Subgroups — C₁₉×#62057 #18068016

Order 4864.

1946 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×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3306	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3294	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3282	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3265	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3257	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3224	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3119	C₂	1	2	yes	maximal, complemented
20	C₁₉×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3045	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×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
27	C₁₉×#560	—	2	2	no	—
28	C₁₉×#559	—	2	1	no	—
29	C₁₉×#559	C₂²	1	1	yes	characteristic
30	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
31	Q₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#554	—	2	1	no	—
33	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#550	C₂²	1	1	yes	characteristic
35	C₁₉×#550	C₂²	1	1	yes	characteristic
36	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#548	C₂²	1	2	yes	complemented
38	C₁₉×#547	—	2	2	no	—
39	C₁₉×#547	C₂²	1	2	yes	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×#542	—	2	2	no	—
46	C₁₉×#542	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×#532	—	2	1	no	—
53	C₁₉×#532	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×#520	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#496	C₂²	1	2	yes	complemented
61	C₁₉×#495	C₂²	1	2	yes	complemented
62	C₁₉×#493	C₂²	1	1	yes	characteristic
63	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#489	C₂²	1	2	yes	complemented
65	C₁₉×#486	C₂²	1	1	yes	characteristic
66	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#486	C₂²	1	2	yes	complemented
68	C₁₉×#483	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#481	C₂²	1	2	yes	complemented
70	C₁₉×#480	C₂²	1	1	yes	characteristic
71	C₁₉×#480	C₂²	1	2	yes	complemented
72	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×#479	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#478	C₂²	1	2	yes	complemented
75	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#476	C₂²	1	2	yes	complemented
78	C₁₉×#474	C₂²	1	2	yes	complemented
79	C₁₉×#469	C₂²	1	2	yes	complemented
80	C₁₉×#468	C₂²	1	2	yes	complemented
81	C₁₉×#466	C₂²	1	2	yes	—
82	C₁₉×#466	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
88	C₁₉×#463	C₂²	1	2	yes	complemented
89	C₁₉×#463	C₂²	1	2	yes	complemented
90	C₁₉×#463	C₂²	1	2	yes	complemented
91	C₁₉×#463	C₂²	1	2	yes	complemented
92	C₁₉×#460	C₂²	1	1	yes	characteristic
93	C₁₉×#460	C₂²	1	1	yes	characteristic
94	C₁₉×#460	C₂²	1	2	yes	complemented
95	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
96	C₁₉×#460	C₂²	1	2	yes	complemented
97	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
98	C₁₉×#460	C₂²	1	2	yes	complemented
99	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
100	C₁₉×#459	C₂²	1	2	yes	complemented
101	C₁₉×#459	C₂²	1	2	yes	complemented
102	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
103	C₁₉×#459	C₂²	1	2	yes	complemented
104	C₁₉×#452	C₂²	1	2	yes	complemented
105	C₁₉×#451	C₂²	1	1	yes	characteristic, complemented
106	C₁₉×#450	C₂²	1	2	yes	complemented
107	C₁₉×#449	C₂²	1	2	yes	complemented
108	C₁₉×#449	C₂²	1	2	yes	complemented
109	C₁₉×#449	C₂²	1	2	yes	complemented
110	C₁₉×#448	C₂²	1	1	yes	characteristic
111	C₁₉×#447	C₂²	1	2	yes	complemented
112	C₁₉×#447	C₂²	1	2	yes	complemented
113	C₁₉×#447	C₂²	1	2	yes	complemented
114	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
116	C₁₉×#442	C₂²	1	2	yes	complemented
117	C₁₉×#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	1	yes	characteristic, complemented
123	C₄×D₈×C₁₉	C₂²	1	2	yes	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×#417	C₂²	1	2	yes	complemented
133	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
134	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	2	no	—
137	C₂×#41×C₁₉	—	2	1	no	—
138	C₂×#41×C₁₉	C₂³	1	2	yes	—
139	C₂×#41×C₁₉	C₂³	1	2	yes	—
140	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₁₉	—	2	2	no	—
142	C₂²×D₄×C₁₉	—	2	1	no	—
143	C₂²×D₄×C₁₉	—	2	1	no	—
144	C₂²×D₄×C₁₉	—	2	1	no	—
145	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
146	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
147	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
148	C₁₉×#135	—	4	4	no	—
149	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₁₉	—	4	4	no	—
152	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
160	C₂×D₈×C₁₉	C₂³	1	2	yes	—
161	C₂×D₈×C₁₉	C₂³	1	2	yes	—
162	C₂×D₈×C₁₉	C₂³	1	2	yes	—
163	C₂×D₈×C₁₉	C₂³	1	2	yes	—
164	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
165	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
166	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
167	C₁₉×C₄⋊Q₈	—	2	1	no	—
168	C₁₉×C₄⋊Q₈	—	2	2	no	—
169	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×#127	—	2	1	no	—
172	C₁₉×#127	—	2	1	no	—
173	C₁₉×#127	—	2	1	no	—
174	C₁₉×#127	—	2	1	no	—
175	C₁₉×#127	C₂³	1	2	yes	—
176	C₁₉×#127	C₂³	1	2	yes	—
177	C₁₉×#127	C₂³	1	1	yes	characteristic
178	C₁₉×#127	C₂³	1	1	yes	characteristic
179	C₁₉×#127	C₂³	1	1	yes	characteristic
180	C₁₉×#126	—	2	2	no	—
181	C₁₉×#126	—	2	1	no	—
182	C₁₉×#126	D₄	1	2	yes	—
183	C₁₉×#125	—	2	1	no	—
184	C₁₉×#125	D₄	1	1	yes	characteristic
185	C₁₉×#125	C₂³	1	1	yes	characteristic
186	C₁₉×#124	—	2	1	no	—
187	C₁₉×#124	—	2	1	no	—
188	C₁₉×#124	—	2	2	no	—
189	C₁₉×#124	—	2	2	no	—
190	C₁₉×#124	—	2	1	no	—
191	C₁₉×#124	D₄	1	1	yes	characteristic
192	C₁₉×#124	C₂³	1	1	yes	characteristic
193	C₁₉×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
203	C₁₉×#123	—	2	2	no	—
204	C₁₉×#123	D₄	1	2	yes	—
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	D₄	1	1	yes	characteristic
210	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₉×#121	—	2	2	no	—
213	C₁₉×#121	—	2	1	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	1	no	—
219	C₁₉×#121	—	2	2	no	—
220	C₁₉×#121	—	2	2	no	—
221	C₁₉×#121	—	2	2	no	—
222	C₁₉×#121	—	2	2	no	—
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	—	2	2	no	—
225	C₁₉×#121	D₄	1	1	yes	characteristic
226	C₁₉×#121	C₂³	1	2	yes	—
227	C₁₉×#121	C₂³	1	2	yes	—
228	C₁₉×#121	C₂³	1	1	yes	characteristic
229	C₁₉×#121	C₂³	1	2	yes	—
230	C₁₉×#121	C₂³	1	2	yes	—
231	C₁₉×#120	—	2	2	no	—
232	C₁₉×#120	—	2	2	no	—
233	C₁₉×#120	—	2	2	no	—
234	C₁₉×#120	—	2	2	no	—
235	C₁₉×#120	—	2	2	no	—
236	C₁₉×#120	—	2	2	no	—
237	C₄×Q₈×C₁₉	—	2	1	no	—
238	C₄×Q₈×C₁₉	—	2	1	no	—
239	C₄×Q₈×C₁₉	—	2	1	no	—
240	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
251	C₄×D₄×C₁₉	—	2	1	no	—
252	C₄×D₄×C₁₉	—	2	1	no	—
253	C₄×D₄×C₁₉	—	2	2	no	—
254	C₄×D₄×C₁₉	—	2	2	no	—
255	C₄×D₄×C₁₉	—	2	2	no	—
256	C₄×D₄×C₁₉	—	2	1	no	—
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	C₄×D₄×C₁₉	C₂³	1	2	yes	—
261	C₄×D₄×C₁₉	C₂³	1	2	yes	—
262	C₄×D₄×C₁₉	C₂³	1	2	yes	—
263	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
264	C₁₉×#117	—	2	2	no	—
265	C₁₉×#117	—	2	1	no	—
266	C₁₉×#117	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
269	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
292	C₁₉×#103	C₂³	1	1	yes	characteristic
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#102	C₂³	1	2	yes	—
295	C₁₉×#102	C₂³	1	1	yes	characteristic
296	C₁₉×#102	C₂³	1	2	yes	—
297	C₁₉×#102	C₂³	1	2	yes	—
298	C₁₉×#102	C₂³	1	2	yes	—
299	C₁₉×#102	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	2	yes	—
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	1	yes	characteristic
304	C₁₉×#102	C₂³	1	2	yes	—
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	2	no	—
316	C₂⁴×C₁₉	—	2	2	no	—
317	#41×C₁₉	—	2	4	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	4	no	—
323	#41×C₁₉	—	8	2	no	—
324	C₂×Q₈×C₁₉	—	2	1	no	—
325	C₂×Q₈×C₁₉	—	2	2	no	—
326	C₂×Q₈×C₁₉	—	2	1	no	—
327	C₂×Q₈×C₁₉	—	2	2	no	—
328	C₂×Q₈×C₁₉	—	4	1	no	—
329	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₁₉	—	2	2	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	1	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	—	2	2	no	—
347	C₂×D₄×C₁₉	—	2	2	no	—
348	C₂×D₄×C₁₉	—	2	2	no	—
349	C₂×D₄×C₁₉	—	2	2	no	—
350	C₂×D₄×C₁₉	—	2	1	no	—
351	C₂×D₄×C₁₉	—	2	1	no	—
352	C₂×D₄×C₁₉	—	4	2	no	—
353	C₂×D₄×C₁₉	—	4	2	no	—
354	C₂×D₄×C₁₉	—	4	2	no	—
355	C₂×D₄×C₁₉	—	4	2	no	—
356	C₂×D₄×C₁₉	—	8	2	no	—
357	C₂×D₄×C₁₉	—	8	2	no	—
358	C₂×D₄×C₁₉	—	8	2	no	—
359	C₂×D₄×C₁₉	—	8	4	no	—
360	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
361	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
362	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
363	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
365	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₁₉	—	2	1	no	—
367	C₂²×C₄×C₁₉	—	2	1	no	—
368	C₂²×C₄×C₁₉	—	2	2	no	—
369	C₂²×C₄×C₁₉	—	2	2	no	—
370	C₂²×C₄×C₁₉	—	2	1	no	—
371	C₂²×C₄×C₁₉	—	2	2	no	—
372	C₂²×C₄×C₁₉	—	2	2	no	—
373	C₂²×C₄×C₁₉	—	2	2	no	—
374	C₂²×C₄×C₁₉	—	2	2	no	—
375	C₂²×C₄×C₁₉	—	2	2	no	—
376	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
380	Q₁₆×C₁₉	—	2	2	no	—
381	Q₁₆×C₁₉	—	4	1	no	—
382	SD₁₆×C₁₉	—	2	4	no	—
383	SD₁₆×C₁₉	—	2	4	no	—
384	SD₁₆×C₁₉	—	2	2	no	—
385	SD₁₆×C₁₉	—	4	2	no	—
386	SD₁₆×C₁₉	—	4	2	no	—
387	SD₁₆×C₁₉	—	4	1	no	—
388	SD₁₆×C₁₉	—	4	2	no	—
389	D₈×C₁₉	—	4	2	no	—
390	D₈×C₁₉	—	4	2	no	—
391	D₈×C₁₉	—	4	2	no	—
392	D₈×C₁₉	—	4	2	no	—
393	D₈×C₁₉	—	4	2	no	—
394	M₁₆×C₁₉	—	4	2	no	—
395	C₂×C₈×C₁₉	—	4	2	no	—
396	C₂×C₈×C₁₉	—	4	2	no	—
397	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
399	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
400	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₁₉	—	2	1	no	—
404	C₄⋊C₄×C₁₉	—	2	2	no	—
405	C₄⋊C₄×C₁₉	—	2	2	no	—
406	C₄⋊C₄×C₁₉	—	2	1	no	—
407	C₄⋊C₄×C₁₉	—	2	1	no	—
408	C₄⋊C₄×C₁₉	—	2	1	no	—
409	C₄⋊C₄×C₁₉	—	2	1	no	—
410	C₄⋊C₄×C₁₉	—	2	1	no	—
411	C₄⋊C₄×C₁₉	—	2	1	no	—
412	C₄⋊C₄×C₁₉	—	2	1	no	—
413	C₄⋊C₄×C₁₉	—	2	1	no	—
414	C₄⋊C₄×C₁₉	—	2	2	no	—
415	C₄⋊C₄×C₁₉	—	2	2	no	—
416	C₄⋊C₄×C₁₉	—	2	1	no	—
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	1	yes	characteristic
420	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
428	C₂²⋊C₄×C₁₉	—	2	1	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	2	no	—
434	C₂²⋊C₄×C₁₉	—	2	1	no	—
435	C₂²⋊C₄×C₁₉	—	2	1	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	2	no	—
440	C₂²⋊C₄×C₁₉	—	2	2	no	—
441	C₂²⋊C₄×C₁₉	—	2	2	no	—
442	C₂²⋊C₄×C₁₉	—	2	2	no	—
443	C₂²⋊C₄×C₁₉	—	2	1	no	—
444	C₂²⋊C₄×C₁₉	—	2	2	no	—
445	C₂²⋊C₄×C₁₉	—	2	2	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	1	no	—
452	C₄²×C₁₉	—	2	1	no	—
453	C₄²×C₁₉	—	2	1	no	—
454	C₄²×C₁₉	—	2	1	no	—
455	C₄²×C₁₉	—	2	1	no	—
456	C₄²×C₁₉	—	2	2	no	—
457	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
460	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
461	C₄²×C₁₉	C₂⁴	1	2	yes	—
462	#62057	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂³×C₁₉	—	2	2	no	—
464	C₂³×C₁₉	—	2	2	no	—
465	C₂³×C₁₉	—	2	1	no	—
466	C₂³×C₁₉	—	2	2	no	—
467	C₂³×C₁₉	—	4	4	no	—
468	C₂³×C₁₉	—	8	2	no	—
469	C₂³×C₁₉	—	8	2	no	—
470	C₂³×C₁₉	—	8	2	no	—
471	C₂³×C₁₉	—	8	2	no	—
472	C₂³×C₁₉	—	8	2	no	—
473	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
474	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
475	Q₈×C₁₉	—	2	2	no	—
476	Q₈×C₁₉	—	2	1	no	—
477	Q₈×C₁₉	—	2	1	no	—
478	Q₈×C₁₉	—	2	1	no	—
479	Q₈×C₁₉	—	2	1	no	—
480	Q₈×C₁₉	—	2	1	no	—
481	Q₈×C₁₉	—	4	2	no	—
482	Q₈×C₁₉	—	8	1	no	—
483	Q₈×C₁₉	—	8	2	no	—
484	Q₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
485	D₄×C₁₉	—	2	4	no	—
486	D₄×C₁₉	—	2	2	no	—
487	D₄×C₁₉	—	2	2	no	—
488	D₄×C₁₉	—	2	1	no	—
489	D₄×C₁₉	—	2	2	no	—
490	D₄×C₁₉	—	2	2	no	—
491	D₄×C₁₉	—	2	2	no	—
492	D₄×C₁₉	—	2	2	no	—
493	D₄×C₁₉	—	2	2	no	—
494	D₄×C₁₉	—	2	1	no	—
495	D₄×C₁₉	—	4	4	no	—
496	D₄×C₁₉	—	4	2	no	—
497	D₄×C₁₉	—	4	4	no	—
498	D₄×C₁₉	—	4	2	no	—
499	D₄×C₁₉	—	4	2	no	—
500	D₄×C₁₉	—	4	2	no	—
501	D₄×C₁₉	—	8	2	no	—
502	D₄×C₁₉	—	8	2	no	—
503	D₄×C₁₉	—	8	2	no	—
504	D₄×C₁₉	—	8	1	no	—
505	D₄×C₁₉	—	8	1	no	—
506	D₄×C₁₉	—	8	2	no	—
507	D₄×C₁₉	—	8	2	no	—
508	D₄×C₁₉	—	8	1	no	—
509	D₄×C₁₉	—	8	2	no	—
510	D₄×C₁₉	—	8	2	no	—
511	D₄×C₁₉	—	8	2	no	—
512	D₄×C₁₉	—	8	2	no	—
513	D₄×C₁₉	—	8	2	no	—
514	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	1	no	—
520	C₂×C₄×C₁₉	—	2	2	no	—
521	C₂×C₄×C₁₉	—	2	1	no	—
522	C₂×C₄×C₁₉	—	2	1	no	—
523	C₂×C₄×C₁₉	—	2	1	no	—
524	C₂×C₄×C₁₉	—	2	1	no	—
525	C₂×C₄×C₁₉	—	2	1	no	—
526	C₂×C₄×C₁₉	—	2	2	no	—
527	C₂×C₄×C₁₉	—	2	1	no	—
528	C₂×C₄×C₁₉	—	4	4	no	—
529	C₂×C₄×C₁₉	—	4	2	no	—
530	C₂×C₄×C₁₉	—	4	2	no	—
531	C₂×C₄×C₁₉	—	4	2	no	—
532	C₂×C₄×C₁₉	—	8	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	—	8	2	no	—
537	C₂×C₄×C₁₉	—	8	2	no	—
538	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
547	C₈×C₁₉	—	2	1	no	—
548	C₈×C₁₉	—	2	2	no	—
549	C₈×C₁₉	—	2	2	no	—
550	C₈×C₁₉	—	2	1	no	—
551	C₈×C₁₉	—	2	1	no	—
552	C₈×C₁₉	—	2	1	no	—
553	#3543	C₂×C₁₉	1	1	yes	characteristic, complemented
554	#3522	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3399	C₂×C₁₉	1	1	yes	characteristic, complemented
556	#3396	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#3375	C₂×C₁₉	1	1	yes	characteristic, complemented
558	#3362	C₂×C₁₉	1	1	yes	characteristic, complemented
559	#3333	C₂×C₁₉	1	1	yes	characteristic, complemented
560	#3306	C₂×C₁₉	1	2	yes	complemented
561	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
562	#3294	C₂×C₁₉	1	2	yes	complemented
563	#3287	C₂×C₁₉	1	1	yes	characteristic, complemented
564	#3282	C₂×C₁₉	1	2	yes	complemented
565	#3274	C₂×C₁₉	1	1	yes	characteristic, complemented
566	#3265	C₂×C₁₉	1	2	yes	complemented
567	#3257	C₂×C₁₉	1	2	yes	complemented
568	#3247	C₂×C₁₉	1	1	yes	characteristic, complemented
569	#3224	C₂×C₁₉	1	2	yes	complemented
570	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
571	#3119	C₂×C₁₉	1	2	yes	complemented
572	#3108	C₂×C₁₉	1	1	yes	characteristic, complemented
573	#3045	C₂×C₁₉	1	2	yes	complemented
574	C₂×#460	C₂×C₁₉	1	1	yes	characteristic, complemented
575	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
576	C₂²×C₁₉	—	2	1	no	—
577	C₂²×C₁₉	—	2	1	no	—
578	C₂²×C₁₉	—	2	2	no	—
579	C₂²×C₁₉	—	2	2	no	—
580	C₂²×C₁₉	—	2	2	no	—
581	C₂²×C₁₉	—	4	2	no	—
582	C₂²×C₁₉	—	4	2	no	—
583	C₂²×C₁₉	—	4	1	no	—
584	C₂²×C₁₉	—	4	2	no	—
585	C₂²×C₁₉	—	4	2	no	—
586	C₂²×C₁₉	—	4	2	no	—
587	C₂²×C₁₉	—	4	1	no	—
588	C₂²×C₁₉	—	4	2	no	—
589	C₂²×C₁₉	—	4	1	no	—
590	C₂²×C₁₉	—	4	2	no	—
591	C₂²×C₁₉	—	4	2	no	—
592	C₂²×C₁₉	—	4	2	no	—
593	C₂²×C₁₉	—	16	4	no	—
594	C₂²×C₁₉	—	16	4	no	—
595	C₂²×C₁₉	#576	1	2	yes	—
596	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₁₉	—	2	2	no	—
598	C₄×C₁₉	—	2	1	no	—
599	C₄×C₁₉	—	2	2	no	—
600	C₄×C₁₉	—	2	1	no	—
601	C₄×C₁₉	—	2	1	no	—
602	C₄×C₁₉	—	2	2	no	—
603	C₄×C₁₉	—	2	1	no	—
604	C₄×C₁₉	—	2	2	no	—
605	C₄×C₁₉	—	4	1	no	—
606	C₄×C₁₉	—	4	1	no	—
607	C₄×C₁₉	—	4	1	no	—
608	C₄×C₁₉	—	4	1	no	—
609	C₄×C₁₉	—	4	1	no	—
610	C₄×C₁₉	—	4	2	no	—
611	C₄×C₁₉	—	4	1	no	—
612	C₄×C₁₉	#577	1	2	yes	—
613	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
614	C₄×C₁₉	#585	1	1	yes	characteristic
615	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
616	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
617	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
618	#560	—	2	2	no	—
619	#559	—	2	1	no	—
620	#559	C₂²×C₁₉	1	1	yes	characteristic
621	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
622	Q₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
623	#554	—	2	1	no	—
624	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
625	#550	C₂²×C₁₉	1	1	yes	characteristic
626	#550	C₂²×C₁₉	1	1	yes	characteristic
627	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
628	#548	C₂²×C₁₉	1	2	yes	complemented
629	#547	—	2	2	no	—
630	#547	C₂²×C₁₉	1	2	yes	complemented
631	#546	—	2	1	no	—
632	#546	C₂²×C₁₉	1	2	yes	—
633	D₄²	—	2	1	no	—
634	D₄²	C₂²×C₁₉	1	2	yes	—
635	D₄²	C₂²×C₁₉	1	1	yes	characteristic
636	#542	—	2	2	no	—
637	#542	C₂²×C₁₉	1	2	yes	complemented
638	#540	—	2	1	no	—
639	#540	C₂²×C₁₉	1	2	yes	—
640	#535	—	2	1	no	—
641	#535	C₂²×C₁₉	1	2	yes	—
642	#534	—	2	2	no	—
643	#532	—	2	1	no	—
644	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
646	#529	—	2	1	no	—
647	#529	C₂²×C₁₉	1	1	yes	characteristic
648	#529	C₂²×C₁₉	1	1	yes	characteristic
649	#520	C₂²×C₁₉	1	2	yes	complemented
650	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
651	#496	C₂²×C₁₉	1	2	yes	complemented
652	#495	C₂²×C₁₉	1	2	yes	complemented
653	#493	C₂²×C₁₉	1	1	yes	characteristic
654	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
655	#489	C₂²×C₁₉	1	2	yes	complemented
656	#486	C₂²×C₁₉	1	1	yes	characteristic
657	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
658	#486	C₂²×C₁₉	1	2	yes	complemented
659	#483	C₂²×C₁₉	1	1	yes	characteristic, complemented
660	#481	C₂²×C₁₉	1	2	yes	complemented
661	#480	C₂²×C₁₉	1	1	yes	characteristic
662	#480	C₂²×C₁₉	1	2	yes	complemented
663	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
664	#479	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	#478	C₂²×C₁₉	1	2	yes	complemented
666	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	#476	C₂²×C₁₉	1	2	yes	complemented
669	#474	C₂²×C₁₉	1	2	yes	complemented
670	#469	C₂²×C₁₉	1	2	yes	complemented
671	#468	C₂²×C₁₉	1	2	yes	complemented
672	#466	C₂²×C₁₉	1	2	yes	—
673	#466	C₂²×C₁₉	1	2	yes	complemented
674	#465	C₂²×C₁₉	1	2	yes	complemented
675	#465	C₂²×C₁₉	1	2	yes	complemented
676	#464	C₂²×C₁₉	1	1	yes	characteristic, complemented
677	#464	C₂²×C₁₉	1	1	yes	characteristic, complemented
678	#464	C₂²×C₁₉	1	2	yes	complemented
679	#463	C₂²×C₁₉	1	2	yes	complemented
680	#463	C₂²×C₁₉	1	2	yes	complemented
681	#463	C₂²×C₁₉	1	2	yes	complemented
682	#463	C₂²×C₁₉	1	2	yes	complemented
683	#460	C₂²×C₁₉	1	1	yes	characteristic
684	#460	C₂²×C₁₉	1	1	yes	characteristic
685	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
686	#460	C₂²×C₁₉	1	2	yes	complemented
687	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
688	#460	C₂²×C₁₉	1	2	yes	complemented
689	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
690	#460	C₂²×C₁₉	1	2	yes	complemented
691	#459	C₂²×C₁₉	1	2	yes	complemented
692	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
693	#459	C₂²×C₁₉	1	2	yes	complemented
694	#459	C₂²×C₁₉	1	2	yes	complemented
695	#452	C₂²×C₁₉	1	2	yes	complemented
696	#451	C₂²×C₁₉	1	1	yes	characteristic, complemented
697	#450	C₂²×C₁₉	1	2	yes	complemented
698	#449	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	1	yes	characteristic
702	#447	C₂²×C₁₉	1	2	yes	complemented
703	#447	C₂²×C₁₉	1	2	yes	complemented
704	#447	C₂²×C₁₉	1	2	yes	complemented
705	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
706	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#442	C₂²×C₁₉	1	2	yes	complemented
708	#440	C₂²×C₁₉	1	2	yes	complemented
709	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
710	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
711	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
712	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
713	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
714	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
715	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
716	#435	C₂²×C₁₉	1	2	yes	complemented
717	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
718	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
719	#433	C₂²×C₁₉	1	2	yes	complemented
720	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
721	#424	C₂²×C₁₉	1	2	yes	complemented
722	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
723	#417	C₂²×C₁₉	1	2	yes	complemented
724	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
725	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
726	C₂×C₁₉	—	2	2	no	—
727	C₂×C₁₉	—	4	2	no	—
728	C₂×C₁₉	—	8	2	no	—
729	C₂×C₁₉	—	8	2	no	—
730	C₂×C₁₉	—	8	2	no	—
731	C₂×C₁₉	—	8	1	no	—
732	C₂×C₁₉	#3488	1	1	yes	characteristic
733	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
734	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	2	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	C₂³×C₁₉	1	2	yes	—
739	C₂×#41	C₂³×C₁₉	1	2	yes	—
740	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
741	C₂²×D₄	—	2	2	no	—
742	C₂²×D₄	—	2	1	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
746	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
747	AGL(1,ℤ/8)	—	4	4	no	—
748	#135	—	4	4	no	—
749	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
750	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
751	C₂×SD₁₆	—	4	4	no	—
752	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
755	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
759	C₂×D₈	C₂³×C₁₉	1	2	yes	—
760	C₂×D₈	C₂³×C₁₉	1	2	yes	—
761	C₂×D₈	C₂³×C₁₉	1	2	yes	—
762	C₂×D₈	C₂³×C₁₉	1	2	yes	—
763	C₂×D₈	C₂³×C₁₉	1	2	yes	—
764	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
765	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
766	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
767	C₄⋊Q₈	—	2	1	no	—
768	C₄⋊Q₈	—	2	2	no	—
769	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
771	#127	—	2	1	no	—
772	#127	—	2	1	no	—
773	#127	—	2	1	no	—
774	#127	—	2	1	no	—
775	#127	C₂³×C₁₉	1	2	yes	—
776	#127	C₂³×C₁₉	1	1	yes	characteristic
777	#127	C₂³×C₁₉	1	1	yes	characteristic
778	#127	C₂³×C₁₉	1	1	yes	characteristic
779	#127	C₂³×C₁₉	1	2	yes	—
780	#126	—	2	2	no	—
781	#126	—	2	1	no	—
782	#126	D₄×C₁₉	1	2	yes	—
783	#125	—	2	1	no	—
784	#125	D₄×C₁₉	1	1	yes	characteristic
785	#125	C₂³×C₁₉	1	1	yes	characteristic
786	#124	—	2	1	no	—
787	#124	—	2	1	no	—
788	#124	—	2	2	no	—
789	#124	—	2	2	no	—
790	#124	—	2	1	no	—
791	#124	D₄×C₁₉	1	1	yes	characteristic
792	#124	C₂³×C₁₉	1	1	yes	characteristic
793	#124	C₂³×C₁₉	1	2	yes	—
794	#124	C₂³×C₁₉	1	2	yes	—
795	#123	—	2	1	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	D₄×C₁₉	1	2	yes	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
810	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
811	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
812	#121	—	2	2	no	—
813	#121	—	2	1	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	D₄×C₁₉	1	1	yes	characteristic
826	#121	C₂³×C₁₉	1	1	yes	characteristic
827	#121	C₂³×C₁₉	1	2	yes	—
828	#121	C₂³×C₁₉	1	2	yes	—
829	#121	C₂³×C₁₉	1	2	yes	—
830	#121	C₂³×C₁₉	1	2	yes	—
831	#120	—	2	2	no	—
832	#120	—	2	2	no	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
841	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
842	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
843	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
844	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
845	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
846	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	C₂³×C₁₉	1	2	yes	—
858	C₄×D₄	C₂³×C₁₉	1	2	yes	—
859	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
860	C₄×D₄	C₂³×C₁₉	1	2	yes	—
861	C₄×D₄	C₂³×C₁₉	1	2	yes	—
862	C₄×D₄	C₂³×C₁₉	1	2	yes	—
863	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
864	#117	—	2	2	no	—
865	#117	—	2	1	no	—
866	#117	C₂³×C₁₉	1	2	yes	—
867	C₂×C₄⋊C₄	—	2	1	no	—
868	C₂×C₄⋊C₄	—	2	2	no	—
869	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
871	C₂×C₂²⋊C₄	—	2	2	no	—
872	C₂×C₄²	—	2	1	no	—
873	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
874	#107	C₂³×C₁₉	1	1	yes	characteristic
875	#107	C₂³×C₁₉	1	1	yes	characteristic
876	#107	C₂³×C₁₉	1	2	yes	—
877	#106	C₂³×C₁₉	1	1	yes	characteristic
878	#106	C₂³×C₁₉	1	2	yes	—
879	#106	C₂³×C₁₉	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
881	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
885	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
886	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
887	#103	C₂³×C₁₉	1	1	yes	characteristic
888	#103	C₂³×C₁₉	1	2	yes	—
889	#103	C₂³×C₁₉	1	1	yes	characteristic
890	#103	C₂³×C₁₉	1	1	yes	characteristic
891	#103	C₂³×C₁₉	1	1	yes	characteristic
892	#103	C₂³×C₁₉	1	1	yes	characteristic
893	#103	C₂³×C₁₉	1	1	yes	characteristic
894	#102	C₂³×C₁₉	1	2	yes	—
895	#102	C₂³×C₁₉	1	1	yes	characteristic
896	#102	C₂³×C₁₉	1	2	yes	—
897	#102	C₂³×C₁₉	1	2	yes	—
898	#102	C₂³×C₁₉	1	2	yes	—
899	#102	C₂³×C₁₉	1	2	yes	—
900	#102	C₂³×C₁₉	1	2	yes	—
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	2	yes	—
905	#102	C₂³×C₁₉	1	2	yes	—
906	#102	C₂³×C₁₉	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
908	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
910	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
911	#97	C₂³×C₁₉	1	2	yes	—
912	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
913	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₁₉	1	2	yes	—
915	C₁₉	#62057	1	1	yes	characteristic, direct product factor, Sylow
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	2	no	—
918	#41	—	2	4	no	—
919	#41	—	4	2	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	8	2	no	—
923	#41	—	8	4	no	—
924	#41	—	8	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	2	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	2	no	—
929	C₂×Q₈	—	4	1	no	—
930	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
931	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
932	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
933	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	4	2	no	—
954	C₂×D₄	—	4	2	no	—
955	C₂×D₄	—	4	2	no	—
956	C₂×D₄	—	4	2	no	—
957	C₂×D₄	—	8	2	no	—
958	C₂×D₄	—	8	2	no	—
959	C₂×D₄	—	8	2	no	—
960	C₂×D₄	—	8	4	no	—
961	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
962	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
963	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
964	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
965	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
966	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
978	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
980	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
981	Q₁₆	—	2	2	no	—
982	Q₁₆	—	4	1	no	—
983	SD₁₆	—	2	4	no	—
984	SD₁₆	—	2	4	no	—
985	SD₁₆	—	2	2	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	SD₁₆	—	4	1	no	—
989	SD₁₆	—	4	2	no	—
990	D₈	—	4	2	no	—
991	D₈	—	4	2	no	—
992	D₈	—	4	2	no	—
993	D₈	—	4	2	no	—
994	D₈	—	4	2	no	—
995	M₁₆	—	4	2	no	—
996	C₂×C₈	—	4	2	no	—
997	C₂×C₈	—	4	2	no	—
998	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1020	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1021	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1022	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1026	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1027	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
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	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1059	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₁₉	1	2	yes	—
1062	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	4	4	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	—	8	2	no	—
1073	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1074	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	1	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	8	1	no	—
1083	Q₈	—	8	2	no	—
1084	Q₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1085	D₄	—	2	4	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	2	no	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	2	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	4	4	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	4	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	1	no	—
1105	D₄	—	8	1	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	2	no	—
1112	D₄	—	8	2	no	—
1113	D₄	—	8	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	1	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
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	C₂²×D₄×C₁₉	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1145	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1146	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1147	C₈	—	2	1	no	—
1148	C₈	—	2	2	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	16	4	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	C₁₉×#576	1	2	yes	—
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	2	no	—
1180	C₄	—	2	1	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	C₁₉×#577	1	2	yes	—
1190	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1191	C₄	C₁₉×#585	1	1	yes	characteristic
1192	C₂	—	2	2	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	8	2	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	2	no	—
1198	C₂	C₁₉×#3488	1	1	yes	characteristic
1199	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
1200	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×#3543	C₂	semidirect
2. C₁₉×#3522	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3396	C₂	semidirect
5. C₁₉×#3375	C₂	semidirect
6. C₁₉×#3362	C₂	semidirect
7. C₁₉×#3333	C₂	semidirect
8. C₁₉×#3306	C₂	semidirect
9. C₁₉×#3295	C₂	semidirect
10. C₁₉×#3294	C₂	semidirect
11. C₁₉×#3287	C₂	semidirect
12. C₁₉×#3282	C₂	semidirect
13. C₁₉×#3274	C₂	semidirect
14. C₁₉×#3265	C₂	semidirect
15. C₁₉×#3257	C₂	semidirect
16. C₁₉×#3247	C₂	semidirect
17. C₁₉×#3224	C₂	semidirect
18. C₁₉×#3205	C₂	semidirect
19. C₁₉×#3119	C₂	semidirect
20. C₁₉×#3108	C₂	semidirect
21. C₁₉×#3045	C₂	semidirect
22. C₂×C₁₉×#460	C₂	semidirect
23. C₁₉×#2994	C₂	semidirect
24. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₉×#135	C₂²	semidirect
26. C₂²×SD₁₆×C₁₉	C₂²	semidirect
30. C₁₉×#559	C₂²	semidirect
31. Q₈²×C₁₉	C₂²	semidirect
33. C₁₉×#554	C₂²	semidirect
36. C₁₉×#550	C₂²	semidirect
37. C₁₉×#548	C₂²	semidirect
39. C₁₉×#547	C₂²	semidirect
46. C₁₉×#542	C₂²	semidirect
53. C₁₉×#532	C₂²	semidirect
58. C₁₉×#520	C₂²	semidirect
59. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
60. C₁₉×#496	C₂²	semidirect
61. C₁₉×#495	C₂²	semidirect
63. C₁₉×#493	C₂²	semidirect
64. C₁₉×#489	C₂²	semidirect
66. C₁₉×#486	C₂²	semidirect
67. C₁₉×#486	C₂²	semidirect
68. C₁₉×#483	C₂²	semidirect
69. C₁₉×#481	C₂²	semidirect
71. C₁₉×#480	C₂²	semidirect
72. C₁₉×#479	C₂²	semidirect
73. C₁₉×#479	C₂²	semidirect
74. C₁₉×#478	C₂²	semidirect
75. C₁₉×#477	C₂²	semidirect
76. C₁₉×#476	C₂²	semidirect
77. C₁₉×#476	C₂²	semidirect
78. C₁₉×#474	C₂²	semidirect
79. C₁₉×#469	C₂²	semidirect
80. C₁₉×#468	C₂²	semidirect
82. C₁₉×#466	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×#463	C₂²	semidirect
89. C₁₉×#463	C₂²	semidirect
90. C₁₉×#463	C₂²	semidirect
91. C₁₉×#463	C₂²	semidirect
94. C₁₉×#460	C₂²	semidirect
95. C₁₉×#460	C₂²	semidirect
96. C₁₉×#460	C₂²	semidirect
97. C₁₉×#460	C₂²	semidirect
98. C₁₉×#460	C₂²	semidirect
99. C₁₉×#460	C₂²	semidirect
100. C₁₉×#459	C₂²	semidirect
101. C₁₉×#459	C₂²	semidirect
102. C₁₉×#459	C₂²	semidirect
103. C₁₉×#459	C₂²	semidirect
104. C₁₉×#452	C₂²	semidirect
105. C₁₉×#451	C₂²	semidirect
106. C₁₉×#450	C₂²	semidirect
107. C₁₉×#449	C₂²	semidirect
108. C₁₉×#449	C₂²	semidirect
109. C₁₉×#449	C₂²	semidirect
111. C₁₉×#447	C₂²	semidirect
112. C₁₉×#447	C₂²	semidirect
113. C₁₉×#447	C₂²	semidirect
114. C₁₉×#446	C₂²	semidirect
115. C₈×Q₈×C₁₉	C₂²	semidirect
116. C₁₉×#442	C₂²	semidirect
117. C₁₉×#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×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×#417	C₂²	semidirect
133. C₂×C₁₉×#102	C₂²	semidirect
134. C₂×C₁₉×#102	C₂²	semidirect
462. #62057	C₁₉	direct (N × H)
553. #3543	C₂×C₁₉	semidirect
554. #3522	C₂×C₁₉	semidirect
555. #3399	C₂×C₁₉	semidirect
556. #3396	C₂×C₁₉	semidirect
557. #3375	C₂×C₁₉	semidirect
558. #3362	C₂×C₁₉	semidirect
559. #3333	C₂×C₁₉	semidirect
560. #3306	C₂×C₁₉	semidirect
561. #3295	C₂×C₁₉	semidirect
562. #3294	C₂×C₁₉	semidirect
563. #3287	C₂×C₁₉	semidirect
564. #3282	C₂×C₁₉	semidirect
565. #3274	C₂×C₁₉	semidirect
566. #3265	C₂×C₁₉	semidirect
567. #3257	C₂×C₁₉	semidirect
568. #3247	C₂×C₁₉	semidirect
569. #3224	C₂×C₁₉	semidirect
570. #3205	C₂×C₁₉	semidirect
571. #3119	C₂×C₁₉	semidirect
572. #3108	C₂×C₁₉	semidirect
573. #3045	C₂×C₁₉	semidirect
574. C₂×#460	C₂×C₁₉	semidirect
575. #2994	C₂×C₁₉	semidirect
615. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
616. C₂×#135	C₂²×C₁₉	semidirect
617. C₂²×SD₁₆	C₂²×C₁₉	semidirect
621. #559	C₂²×C₁₉	semidirect
622. Q₈²	C₂²×C₁₉	semidirect
624. #554	C₂²×C₁₉	semidirect
627. #550	C₂²×C₁₉	semidirect
628. #548	C₂²×C₁₉	semidirect
630. #547	C₂²×C₁₉	semidirect
637. #542	C₂²×C₁₉	semidirect
644. #532	C₂²×C₁₉	semidirect
649. #520	C₂²×C₁₉	semidirect
650. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
651. #496	C₂²×C₁₉	semidirect
652. #495	C₂²×C₁₉	semidirect
654. #493	C₂²×C₁₉	semidirect
655. #489	C₂²×C₁₉	semidirect
657. #486	C₂²×C₁₉	semidirect
658. #486	C₂²×C₁₉	semidirect
659. #483	C₂²×C₁₉	semidirect
660. #481	C₂²×C₁₉	semidirect
662. #480	C₂²×C₁₉	semidirect
663. #479	C₂²×C₁₉	semidirect
664. #479	C₂²×C₁₉	semidirect
665. #478	C₂²×C₁₉	semidirect
666. #477	C₂²×C₁₉	semidirect
667. #476	C₂²×C₁₉	semidirect
668. #476	C₂²×C₁₉	semidirect
669. #474	C₂²×C₁₉	semidirect
670. #469	C₂²×C₁₉	semidirect
671. #468	C₂²×C₁₉	semidirect
673. #466	C₂²×C₁₉	semidirect
674. #465	C₂²×C₁₉	semidirect
675. #465	C₂²×C₁₉	semidirect
676. #464	C₂²×C₁₉	semidirect
677. #464	C₂²×C₁₉	semidirect
678. #464	C₂²×C₁₉	semidirect
679. #463	C₂²×C₁₉	semidirect
680. #463	C₂²×C₁₉	semidirect
681. #463	C₂²×C₁₉	semidirect
682. #463	C₂²×C₁₉	semidirect
685. #460	C₂²×C₁₉	semidirect
686. #460	C₂²×C₁₉	semidirect
687. #460	C₂²×C₁₉	semidirect
688. #460	C₂²×C₁₉	semidirect
689. #460	C₂²×C₁₉	semidirect
690. #460	C₂²×C₁₉	semidirect
691. #459	C₂²×C₁₉	semidirect
692. #459	C₂²×C₁₉	semidirect
693. #459	C₂²×C₁₉	semidirect
694. #459	C₂²×C₁₉	semidirect
695. #452	C₂²×C₁₉	semidirect
696. #451	C₂²×C₁₉	semidirect
697. #450	C₂²×C₁₉	semidirect
698. #449	C₂²×C₁₉	semidirect
699. #449	C₂²×C₁₉	semidirect
700. #449	C₂²×C₁₉	semidirect
702. #447	C₂²×C₁₉	semidirect
703. #447	C₂²×C₁₉	semidirect
704. #447	C₂²×C₁₉	semidirect
705. #446	C₂²×C₁₉	semidirect
706. C₈×Q₈	C₂²×C₁₉	semidirect
707. #442	C₂²×C₁₉	semidirect
708. #440	C₂²×C₁₉	semidirect
709. C₄×Q₁₆	C₂²×C₁₉	semidirect
710. C₄×Q₁₆	C₂²×C₁₉	semidirect
711. C₄×SD₁₆	C₂²×C₁₉	semidirect
712. C₄×SD₁₆	C₂²×C₁₉	semidirect
713. C₄×SD₁₆	C₂²×C₁₉	semidirect
714. C₄×D₈	C₂²×C₁₉	semidirect
715. #436	C₂²×C₁₉	semidirect
716. #435	C₂²×C₁₉	semidirect
717. C₈×D₄	C₂²×C₁₉	semidirect
718. C₈×D₄	C₂²×C₁₉	semidirect
719. #433	C₂²×C₁₉	semidirect
720. #431	C₂²×C₁₉	semidirect
721. #424	C₂²×C₁₉	semidirect
722. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
723. #417	C₂²×C₁₉	semidirect
724. C₂×#102	C₂²×C₁₉	semidirect
725. C₂×#102	C₂²×C₁₉	semidirect
915. C₁₉	#62057	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×#3522	2
C₁₉×#3399	2
C₁₉×#3396	2
C₁₉×#3375	2
C₁₉×#3362	2
C₁₉×#3333	2
C₁₉×#3306	2
C₁₉×#3295	2
C₁₉×#3294	2
C₁₉×#3287	2
C₁₉×#3282	2
C₁₉×#3274	2
C₁₉×#3265	2
C₁₉×#3257	2
C₁₉×#3247	2
C₁₉×#3224	2
C₁₉×#3205	2
C₁₉×#3119	2
C₁₉×#3108	2
C₁₉×#3045	2
C₂×C₁₉×#460	2
C₁₉×#2994	2
#62057	19

Subgroups — C19×#62057 #18068016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62057 #18068016