂²×C₁₉	1	2	yes	complemented
708	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
709	#424	C₂²×C₁₉	1	2	yes	complemented
710	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
711	#418	C₂²×C₁₉	1	2	yes	complemented
712	#416	C₂²×C₁₉	1	2	yes	complemented
713	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
714	C₂×C₁₉	—	2	2	no	—
715	C₂×C₁₉	—	4	2	no	—
716	C₂×C₁₉	—	8	2	no	—
717	C₂×C₁₉	—	8	1	no	—
718	C₂×C₁₉	—	8	2	no	—
719	C₂×C₁₉	#3488	1	1	yes	characteristic
720	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
721	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₁₉	1	2	yes	—
724	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
725	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
731	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
732	#137	—	4	4	no	—
733	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
734	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
736	C₂×SD₁₆	—	4	4	no	—
737	C₂×SD₁₆	—	4	4	no	—
738	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
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	1	yes	characteristic
747	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
749	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
750	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
751	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
752	C₄⋊Q₈	—	2	1	no	—
753	C₄⋊Q₈	—	2	1	no	—
754	C₄⋊Q₈	—	2	2	no	—
755	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
756	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
757	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
758	#127	—	2	1	no	—
759	#127	—	2	1	no	—
760	#127	—	2	1	no	—
761	#127	C₂³×C₁₉	1	2	yes	—
762	#127	C₂³×C₁₉	1	1	yes	characteristic
763	#127	C₂³×C₁₉	1	1	yes	characteristic
764	#127	C₂³×C₁₉	1	2	yes	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#126	—	2	2	no	—
768	#126	—	2	2	no	—
769	#126	—	2	1	no	—
770	#126	D₄×C₁₉	1	2	yes	—
771	#125	—	2	1	no	—
772	#125	—	2	2	no	—
773	#125	—	2	2	no	—
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	1	no	—
782	#124	—	2	1	no	—
783	#124	D₄×C₁₉	1	1	yes	characteristic
784	#124	C₂³×C₁₉	1	1	yes	characteristic
785	#124	C₂³×C₁₉	1	2	yes	—
786	#123	—	2	2	no	—
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	D₄×C₁₉	1	2	yes	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	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	D₄×C₁₉	1	1	yes	characteristic
813	#121	C₂³×C₁₉	1	1	yes	characteristic
814	#121	C₂³×C₁₉	1	2	yes	—
815	#121	C₂³×C₁₉	1	2	yes	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	—	2	2	no	—
824	C₄×Q₈	—	2	2	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	—	2	1	no	—
827	C₄×Q₈	—	2	1	no	—
828	C₄×Q₈	—	2	1	no	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
831	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
832	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
833	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
834	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
835	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
836	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
837	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
838	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₁₉	1	2	yes	—
846	C₄×D₄	C₂³×C₁₉	1	2	yes	—
847	C₄×D₄	C₂³×C₁₉	1	2	yes	—
848	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
849	#117	—	2	1	no	—
850	#117	—	2	2	no	—
851	#117	—	2	2	no	—
852	#117	—	2	2	no	—
853	#117	—	2	1	no	—
854	#117	C₂³×C₁₉	1	2	yes	—
855	#117	C₂³×C₁₉	1	2	yes	—
856	C₂×C₄⋊C₄	—	2	1	no	—
857	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₄²	—	2	1	no	—
860	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
861	#107	C₂³×C₁₉	1	1	yes	characteristic
862	#107	C₂³×C₁₉	1	1	yes	characteristic
863	#107	C₂³×C₁₉	1	2	yes	—
864	#106	C₂³×C₁₉	1	1	yes	characteristic
865	#106	C₂³×C₁₉	1	2	yes	—
866	#106	C₂³×C₁₉	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
868	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
872	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
873	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
874	#103	C₂³×C₁₉	1	1	yes	characteristic
875	#103	C₂³×C₁₉	1	2	yes	—
876	#103	C₂³×C₁₉	1	1	yes	characteristic
877	#103	C₂³×C₁₉	1	1	yes	characteristic
878	#103	C₂³×C₁₉	1	2	yes	—
879	#103	C₂³×C₁₉	1	1	yes	characteristic
880	#103	C₂³×C₁₉	1	1	yes	characteristic
881	#103	C₂³×C₁₉	1	1	yes	characteristic
882	#103	C₂³×C₁₉	1	2	yes	—
883	#102	C₂³×C₁₉	1	2	yes	—
884	#102	C₂³×C₁₉	1	2	yes	—
885	#102	C₂³×C₁₉	1	2	yes	—
886	#102	C₂³×C₁₉	1	2	yes	—
887	#102	C₂³×C₁₉	1	2	yes	—
888	#102	C₂³×C₁₉	1	1	yes	characteristic
889	#102	C₂³×C₁₉	1	2	yes	—
890	#102	C₂³×C₁₉	1	2	yes	—
891	#102	C₂³×C₁₉	1	2	yes	—
892	#102	C₂³×C₁₉	1	1	yes	characteristic
893	#102	C₂³×C₁₉	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
895	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
898	#97	C₂³×C₁₉	1	2	yes	—
899	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₁₉	1	2	yes	—
902	C₁₉	#62055	1	1	yes	characteristic, direct product factor, Sylow
903	C₂⁴	—	2	2	no	—
904	C₂⁴	—	2	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	8	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	2	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	4	no	—
913	C₂×Q₈	—	4	1	no	—
914	C₂×Q₈	—	4	2	no	—
915	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
919	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	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	—	4	2	no	—
935	C₂×D₄	—	4	2	no	—
936	C₂×D₄	—	4	2	no	—
937	C₂×D₄	—	4	2	no	—
938	C₂×D₄	—	8	2	no	—
939	C₂×D₄	—	8	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	2	yes	—
945	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
955	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
958	Q₁₆	—	2	2	no	—
959	Q₁₆	—	4	1	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	2	4	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	2	no	—
968	SD₁₆	—	4	1	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	M₁₆	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
980	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	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	2	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1005	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1008	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1009	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1011	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1044	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1046	C₄²	C₂⁴×C₁₉	1	2	yes	—
1047	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	4	4	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	—	8	2	no	—
1057	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1058	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	4	4	no	—
1068	Q₈	—	4	2	no	—
1069	Q₈	—	4	2	no	—
1070	Q₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1071	D₄	—	2	4	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	1	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	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	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1123	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1124	C₈	—	2	1	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	—	16	4	no	—
1146	C₂²	C₁₉×#577	1	2	yes	—
1147	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	C₁₉×#577	1	2	yes	—
1165	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1166	C₄	C₁₉×#585	1	1	yes	characteristic
1167	C₂	—	2	2	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	2	no	—
1172	C₂	C₁₉×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1174	C₂	C₂×C₁₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3543	C₂
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
2. C₁₉×#3523	C₂	semidirect
3. C₁₉×#3400	C₂	semidirect
4. C₁₉×#3392	C₂	semidirect
5. C₁₉×#3368	C₂	semidirect
6. C₁₉×#3365	C₂	semidirect
7. C₁₉×#3324	C₂	semidirect
8. C₁₉×#3310	C₂	semidirect
9. C₁₉×#3304	C₂	semidirect
10. C₁₉×#3296	C₂	semidirect
11. D₄×SD₁₆×C₁₉	C₂	semidirect
12. D₄×SD₁₆×C₁₉	C₂	semidirect
13. C₁₉×#3278	C₂	semidirect
14. C₁₉×#3266	C₂	semidirect
15. C₁₉×#3260	C₂	semidirect
16. C₁₉×#3248	C₂	semidirect
17. C₁₉×#3222	C₂	semidirect
18. C₁₉×#3208	C₂	semidirect
19. C₁₉×#3126	C₂	semidirect
20. C₁₉×#3108	C₂	semidirect
21. C₁₉×#3043	C₂	semidirect
22. C₂×C₁₉×#460	C₂	semidirect
23. C₁₉×#2994	C₂	semidirect
24. C₂×C₁₉×#137	C₂²	semidirect
25. C₂²×SD₁₆×C₁₉	C₂²	semidirect
26. C₂²×SD₁₆×C₁₉	C₂²	semidirect
30. C₁₉×#557	C₂²	semidirect
31. C₁₉×#557	C₂²	semidirect
33. C₁₉×#556	C₂²	semidirect
35. C₁₉×#552	C₂²	semidirect
38. D₄×Q₈×C₁₉	C₂²	semidirect
39. D₄×Q₈×C₁₉	C₂²	semidirect
46. C₁₉×#541	C₂²	semidirect
53. C₁₉×#533	C₂²	semidirect
58. C₁₉×#519	C₂²	semidirect
59. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
60. C₁₉×#497	C₂²	semidirect
62. C₁₉×#492	C₂²	semidirect
63. C₁₉×#492	C₂²	semidirect
64. C₁₉×#490	C₂²	semidirect
65. C₁₉×#488	C₂²	semidirect
67. C₁₉×#486	C₂²	semidirect
68. C₁₉×#483	C₂²	semidirect
69. C₁₉×#482	C₂²	semidirect
70. C₁₉×#482	C₂²	semidirect
72. C₁₉×#479	C₂²	semidirect
73. C₁₉×#479	C₂²	semidirect
74. C₁₉×#479	C₂²	semidirect
75. C₁₉×#478	C₂²	semidirect
76. C₁₉×#478	C₂²	semidirect
77. C₁₉×#475	C₂²	semidirect
78. C₁₉×#474	C₂²	semidirect
79. C₁₉×#468	C₂²	semidirect
80. C₁₉×#468	C₂²	semidirect
81. C₁₉×#467	C₂²	semidirect
83. C₁₉×#465	C₂²	semidirect
84. C₁₉×#465	C₂²	semidirect
85. C₁₉×#464	C₂²	semidirect
86. C₁₉×#464	C₂²	semidirect
87. C₁₉×#464	C₂²	semidirect
88. C₁₉×#464	C₂²	semidirect
89. C₁₉×#464	C₂²	semidirect
90. C₁₉×#462	C₂²	semidirect
91. C₁₉×#461	C₂²	semidirect
92. C₁₉×#461	C₂²	semidirect
93. C₁₉×#461	C₂²	semidirect
96. C₁₉×#460	C₂²	semidirect
97. C₁₉×#460	C₂²	semidirect
98. C₁₉×#460	C₂²	semidirect
99. C₁₉×#460	C₂²	semidirect
100. C₁₉×#460	C₂²	semidirect
101. C₁₉×#460	C₂²	semidirect
102. C₁₉×#460	C₂²	semidirect
103. C₁₉×#460	C₂²	semidirect
104. C₁₉×#452	C₂²	semidirect
105. C₁₉×#452	C₂²	semidirect
106. C₁₉×#451	C₂²	semidirect
107. C₁₉×#450	C₂²	semidirect
108. C₁₉×#450	C₂²	semidirect
109. C₁₉×#450	C₂²	semidirect
110. C₁₉×#450	C₂²	semidirect
112. C₁₉×#448	C₂²	semidirect
113. C₁₉×#448	C₂²	semidirect
114. C₁₉×#446	C₂²	semidirect
115. C₈×Q₈×C₁₉	C₂²	semidirect
116. C₁₉×#440	C₂²	semidirect
117. C₁₉×#440	C₂²	semidirect
118. C₄×Q₁₆×C₁₉	C₂²	semidirect
119. C₄×Q₁₆×C₁₉	C₂²	semidirect
120. C₄×SD₁₆×C₁₉	C₂²	semidirect
121. C₄×SD₁₆×C₁₉	C₂²	semidirect
122. C₄×SD₁₆×C₁₉	C₂²	semidirect
123. C₄×SD₁₆×C₁₉	C₂²	semidirect
124. C₁₉×#436	C₂²	semidirect
125. C₁₉×#435	C₂²	semidirect
126. C₈×D₄×C₁₉	C₂²	semidirect
127. C₈×D₄×C₁₉	C₂²	semidirect
128. C₁₉×#433	C₂²	semidirect
129. C₁₉×#431	C₂²	semidirect
130. C₁₉×#424	C₂²	semidirect
131. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
132. C₁₉×#418	C₂²	semidirect
133. C₁₉×#416	C₂²	semidirect
134. C₂×C₁₉×#102	C₂²	semidirect
460. #62055	C₁₉	direct (N × H)
544. #3523	C₂×C₁₉	semidirect
545. #3400	C₂×C₁₉	semidirect
546. #3392	C₂×C₁₉	semidirect
547. #3368	C₂×C₁₉	semidirect
548. #3365	C₂×C₁₉	semidirect
549. #3324	C₂×C₁₉	semidirect
550. #3310	C₂×C₁₉	semidirect
551. #3304	C₂×C₁₉	semidirect
552. #3296	C₂×C₁₉	semidirect
553. D₄×SD₁₆	C₂×C₁₉	semidirect
554. D₄×SD₁₆	C₂×C₁₉	semidirect
555. #3278	C₂×C₁₉	semidirect
556. #3266	C₂×C₁₉	semidirect
557. #3260	C₂×C₁₉	semidirect
558. #3248	C₂×C₁₉	semidirect
559. #3222	C₂×C₁₉	semidirect
560. #3208	C₂×C₁₉	semidirect
561. #3126	C₂×C₁₉	semidirect
562. #3108	C₂×C₁₉	semidirect
563. #3043	C₂×C₁₉	semidirect
564. C₂×#460	C₂×C₁₉	semidirect
565. #2994	C₂×C₁₉	semidirect
603. C₂×#137	C₂²×C₁₉	semidirect
604. C₂²×SD₁₆	C₂²×C₁₉	semidirect
605. C₂²×SD₁₆	C₂²×C₁₉	semidirect
609. #557	C₂²×C₁₉	semidirect
610. #557	C₂²×C₁₉	semidirect
612. #556	C₂²×C₁₉	semidirect
614. #552	C₂²×C₁₉	semidirect
617. D₄×Q₈	C₂²×C₁₉	semidirect
618. D₄×Q₈	C₂²×C₁₉	semidirect
625. #541	C₂²×C₁₉	semidirect
632. #533	C₂²×C₁₉	semidirect
637. #519	C₂²×C₁₉	semidirect
638. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
639. #497	C₂²×C₁₉	semidirect
641. #492	C₂²×C₁₉	semidirect
642. #492	C₂²×C₁₉	semidirect
643. #490	C₂²×C₁₉	semidirect
644. #488	C₂²×C₁₉	semidirect
646. #486	C₂²×C₁₉	semidirect
647. #483	C₂²×C₁₉	semidirect
648. #482	C₂²×C₁₉	semidirect
649. #482	C₂²×C₁₉	semidirect
651. #479	C₂²×C₁₉	semidirect
652. #479	C₂²×C₁₉	semidirect
653. #479	C₂²×C₁₉	semidirect
654. #478	C₂²×C₁₉	semidirect
655. #478	C₂²×C₁₉	semidirect
656. #475	C₂²×C₁₉	semidirect
657. #474	C₂²×C₁₉	semidirect
658. #468	C₂²×C₁₉	semidirect
659. #468	C₂²×C₁₉	semidirect
660. #467	C₂²×C₁₉	semidirect
662. #465	C₂²×C₁₉	semidirect
663. #465	C₂²×C₁₉	semidirect
664. #464	C₂²×C₁₉	semidirect
665. #464	C₂²×C₁₉	semidirect
666. #464	C₂²×C₁₉	semidirect
667. #464	C₂²×C₁₉	semidirect
668. #464	C₂²×C₁₉	semidirect
669. #462	C₂²×C₁₉	semidirect
670. #461	C₂²×C₁₉	semidirect
671. #461	C₂²×C₁₉	semidirect
672. #461	C₂²×C₁₉	semidirect
675. #460	C₂²×C₁₉	semidirect
676. #460	C₂²×C₁₉	semidirect
677. #460	C₂²×C₁₉	semidirect
678. #460	C₂²×C₁₉	semidirect
679. #460	C₂²×C₁₉	semidirect
680. #460	C₂²×C₁₉	semidirect
681. #460	C₂²×C₁₉	semidirect
682. #460	C₂²×C₁₉	semidirect
683. #452	C₂²×C₁₉	semidirect
684. #452	C₂²×C₁₉	semidirect
685. #451	C₂²×C₁₉	semidirect
686. #450	C₂²×C₁₉	semidirect
687. #450	C₂²×C₁₉	semidirect
688. #450	C₂²×C₁₉	semidirect
689. #450	C₂²×C₁₉	semidirect
691. #448	C₂²×C₁₉	semidirect
692. #448	C₂²×C₁₉	semidirect
693. #446	C₂²×C₁₉	semidirect
694. C₈×Q₈	C₂²×C₁₉	semidirect
695. #440	C₂²×C₁₉	semidirect
696. #440	C₂²×C₁₉	semidirect
697. C₄×Q₁₆	C₂²×C₁₉	semidirect
698. C₄×Q₁₆	C₂²×C₁₉	semidirect
699. C₄×SD₁₆	C₂²×C₁₉	semidirect
700. C₄×SD₁₆	C₂²×C₁₉	semidirect
701. C₄×SD₁₆	C₂²×C₁₉	semidirect
702. C₄×SD₁₆	C₂²×C₁₉	semidirect
703. #436	C₂²×C₁₉	semidirect
704. #435	C₂²×C₁₉	semidirect
705. C₈×D₄	C₂²×C₁₉	semidirect
706. C₈×D₄	C₂²×C₁₉	semidirect
707. #433	C₂²×C₁₉	semidirect
708. #431	C₂²×C₁₉	semidirect
709. #424	C₂²×C₁₉	semidirect
710. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
711. #418	C₂²×C₁₉	semidirect
712. #416	C₂²×C₁₉	semidirect
713. C₂×#102	C₂²×C₁₉	semidirect
902. C₁₉	#62055	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3543	2
C₁₉×#3523	2
C₁₉×#3400	2
C₁₉×#3392	2
C₁₉×#3368	2
C₁₉×#3365	2
C₁₉×#3324	2
C₁₉×#3310	2
C₁₉×#3304	2
C₁₉×#3296	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3278	2
C₁₉×#3266	2
C₁₉×#3260	2
C₁₉×#3248	2
C₁₉×#3222	2
C₁₉×#3208	2
C₁₉×#3126	2
C₁₉×#3108	2
C₁₉×#3043	2
C₂×C₁₉×#460	2
C₁₉×#2994	2
#62055	19

Subgroups — C19×#62055 #18068014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62055 #18068014