Subgroups — C₁₉×#60344 #18066303

Order 4864.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2995	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2995	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2993	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2985	C₂	1	2	yes	maximal, complemented
12	C₁₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2969	C₂	1	2	yes	maximal, complemented
16	C₁₉×#2968	C₂	1	2	yes	maximal, complemented
17	C₁₉×#2967	C₂	1	2	yes	maximal, complemented
18	C₁₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₉×#2961	C₂	1	2	yes	maximal, complemented
23	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×#544	C₄	1	1	yes	characteristic
25	C₁₉×#542	C₄	1	1	yes	characteristic
26	C₁₉×#542	C₄	1	1	yes	characteristic
27	C₁₉×#542	C₄	1	2	yes	—
28	C₁₉×#541	C₄	1	1	yes	characteristic
29	C₁₉×#541	C₄	1	1	yes	characteristic
30	C₁₉×#541	C₄	1	2	yes	—
31	C₁₉×#539	C₄	1	2	yes	—
32	C₁₉×#539	C₄	1	2	yes	—
33	C₁₉×#537	C₄	1	1	yes	characteristic
34	C₁₉×#536	C₄	1	1	yes	characteristic
35	C₁₉×#536	C₄	1	1	yes	characteristic
36	C₁₉×#533	C₂²	1	1	yes	characteristic
37	C₁₉×#533	C₂²	1	2	yes	—
38	C₁₉×#533	C₂²	1	1	yes	characteristic
39	C₁₉×#529	C₂²	1	1	yes	characteristic
40	C₁₉×#529	C₂²	1	2	yes	—
41	C₁₉×#529	C₂²	1	2	yes	—
42	C₁₉×#529	C₂²	1	1	yes	characteristic
43	C₁₉×#529	C₂²	1	2	yes	—
44	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#446	C₂²	1	2	yes	—
48	C₁₉×#446	C₂²	1	1	yes	characteristic
49	C₁₉×#446	C₂²	1	1	yes	characteristic
50	C₁₉×#446	C₂²	1	1	yes	characteristic
51	C₁₉×#446	C₂²	1	2	yes	—
52	C₁₉×#446	C₂²	1	2	yes	—
53	C₁₉×#446	C₂²	1	2	yes	—
54	C₁₉×#446	C₂²	1	2	yes	—
55	C₁₉×#446	C₂²	1	2	yes	—
56	C₁₉×#446	C₂²	1	2	yes	—
57	C₁₉×#446	C₂²	1	1	yes	characteristic
58	C₁₉×#446	C₂²	1	2	yes	—
59	C₁₉×#446	C₂²	1	1	yes	characteristic
60	C₁₉×#446	C₂²	1	2	yes	—
61	C₁₉×#446	C₂²	1	1	yes	characteristic
62	C₁₉×#446	C₂²	1	1	yes	characteristic
63	C₁₉×#446	C₂²	1	2	yes	—
64	C₁₉×#446	C₂²	1	2	yes	—
65	C₁₉×#446	C₂²	1	1	yes	characteristic
66	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
67	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
68	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
69	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
70	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
71	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
72	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
73	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
74	C₁₉×#436	C₂²	1	1	yes	characteristic
75	C₁₉×#436	C₂²	1	1	yes	characteristic
76	C₁₉×#436	C₂²	1	1	yes	characteristic
77	C₁₉×#436	C₂²	1	2	yes	—
78	C₁₉×#436	C₂²	1	2	yes	—
79	C₁₉×#436	C₂²	1	1	yes	characteristic
80	C₁₉×#436	C₂²	1	2	yes	—
81	C₁₉×#436	C₂²	1	2	yes	—
82	C₁₉×#436	C₂²	1	2	yes	—
83	C₁₉×#435	C₂²	1	1	yes	characteristic
84	C₁₉×#435	C₂²	1	1	yes	characteristic
85	C₁₉×#435	C₂²	1	1	yes	characteristic
86	C₁₉×#435	C₂²	1	1	yes	characteristic
87	C₁₉×#435	C₂²	1	2	yes	—
88	C₁₉×#435	C₂²	1	2	yes	—
89	C₁₉×#435	C₂²	1	2	yes	—
90	C₁₉×#435	C₂²	1	2	yes	—
91	C₁₉×#435	C₂²	1	2	yes	—
92	C₁₉×#435	C₂²	1	2	yes	—
93	C₁₉×#435	C₂²	1	2	yes	—
94	C₁₉×#435	C₂²	1	2	yes	—
95	C₈×D₄×C₁₉	C₂²	1	2	yes	—
96	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
97	C₈×D₄×C₁₉	C₂²	1	2	yes	—
98	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
99	C₁₉×#433	C₂²	1	2	yes	—
100	C₁₉×#433	C₂²	1	2	yes	—
101	C₁₉×#433	C₂²	1	2	yes	—
102	C₁₉×#433	C₂²	1	2	yes	—
103	C₁₉×#433	C₂²	1	2	yes	—
104	C₁₉×#433	C₂²	1	2	yes	—
105	C₁₉×#433	C₂²	1	2	yes	—
106	C₁₉×#433	C₂²	1	2	yes	—
107	C₁₉×#432	C₂²	1	1	yes	characteristic
108	C₁₉×#432	C₂²	1	2	yes	—
109	C₁₉×#432	C₂²	1	1	yes	characteristic
110	C₁₉×#432	C₂²	1	2	yes	—
111	C₁₉×#431	C₂²	1	1	yes	characteristic
112	C₁₉×#431	C₂²	1	1	yes	characteristic
113	C₁₉×#431	C₂²	1	1	yes	characteristic
114	C₁₉×#431	C₂²	1	2	yes	—
115	C₁₉×#431	C₂²	1	2	yes	—
116	C₁₉×#431	C₂²	1	1	yes	characteristic
117	C₁₉×#424	C₂²	1	2	yes	—
118	C₁₉×#424	C₂²	1	2	yes	—
119	C₁₉×#424	C₂²	1	2	yes	—
120	C₁₉×#424	C₂²	1	2	yes	—
121	C₁₉×#423	C₂²	1	1	yes	characteristic
122	C₁₉×#423	C₂²	1	2	yes	—
123	C₁₉×#423	C₂²	1	1	yes	characteristic
124	C₁₉×#423	C₂²	1	2	yes	—
125	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₁₉×#405	C₂²	1	2	yes	—
127	C₁₉×#405	C₂²	1	2	yes	—
128	C₁₉×#405	C₂²	1	2	yes	—
129	C₁₉×#405	C₂²	1	2	yes	—
130	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
131	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
132	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
133	C₂×C₁₉×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
137	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
138	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
142	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
144	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
145	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
148	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
150	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
151	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
152	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
153	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
154	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
155	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
156	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
157	C₁₉×#126	C₂×C₄	1	2	yes	—
158	C₁₉×#126	C₂×C₄	1	2	yes	—
159	C₁₉×#126	C₂×C₄	1	2	yes	—
160	C₁₉×#126	C₂×C₄	1	2	yes	—
161	C₁₉×#126	C₂×C₄	1	2	yes	—
162	C₁₉×#126	C₂×C₄	1	2	yes	—
163	C₁₉×#126	C₂×C₄	1	2	yes	—
164	C₁₉×#126	C₂×C₄	1	2	yes	—
165	C₁₉×#125	C₂×C₄	1	2	yes	—
166	C₁₉×#125	C₂×C₄	1	2	yes	—
167	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
168	C₁₉×#125	C₂×C₄	1	2	yes	—
169	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
170	C₁₉×#125	C₂×C₄	1	2	yes	—
171	C₁₉×#125	C₂×C₄	1	2	yes	—
172	C₁₉×#125	C₂×C₄	1	2	yes	—
173	C₁₉×#125	C₂×C₄	1	2	yes	—
174	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
175	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
176	C₁₉×#124	C₂×C₄	1	2	yes	—
177	C₁₉×#124	C₂×C₄	1	2	yes	—
178	C₁₉×#124	C₂×C₄	1	2	yes	—
179	C₁₉×#123	C₂×C₄	1	2	yes	—
180	C₁₉×#123	C₂×C₄	1	2	yes	—
181	C₁₉×#123	C₂×C₄	1	2	yes	—
182	C₁₉×#123	C₂×C₄	1	2	yes	—
183	C₁₉×#123	C₂×C₄	1	2	yes	—
184	C₁₉×#123	C₂×C₄	1	2	yes	—
185	C₁₉×#123	C₂×C₄	1	2	yes	—
186	C₁₉×#123	C₂×C₄	1	2	yes	—
187	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
188	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
189	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
193	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
194	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
195	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
196	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
197	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
198	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
199	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
200	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
201	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
202	C₁₉×#121	C₂×C₄	1	2	yes	—
203	C₁₉×#121	C₂×C₄	1	2	yes	—
204	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
205	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
206	C₁₉×#121	C₂×C₄	1	2	yes	—
207	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
208	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
209	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
210	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
211	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
212	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
216	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
218	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
222	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
223	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₁₉	C₂³	1	2	yes	—
226	C₄×D₄×C₁₉	C₂³	1	2	yes	—
227	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₁₉	C₂³	1	2	yes	—
230	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
231	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
232	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
233	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
234	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
235	C₁₉×#117	C₂×C₄	1	2	yes	—
236	C₁₉×#117	C₂³	1	2	yes	—
237	C₁₉×#117	C₂³	1	2	yes	—
238	C₁₉×#117	C₂³	1	2	yes	—
239	C₁₉×#117	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
242	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
244	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
247	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
248	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
252	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
255	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
258	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
259	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
260	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
263	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
264	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
265	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
268	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
271	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
272	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₁₉×#97	C₂³	1	1	yes	characteristic
286	C₁₉×#97	C₂³	1	2	yes	—
287	C₁₉×#97	C₂³	1	2	yes	—
288	C₁₉×#97	C₂³	1	2	yes	—
289	C₁₉×#97	C₂³	1	1	yes	characteristic
290	C₁₉×#97	C₂³	1	2	yes	—
291	C₁₉×#97	C₂³	1	1	yes	characteristic
292	C₁₉×#97	C₂³	1	1	yes	characteristic
293	C₁₉×#97	C₂³	1	2	yes	—
294	C₁₉×#97	C₂³	1	2	yes	—
295	C₁₉×#97	C₂³	1	2	yes	—
296	C₁₉×#97	C₂³	1	2	yes	—
297	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
299	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
300	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
301	C₄×C₈×C₁₉	C₂³	1	2	yes	—
302	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
303	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
304	C₄×C₈×C₁₉	C₂³	1	2	yes	—
305	C₄×C₈×C₁₉	C₂³	1	2	yes	—
306	C₄×C₈×C₁₉	C₂³	1	2	yes	—
307	C₄×C₈×C₁₉	C₂³	1	2	yes	—
308	C₄×C₈×C₁₉	C₂³	1	2	yes	—
309	C₄×C₈×C₁₉	C₂³	1	2	yes	—
310	#41×C₁₉	—	4	2	no	—
311	#41×C₁₉	—	4	2	no	—
312	C₂×Q₈×C₁₉	—	4	2	no	—
313	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
314	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
315	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
317	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
319	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
320	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
321	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
324	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
326	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
327	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
328	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
329	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
331	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
332	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
333	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
334	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
336	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
341	M₁₆×C₁₉	—	2	2	no	—
342	M₁₆×C₁₉	—	2	2	no	—
343	M₁₆×C₁₉	—	4	1	no	—
344	M₁₆×C₁₉	—	4	2	no	—
345	M₁₆×C₁₉	—	4	2	no	—
346	M₁₆×C₁₉	—	4	1	no	—
347	M₁₆×C₁₉	—	4	2	no	—
348	M₁₆×C₁₉	—	4	2	no	—
349	C₂×C₈×C₁₉	—	2	2	no	—
350	C₂×C₈×C₁₉	—	2	4	no	—
351	C₂×C₈×C₁₉	—	4	2	no	—
352	C₂×C₈×C₁₉	—	4	2	no	—
353	C₂×C₈×C₁₉	—	4	1	no	—
354	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
356	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
359	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
361	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
362	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
368	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
369	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
376	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
379	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
381	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
383	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
384	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
385	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
386	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
388	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
389	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
390	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
391	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
392	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
394	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
395	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
397	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
398	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
399	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
400	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
401	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
402	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
403	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
405	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
407	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
409	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
410	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
411	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
413	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
415	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
417	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
420	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
421	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
422	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
423	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
424	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
426	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
427	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
428	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
429	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
430	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
431	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
432	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
433	C₄²×C₁₉	C₂⁴	1	2	yes	—
434	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
435	C₄²×C₁₉	C₂⁴	1	2	yes	—
436	C₄²×C₁₉	C₂⁴	1	2	yes	—
437	#60344	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
439	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
440	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
441	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
442	Q₈×C₁₉	—	2	2	no	—
443	Q₈×C₁₉	—	2	2	no	—
444	Q₈×C₁₉	—	2	2	no	—
445	Q₈×C₁₉	—	4	2	no	—
446	Q₈×C₁₉	—	4	2	no	—
447	Q₈×C₁₉	—	4	2	no	—
448	Q₈×C₁₉	—	4	1	no	—
449	D₄×C₁₉	—	2	2	no	—
450	D₄×C₁₉	—	4	2	no	—
451	D₄×C₁₉	—	4	2	no	—
452	D₄×C₁₉	—	4	1	no	—
453	D₄×C₁₉	—	4	1	no	—
454	D₄×C₁₉	—	4	1	no	—
455	D₄×C₁₉	—	4	2	no	—
456	C₂×C₄×C₁₉	—	2	2	no	—
457	C₂×C₄×C₁₉	—	2	2	no	—
458	C₂×C₄×C₁₉	—	2	2	no	—
459	C₂×C₄×C₁₉	—	2	1	no	—
460	C₂×C₄×C₁₉	—	2	2	no	—
461	C₂×C₄×C₁₉	—	2	1	no	—
462	C₂×C₄×C₁₉	—	2	1	no	—
463	C₂×C₄×C₁₉	—	2	1	no	—
464	C₂×C₄×C₁₉	—	2	2	no	—
465	C₂×C₄×C₁₉	—	2	1	no	—
466	C₂×C₄×C₁₉	—	2	1	no	—
467	C₂×C₄×C₁₉	—	4	1	no	—
468	C₂×C₄×C₁₉	—	4	1	no	—
469	C₂×C₄×C₁₉	—	4	2	no	—
470	C₂×C₄×C₁₉	—	4	1	no	—
471	C₂×C₄×C₁₉	—	4	2	no	—
472	C₂×C₄×C₁₉	—	4	2	no	—
473	C₂×C₄×C₁₉	—	4	2	no	—
474	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
477	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
479	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
480	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
481	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
483	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
484	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
485	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
486	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
487	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
488	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
490	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
491	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
493	C₈×C₁₉	—	2	1	no	—
494	C₈×C₁₉	—	2	2	no	—
495	C₈×C₁₉	—	2	1	no	—
496	C₈×C₁₉	—	2	1	no	—
497	C₈×C₁₉	—	2	1	no	—
498	C₈×C₁₉	—	2	2	no	—
499	C₈×C₁₉	—	2	2	no	—
500	C₈×C₁₉	—	2	1	no	—
501	C₈×C₁₉	—	2	1	no	—
502	C₈×C₁₉	—	2	2	no	—
503	C₈×C₁₉	—	2	1	no	—
504	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
505	#3461	C₂×C₁₉	1	1	yes	characteristic
506	#2995	C₂×C₁₉	1	2	yes	complemented
507	#2995	C₂×C₁₉	1	2	yes	complemented
508	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
509	#2993	C₂×C₁₉	1	1	yes	characteristic, complemented
510	#2993	C₂×C₁₉	1	2	yes	complemented
511	#2991	C₂×C₁₉	1	1	yes	characteristic, complemented
512	#2989	C₂×C₁₉	1	1	yes	characteristic, complemented
513	#2986	C₂×C₁₉	1	1	yes	characteristic, complemented
514	#2985	C₂×C₁₉	1	1	yes	characteristic, complemented
515	#2985	C₂×C₁₉	1	2	yes	complemented
516	#2984	C₂×C₁₉	1	1	yes	characteristic, complemented
517	#2970	C₂×C₁₉	1	1	yes	characteristic, complemented
518	#2969	C₂×C₁₉	1	1	yes	characteristic, complemented
519	#2969	C₂×C₁₉	1	2	yes	complemented
520	#2968	C₂×C₁₉	1	2	yes	complemented
521	#2967	C₂×C₁₉	1	2	yes	complemented
522	#2966	C₂×C₁₉	1	1	yes	characteristic, complemented
523	#2965	C₂×C₁₉	1	1	yes	characteristic, complemented
524	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
525	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
526	#2961	C₂×C₁₉	1	2	yes	complemented
527	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
528	C₂²×C₁₉	—	2	1	no	—
529	C₂²×C₁₉	—	2	2	no	—
530	C₂²×C₁₉	—	2	1	no	—
531	C₂²×C₁₉	—	2	1	no	—
532	C₂²×C₁₉	—	2	1	no	—
533	C₂²×C₁₉	—	2	1	no	—
534	C₂²×C₁₉	—	2	1	no	—
535	C₂²×C₁₉	—	2	2	no	—
536	C₂²×C₁₉	—	2	1	no	—
537	C₂²×C₁₉	—	2	1	no	—
538	C₂²×C₁₉	—	2	1	no	—
539	C₂²×C₁₉	—	2	2	no	—
540	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
541	C₄×C₁₉	—	2	1	no	—
542	C₄×C₁₉	—	2	2	no	—
543	C₄×C₁₉	—	2	1	no	—
544	C₄×C₁₉	—	2	1	no	—
545	C₄×C₁₉	—	2	1	no	—
546	C₄×C₁₉	—	2	1	no	—
547	C₄×C₁₉	—	2	1	no	—
548	C₄×C₁₉	—	2	2	no	—
549	C₄×C₁₉	—	2	2	no	—
550	C₄×C₁₉	—	2	2	no	—
551	C₄×C₁₉	—	2	1	no	—
552	C₄×C₁₉	—	2	1	no	—
553	C₄×C₁₉	—	2	2	no	—
554	C₄×C₁₉	—	2	2	no	—
555	C₄×C₁₉	—	2	1	no	—
556	C₄×C₁₉	—	2	2	no	—
557	C₄×C₁₉	—	2	1	no	—
558	C₄×C₁₉	#568	1	2	yes	—
559	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
560	C₄×C₁₉	#585	1	1	yes	characteristic
561	#544	C₄×C₁₉	1	1	yes	characteristic
562	#542	C₄×C₁₉	1	1	yes	characteristic
563	#542	C₄×C₁₉	1	1	yes	characteristic
564	#542	C₄×C₁₉	1	2	yes	—
565	#541	C₄×C₁₉	1	1	yes	characteristic
566	#541	C₄×C₁₉	1	1	yes	characteristic
567	#541	C₄×C₁₉	1	2	yes	—
568	#539	C₄×C₁₉	1	2	yes	—
569	#539	C₄×C₁₉	1	2	yes	—
570	#537	C₄×C₁₉	1	1	yes	characteristic
571	#536	C₄×C₁₉	1	1	yes	characteristic
572	#536	C₄×C₁₉	1	1	yes	characteristic
573	#533	C₂²×C₁₉	1	1	yes	characteristic
574	#533	C₂²×C₁₉	1	2	yes	—
575	#533	C₂²×C₁₉	1	1	yes	characteristic
576	#529	C₂²×C₁₉	1	1	yes	characteristic
577	#529	C₂²×C₁₉	1	2	yes	—
578	#529	C₂²×C₁₉	1	2	yes	—
579	#529	C₂²×C₁₉	1	1	yes	characteristic
580	#529	C₂²×C₁₉	1	2	yes	—
581	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
582	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
583	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
584	#446	C₂²×C₁₉	1	2	yes	—
585	#446	C₂²×C₁₉	1	1	yes	characteristic
586	#446	C₂²×C₁₉	1	1	yes	characteristic
587	#446	C₂²×C₁₉	1	1	yes	characteristic
588	#446	C₂²×C₁₉	1	2	yes	—
589	#446	C₂²×C₁₉	1	2	yes	—
590	#446	C₂²×C₁₉	1	2	yes	—
591	#446	C₂²×C₁₉	1	2	yes	—
592	#446	C₂²×C₁₉	1	2	yes	—
593	#446	C₂²×C₁₉	1	2	yes	—
594	#446	C₂²×C₁₉	1	1	yes	characteristic
595	#446	C₂²×C₁₉	1	2	yes	—
596	#446	C₂²×C₁₉	1	1	yes	characteristic
597	#446	C₂²×C₁₉	1	2	yes	—
598	#446	C₂²×C₁₉	1	1	yes	characteristic
599	#446	C₂²×C₁₉	1	1	yes	characteristic
600	#446	C₂²×C₁₉	1	2	yes	—
601	#446	C₂²×C₁₉	1	2	yes	—
602	#446	C₂²×C₁₉	1	1	yes	characteristic
603	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
604	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
605	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
606	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
607	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
608	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
609	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
610	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
611	#436	C₂²×C₁₉	1	1	yes	characteristic
612	#436	C₂²×C₁₉	1	1	yes	characteristic
613	#436	C₂²×C₁₉	1	1	yes	characteristic
614	#436	C₂²×C₁₉	1	2	yes	—
615	#436	C₂²×C₁₉	1	2	yes	—
616	#436	C₂²×C₁₉	1	1	yes	characteristic
617	#436	C₂²×C₁₉	1	2	yes	—
618	#436	C₂²×C₁₉	1	2	yes	—
619	#436	C₂²×C₁₉	1	2	yes	—
620	#435	C₂²×C₁₉	1	1	yes	characteristic
621	#435	C₂²×C₁₉	1	1	yes	characteristic
622	#435	C₂²×C₁₉	1	1	yes	characteristic
623	#435	C₂²×C₁₉	1	1	yes	characteristic
624	#435	C₂²×C₁₉	1	2	yes	—
625	#435	C₂²×C₁₉	1	2	yes	—
626	#435	C₂²×C₁₉	1	2	yes	—
627	#435	C₂²×C₁₉	1	2	yes	—
628	#435	C₂²×C₁₉	1	2	yes	—
629	#435	C₂²×C₁₉	1	2	yes	—
630	#435	C₂²×C₁₉	1	2	yes	—
631	#435	C₂²×C₁₉	1	2	yes	—
632	C₈×D₄	C₂²×C₁₉	1	2	yes	—
633	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
634	C₈×D₄	C₂²×C₁₉	1	2	yes	—
635	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
636	#433	C₂²×C₁₉	1	2	yes	—
637	#433	C₂²×C₁₉	1	2	yes	—
638	#433	C₂²×C₁₉	1	2	yes	—
639	#433	C₂²×C₁₉	1	2	yes	—
640	#433	C₂²×C₁₉	1	2	yes	—
641	#433	C₂²×C₁₉	1	2	yes	—
642	#433	C₂²×C₁₉	1	2	yes	—
643	#433	C₂²×C₁₉	1	2	yes	—
644	#432	C₂²×C₁₉	1	1	yes	characteristic
645	#432	C₂²×C₁₉	1	2	yes	—
646	#432	C₂²×C₁₉	1	1	yes	characteristic
647	#432	C₂²×C₁₉	1	2	yes	—
648	#431	C₂²×C₁₉	1	1	yes	characteristic
649	#431	C₂²×C₁₉	1	1	yes	characteristic
650	#431	C₂²×C₁₉	1	1	yes	characteristic
651	#431	C₂²×C₁₉	1	2	yes	—
652	#431	C₂²×C₁₉	1	2	yes	—
653	#431	C₂²×C₁₉	1	1	yes	characteristic
654	#424	C₂²×C₁₉	1	2	yes	—
655	#424	C₂²×C₁₉	1	2	yes	—
656	#424	C₂²×C₁₉	1	2	yes	—
657	#424	C₂²×C₁₉	1	2	yes	—
658	#423	C₂²×C₁₉	1	1	yes	characteristic
659	#423	C₂²×C₁₉	1	2	yes	—
660	#423	C₂²×C₁₉	1	1	yes	characteristic
661	#423	C₂²×C₁₉	1	2	yes	—
662	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
663	#405	C₂²×C₁₉	1	2	yes	—
664	#405	C₂²×C₁₉	1	2	yes	—
665	#405	C₂²×C₁₉	1	2	yes	—
666	#405	C₂²×C₁₉	1	2	yes	—
667	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
668	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
669	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
670	C₂×#97	C₂²×C₁₉	1	2	yes	—
671	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
672	C₂×C₁₉	—	4	1	no	—
673	C₂×C₁₉	—	4	1	no	—
674	C₂×C₁₉	—	4	1	no	—
675	C₂×C₁₉	—	4	2	no	—
676	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
677	C₂×C₁₉	C₂×#568	1	1	yes	characteristic
678	C₂×C₁₉	#3573	1	1	yes	characteristic
679	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
680	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
681	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
682	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
686	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
688	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
689	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
690	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
692	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
693	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
694	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
695	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
696	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
697	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
698	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
699	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
700	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
701	#126	C₂×C₄×C₁₉	1	2	yes	—
702	#126	C₂×C₄×C₁₉	1	2	yes	—
703	#126	C₂×C₄×C₁₉	1	2	yes	—
704	#126	C₂×C₄×C₁₉	1	2	yes	—
705	#126	C₂×C₄×C₁₉	1	2	yes	—
706	#126	C₂×C₄×C₁₉	1	2	yes	—
707	#126	C₂×C₄×C₁₉	1	2	yes	—
708	#126	C₂×C₄×C₁₉	1	2	yes	—
709	#125	C₂×C₄×C₁₉	1	2	yes	—
710	#125	C₂×C₄×C₁₉	1	2	yes	—
711	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
712	#125	C₂×C₄×C₁₉	1	2	yes	—
713	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
714	#125	C₂×C₄×C₁₉	1	2	yes	—
715	#125	C₂×C₄×C₁₉	1	2	yes	—
716	#125	C₂×C₄×C₁₉	1	2	yes	—
717	#125	C₂×C₄×C₁₉	1	2	yes	—
718	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
719	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
720	#124	C₂×C₄×C₁₉	1	2	yes	—
721	#124	C₂×C₄×C₁₉	1	2	yes	—
722	#124	C₂×C₄×C₁₉	1	2	yes	—
723	#123	C₂×C₄×C₁₉	1	2	yes	—
724	#123	C₂×C₄×C₁₉	1	2	yes	—
725	#123	C₂×C₄×C₁₉	1	2	yes	—
726	#123	C₂×C₄×C₁₉	1	2	yes	—
727	#123	C₂×C₄×C₁₉	1	2	yes	—
728	#123	C₂×C₄×C₁₉	1	2	yes	—
729	#123	C₂×C₄×C₁₉	1	2	yes	—
730	#123	C₂×C₄×C₁₉	1	2	yes	—
731	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
732	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
733	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
734	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
735	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
736	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
737	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
738	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
739	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
740	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
741	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
742	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
743	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
744	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
745	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
746	#121	C₂×C₄×C₁₉	1	2	yes	—
747	#121	C₂×C₄×C₁₉	1	2	yes	—
748	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
749	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
750	#121	C₂×C₄×C₁₉	1	2	yes	—
751	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
752	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
753	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
754	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
755	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
759	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
760	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
762	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
763	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
764	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
765	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
766	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
767	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₁₉	1	2	yes	—
773	C₄×D₄	C₂³×C₁₉	1	2	yes	—
774	C₄×D₄	C₂³×C₁₉	1	2	yes	—
775	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
776	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
777	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
778	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
779	#117	C₂×C₄×C₁₉	1	2	yes	—
780	#117	C₂³×C₁₉	1	2	yes	—
781	#117	C₂³×C₁₉	1	2	yes	—
782	#117	C₂³×C₁₉	1	2	yes	—
783	#117	C₂³×C₁₉	1	2	yes	—
784	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
786	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
788	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
789	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
790	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
791	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
792	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
793	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
794	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
795	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
796	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
797	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
798	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
799	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
800	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
801	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
802	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
803	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
804	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
805	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
807	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
808	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
809	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
812	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
815	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
817	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
819	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
820	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
821	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
822	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
825	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
826	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
827	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
828	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
829	#97	C₂³×C₁₉	1	1	yes	characteristic
830	#97	C₂³×C₁₉	1	2	yes	—
831	#97	C₂³×C₁₉	1	2	yes	—
832	#97	C₂³×C₁₉	1	2	yes	—
833	#97	C₂³×C₁₉	1	1	yes	characteristic
834	#97	C₂³×C₁₉	1	2	yes	—
835	#97	C₂³×C₁₉	1	1	yes	characteristic
836	#97	C₂³×C₁₉	1	1	yes	characteristic
837	#97	C₂³×C₁₉	1	2	yes	—
838	#97	C₂³×C₁₉	1	2	yes	—
839	#97	C₂³×C₁₉	1	2	yes	—
840	#97	C₂³×C₁₉	1	2	yes	—
841	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
842	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
843	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
844	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
845	C₄×C₈	C₂³×C₁₉	1	2	yes	—
846	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
847	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₁₉	1	2	yes	—
849	C₄×C₈	C₂³×C₁₉	1	2	yes	—
850	C₄×C₈	C₂³×C₁₉	1	2	yes	—
851	C₄×C₈	C₂³×C₁₉	1	2	yes	—
852	C₄×C₈	C₂³×C₁₉	1	2	yes	—
853	C₄×C₈	C₂³×C₁₉	1	2	yes	—
854	C₁₉	#60344	1	1	yes	characteristic, direct product factor, Sylow
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	C₂×Q₈	—	4	2	no	—
858	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
859	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
860	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
861	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
862	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
863	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
864	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
865	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
866	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
867	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
868	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
869	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
870	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
871	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
872	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
873	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
874	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
875	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
876	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
877	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
878	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
879	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
880	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
881	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
886	M₁₆	—	2	2	no	—
887	M₁₆	—	2	2	no	—
888	M₁₆	—	4	1	no	—
889	M₁₆	—	4	2	no	—
890	M₁₆	—	4	2	no	—
891	M₁₆	—	4	1	no	—
892	M₁₆	—	4	2	no	—
893	M₁₆	—	4	2	no	—
894	C₂×C₈	—	2	2	no	—
895	C₂×C₈	—	2	4	no	—
896	C₂×C₈	—	4	2	no	—
897	C₂×C₈	—	4	2	no	—
898	C₂×C₈	—	4	1	no	—
899	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
904	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
905	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
908	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
910	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
911	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
912	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
913	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
914	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
915	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
916	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
917	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
918	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
919	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
920	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
922	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
923	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
924	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
925	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
926	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
927	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
928	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
929	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
930	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
931	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
932	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
933	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
934	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
935	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
936	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
937	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
938	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
939	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
940	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
941	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
942	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
943	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
944	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
945	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
946	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
947	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
948	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
949	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
950	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
951	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
952	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
956	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
957	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
958	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
959	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
960	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
961	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
962	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
963	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
965	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
966	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
967	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
968	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
969	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
970	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
971	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
972	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
973	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
974	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
975	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
976	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
977	C₄²	C₂⁴×C₁₉	1	2	yes	—
978	C₄²	C₂⁴×C₁₉	1	2	yes	—
979	C₄²	C₂⁴×C₁₉	1	2	yes	—
980	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
981	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
982	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
983	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
984	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
985	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
986	Q₈	—	2	2	no	—
987	Q₈	—	2	2	no	—
988	Q₈	—	2	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	4	1	no	—
991	Q₈	—	4	2	no	—
992	Q₈	—	4	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	4	1	no	—
995	D₄	—	4	1	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	2	no	—
998	D₄	—	4	2	no	—
999	D₄	—	4	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	2	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	1	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	4	1	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1019	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1020	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1021	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1022	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
1023	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1024	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1025	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
1026	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
1027	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
1028	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1029	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1030	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1031	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1032	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
1033	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
1034	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
1035	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1036	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1037	C₈	—	2	1	no	—
1038	C₈	—	2	2	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₈	—	2	2	no	—
1043	C₈	—	2	2	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	2	no	—
1048	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	C₁₉×#568	1	2	yes	—
1080	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₄	C₁₉×#585	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
1087	C₂	C₂×C₁₉×#568	1	1	yes	characteristic
1088	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#537	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2995	C₂	semidirect
3. C₁₉×#2995	C₂	semidirect
4. C₁₉×#2994	C₂	semidirect
5. C₁₉×#2993	C₂	semidirect
6. C₁₉×#2993	C₂	semidirect
7. C₁₉×#2991	C₂	semidirect
8. C₁₉×#2989	C₂	semidirect
9. C₁₉×#2986	C₂	semidirect
10. C₁₉×#2985	C₂	semidirect
11. C₁₉×#2985	C₂	semidirect
12. C₁₉×#2984	C₂	semidirect
13. C₁₉×#2970	C₂	semidirect
14. C₁₉×#2969	C₂	semidirect
15. C₁₉×#2969	C₂	semidirect
16. C₁₉×#2968	C₂	semidirect
17. C₁₉×#2967	C₂	semidirect
18. C₁₉×#2966	C₂	semidirect
19. C₁₉×#2965	C₂	semidirect
20. Q₈×M₁₆×C₁₉	C₂	semidirect
21. C₁₉×#2962	C₂	semidirect
22. C₁₉×#2961	C₂	semidirect
23. C₁₉×#2960	C₂	semidirect
437. #60344	C₁₉	direct (N × H)
506. #2995	C₂×C₁₉	semidirect
507. #2995	C₂×C₁₉	semidirect
508. #2994	C₂×C₁₉	semidirect
509. #2993	C₂×C₁₉	semidirect
510. #2993	C₂×C₁₉	semidirect
511. #2991	C₂×C₁₉	semidirect
512. #2989	C₂×C₁₉	semidirect
513. #2986	C₂×C₁₉	semidirect
514. #2985	C₂×C₁₉	semidirect
515. #2985	C₂×C₁₉	semidirect
516. #2984	C₂×C₁₉	semidirect
517. #2970	C₂×C₁₉	semidirect
518. #2969	C₂×C₁₉	semidirect
519. #2969	C₂×C₁₉	semidirect
520. #2968	C₂×C₁₉	semidirect
521. #2967	C₂×C₁₉	semidirect
522. #2966	C₂×C₁₉	semidirect
523. #2965	C₂×C₁₉	semidirect
524. Q₈×M₁₆	C₂×C₁₉	semidirect
525. #2962	C₂×C₁₉	semidirect
526. #2961	C₂×C₁₉	semidirect
527. #2960	C₂×C₁₉	semidirect
854. C₁₉	#60344	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×#3461	2
C₁₉×#2995	2
C₁₉×#2994	2
C₁₉×#2993	2
C₁₉×#2991	2
C₁₉×#2989	2
C₁₉×#2986	2
C₁₉×#2985	2
C₁₉×#2984	2
C₁₉×#2970	2
C₁₉×#2969	2
C₁₉×#2968	2
C₁₉×#2967	2
C₁₉×#2966	2
C₁₉×#2965	2
Q₈×M₁₆×C₁₉	2
C₁₉×#2962	2
C₁₉×#2961	2
C₁₉×#2960	2
#60344	19

Subgroups — C19×#60344 #18066303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60344 #18066303