Subgroups — C₁₉×#60889 #18066848

Order 4864.

1672 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3244	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3242	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3239	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3237	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3233	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3229	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3163	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3099	C₂	1	2	yes	maximal
12	C₁₉×#3097	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₁₉	—	2	1	no	—
19	C₁₉×#557	—	2	1	no	—
20	C₁₉×#554	—	2	2	no	—
21	C₁₉×#554	—	2	1	no	—
22	D₄×Q₈×C₁₉	—	2	2	no	—
23	D₄×Q₈×C₁₉	—	2	1	no	—
24	C₁₉×#544	C₂²	1	1	yes	characteristic
25	C₁₉×#544	C₂²	1	4	yes	—
26	C₁₉×#544	C₂²	1	2	yes	—
27	C₁₉×#542	—	2	1	no	—
28	C₁₉×#542	C₂²	1	2	yes	—
29	C₁₉×#541	—	2	1	no	—
30	C₁₉×#541	C₂²	1	2	yes	—
31	C₁₉×#539	—	2	2	no	—
32	C₁₉×#537	C₂²	1	1	yes	characteristic
33	C₁₉×#536	C₂²	1	1	yes	characteristic
34	C₁₉×#536	C₂²	1	1	yes	characteristic
35	C₁₉×#533	—	2	1	no	—
36	C₁₉×#533	C₂²	1	2	yes	—
37	C₁₉×#533	C₂²	1	2	yes	—
38	C₁₉×#533	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₉×#529	—	2	2	no	—
42	C₁₉×#529	—	2	1	no	—
43	C₁₉×#529	C₂²	1	2	yes	—
44	C₁₉×#520	C₂²	1	2	yes	—
45	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#501	C₂²	1	4	yes	—
49	C₁₉×#501	C₂²	1	4	yes	—
50	C₁₉×#499	C₂²	1	4	yes	—
51	C₁₉×#498	C₂²	1	4	yes	—
52	C₁₉×#491	C₂²	1	4	yes	—
53	C₁₉×#489	C₂²	1	4	yes	—
54	C₁₉×#488	C₂²	1	4	yes	—
55	C₁₉×#487	C₂²	1	4	yes	—
56	C₁₉×#485	C₂²	1	4	yes	—
57	C₁₉×#485	C₂²	1	4	yes	—
58	C₁₉×#485	C₂²	1	4	yes	—
59	C₁₉×#484	C₂²	1	4	yes	—
60	C₁₉×#483	C₂²	1	4	yes	—
61	C₁₉×#483	C₂²	1	4	yes	—
62	C₁₉×#482	C₂²	1	4	yes	—
63	C₁₉×#481	C₂²	1	4	yes	—
64	C₁₉×#479	C₂²	1	2	yes	—
65	C₁₉×#479	C₂²	1	4	yes	—
66	C₁₉×#478	C₂²	1	2	yes	—
67	C₁₉×#477	C₂²	1	2	yes	—
68	C₁₉×#477	C₂²	1	1	yes	characteristic
69	C₁₉×#477	C₂²	1	2	yes	—
70	C₁₉×#476	C₂²	1	1	yes	characteristic
71	C₁₉×#476	C₂²	1	2	yes	—
72	C₁₉×#475	C₂²	1	1	yes	characteristic
73	C₁₉×#475	C₂²	1	2	yes	—
74	C₁₉×#475	C₂²	1	2	yes	—
75	C₁₉×#475	C₂²	1	2	yes	—
76	C₁₉×#475	C₂²	1	2	yes	—
77	C₁₉×#475	C₂²	1	4	yes	—
78	C₁₉×#474	C₂²	1	2	yes	—
79	C₁₉×#474	C₂²	1	1	yes	characteristic
80	C₁₉×#433	C₂²	1	4	yes	—
81	C₁₉×#432	C₂²	1	2	yes	—
82	C₁₉×#431	C₂²	1	2	yes	—
83	C₁₉×#428	C₂²	1	2	yes	—
84	C₁₉×#428	C₂²	1	2	yes	—
85	C₁₉×#427	C₂²	1	2	yes	—
86	C₂×C₁₉×#106	C₂²	1	2	yes	—
87	C₁₉×#423	C₂²	1	1	yes	characteristic
88	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₁₉×#419	C₂²	1	2	yes	—
90	C₁₉×#417	C₂²	1	2	yes	—
91	C₁₉×#416	C₂²	1	2	yes	—
92	C₂×C₁₉×#103	C₂²	1	2	yes	—
93	C₁₉×#408	C₂²	1	2	yes	—
94	C₁₉×#405	C₂²	1	2	yes	—
95	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₉	—	2	1	no	—
98	C₂²×Q₈×C₁₉	—	2	2	no	—
99	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
101	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
102	C₁₉×C₄⋊Q₈	—	2	1	no	—
103	C₁₉×C₄⋊Q₈	—	2	1	no	—
104	C₁₉×C₄⋊Q₈	—	2	2	no	—
105	C₁₉×C₄⋊Q₈	—	2	4	no	—
106	C₁₉×C₄⋊Q₈	—	2	1	no	—
107	C₁₉×C₄⋊Q₈	—	2	2	no	—
108	C₁₉×C₄⋊Q₈	—	2	1	no	—
109	C₁₉×C₄⋊Q₈	—	2	2	no	—
110	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₉×#126	—	2	2	no	—
118	C₁₉×#126	—	2	2	no	—
119	C₁₉×#126	—	2	2	no	—
120	C₁₉×#126	—	2	2	no	—
121	C₁₉×#125	—	2	2	no	—
122	C₁₉×#125	—	2	1	no	—
123	C₁₉×#125	—	2	2	no	—
124	C₁₉×#125	—	2	4	no	—
125	C₁₉×#125	—	2	2	no	—
126	C₁₉×#125	—	2	2	no	—
127	C₁₉×#125	C₂³	1	2	yes	—
128	C₁₉×#125	C₂³	1	4	yes	—
129	C₁₉×#125	C₂³	1	2	yes	—
130	C₁₉×#124	—	2	1	no	—
131	C₁₉×#124	—	2	2	no	—
132	C₁₉×#124	C₂³	1	2	yes	—
133	C₁₉×#123	—	2	2	no	—
134	C₁₉×#123	—	2	2	no	—
135	C₁₉×#123	—	2	2	no	—
136	C₁₉×#123	—	2	2	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	—	2	2	no	—
139	C₁₉×C₂²⋊Q₈	—	2	1	no	—
140	C₁₉×C₂²⋊Q₈	—	2	2	no	—
141	C₁₉×C₂²⋊Q₈	—	2	1	no	—
142	C₁₉×C₂²⋊Q₈	—	2	2	no	—
143	C₁₉×C₂²⋊Q₈	—	2	1	no	—
144	C₁₉×C₂²⋊Q₈	—	2	1	no	—
145	C₁₉×C₂²⋊Q₈	—	2	2	no	—
146	C₁₉×C₂²⋊Q₈	—	2	2	no	—
147	C₁₉×C₂²⋊Q₈	—	2	4	no	—
148	C₁₉×C₂²⋊Q₈	—	2	4	no	—
149	C₁₉×C₂²⋊Q₈	—	2	4	no	—
150	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₉×#121	—	2	2	no	—
154	C₁₉×#121	—	2	1	no	—
155	C₁₉×#121	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₉	—	2	2	no	—
157	C₄×Q₈×C₁₉	—	2	1	no	—
158	C₄×Q₈×C₁₉	—	2	1	no	—
159	C₄×Q₈×C₁₉	—	2	2	no	—
160	C₄×Q₈×C₁₉	—	2	1	no	—
161	C₄×Q₈×C₁₉	—	2	2	no	—
162	C₄×Q₈×C₁₉	—	2	1	no	—
163	C₄×Q₈×C₁₉	—	2	2	no	—
164	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₁₉	—	2	4	no	—
171	C₄×D₄×C₁₉	—	2	2	no	—
172	C₄×D₄×C₁₉	—	2	1	no	—
173	C₄×D₄×C₁₉	—	2	1	no	—
174	C₄×D₄×C₁₉	—	2	2	no	—
175	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
176	C₄×D₄×C₁₉	D₄	1	2	yes	—
177	C₄×D₄×C₁₉	D₄	1	2	yes	—
178	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
179	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
181	C₁₉×#117	—	2	2	no	—
182	C₁₉×#117	—	2	1	no	—
183	C₁₉×#117	—	2	2	no	—
184	C₁₉×#117	C₂³	1	2	yes	—
185	C₁₉×#117	C₂³	1	1	yes	characteristic
186	C₁₉×#117	C₂³	1	4	yes	—
187	C₁₉×#117	C₂³	1	1	yes	characteristic
188	C₁₉×#117	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
195	C₂×C₄²×C₁₉	—	2	1	no	—
196	C₂×C₄²×C₁₉	—	2	1	no	—
197	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
199	C₁₉×#107	C₂³	1	2	yes	—
200	C₁₉×#107	C₂³	1	2	yes	—
201	C₁₉×#107	C₂³	1	4	yes	—
202	C₁₉×#107	C₂³	1	4	yes	—
203	C₁₉×#106	C₂³	1	4	yes	—
204	C₁₉×#106	C₂³	1	4	yes	—
205	C₁₉×#106	C₂³	1	2	yes	—
206	C₁₉×#106	C₂³	1	2	yes	—
207	C₁₉×#106	C₂³	1	4	yes	—
208	C₁₉×#106	C₂³	1	4	yes	—
209	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₉×#103	C₂³	1	4	yes	—
215	C₁₉×#103	C₂³	1	4	yes	—
216	C₁₉×#103	C₂³	1	2	yes	—
217	C₁₉×#103	C₂³	1	2	yes	—
218	C₁₉×#103	C₂³	1	4	yes	—
219	C₁₉×#103	C₂³	1	4	yes	—
220	C₁₉×#103	C₂³	1	4	yes	—
221	C₁₉×#102	C₂³	1	2	yes	—
222	C₁₉×#102	C₂³	1	2	yes	—
223	C₁₉×#102	C₂³	1	4	yes	—
224	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₉×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₉	C₂³	1	4	yes	—
228	#41×C₁₉	—	2	2	no	—
229	#41×C₁₉	—	2	2	no	—
230	#41×C₁₉	—	2	2	no	—
231	#41×C₁₉	—	2	2	no	—
232	C₂×Q₈×C₁₉	—	2	1	no	—
233	C₂×Q₈×C₁₉	—	2	1	no	—
234	C₂×Q₈×C₁₉	—	2	1	no	—
235	C₂×Q₈×C₁₉	—	2	2	no	—
236	C₂×Q₈×C₁₉	—	2	2	no	—
237	C₂×Q₈×C₁₉	—	2	2	no	—
238	C₂×Q₈×C₁₉	—	2	4	no	—
239	C₂×Q₈×C₁₉	—	2	2	no	—
240	C₂×Q₈×C₁₉	—	2	2	no	—
241	C₂×Q₈×C₁₉	—	8	2	no	—
242	C₂×Q₈×C₁₉	—	8	4	no	—
243	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₁₉	—	2	1	no	—
247	C₂×D₄×C₁₉	—	2	2	no	—
248	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₉	—	2	1	no	—
252	C₂²×C₄×C₁₉	—	2	1	no	—
253	C₂²×C₄×C₁₉	—	2	4	no	—
254	C₂²×C₄×C₁₉	—	2	2	no	—
255	C₂²×C₄×C₁₉	—	2	1	no	—
256	C₂²×C₄×C₁₉	—	2	1	no	—
257	C₂²×C₄×C₁₉	—	2	1	no	—
258	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
264	M₁₆×C₁₉	—	2	4	no	—
265	C₂×C₈×C₁₉	—	2	4	no	—
266	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₁₉	—	2	2	no	—
270	C₄⋊C₄×C₁₉	—	2	1	no	—
271	C₄⋊C₄×C₁₉	—	2	2	no	—
272	C₄⋊C₄×C₁₉	—	2	2	no	—
273	C₄⋊C₄×C₁₉	—	2	2	no	—
274	C₄⋊C₄×C₁₉	—	2	4	no	—
275	C₄⋊C₄×C₁₉	—	2	4	no	—
276	C₄⋊C₄×C₁₉	—	2	2	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	1	no	—
280	C₄⋊C₄×C₁₉	—	2	2	no	—
281	C₄⋊C₄×C₁₉	—	2	2	no	—
282	C₄⋊C₄×C₁₉	—	2	2	no	—
283	C₄⋊C₄×C₁₉	—	2	2	no	—
284	C₄⋊C₄×C₁₉	—	2	2	no	—
285	C₄⋊C₄×C₁₉	—	2	1	no	—
286	C₄⋊C₄×C₁₉	—	2	2	no	—
287	C₄⋊C₄×C₁₉	—	2	2	no	—
288	C₄⋊C₄×C₁₉	—	2	4	no	—
289	C₄⋊C₄×C₁₉	—	2	2	no	—
290	C₄⋊C₄×C₁₉	—	2	4	no	—
291	C₄⋊C₄×C₁₉	—	2	2	no	—
292	C₄⋊C₄×C₁₉	—	2	2	no	—
293	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₁₉	—	2	2	no	—
304	C₂²⋊C₄×C₁₉	—	2	2	no	—
305	C₂²⋊C₄×C₁₉	—	2	4	no	—
306	C₂²⋊C₄×C₁₉	—	2	2	no	—
307	C₂²⋊C₄×C₁₉	—	2	1	no	—
308	C₂²⋊C₄×C₁₉	—	2	2	no	—
309	C₂²⋊C₄×C₁₉	—	2	1	no	—
310	C₂²⋊C₄×C₁₉	—	2	1	no	—
311	C₂²⋊C₄×C₁₉	—	2	2	no	—
312	C₂²⋊C₄×C₁₉	—	2	2	no	—
313	C₂²⋊C₄×C₁₉	—	2	2	no	—
314	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
317	C₄²×C₁₉	—	2	2	no	—
318	C₄²×C₁₉	—	2	1	no	—
319	C₄²×C₁₉	—	2	1	no	—
320	C₄²×C₁₉	—	2	1	no	—
321	C₄²×C₁₉	—	2	2	no	—
322	C₄²×C₁₉	—	2	4	no	—
323	C₄²×C₁₉	—	2	2	no	—
324	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₁₉	C₂×D₄	1	2	yes	—
326	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₁₉	C₂×D₄	1	2	yes	—
328	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
329	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
330	C₄²×C₁₉	C₂⁴	1	2	yes	—
331	#60889	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂³×C₁₉	—	2	1	no	—
333	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
334	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₁₉	—	2	2	no	—
336	Q₈×C₁₉	—	2	2	no	—
337	Q₈×C₁₉	—	2	2	no	—
338	Q₈×C₁₉	—	2	1	no	—
339	Q₈×C₁₉	—	2	1	no	—
340	Q₈×C₁₉	—	4	2	no	—
341	Q₈×C₁₉	—	4	2	no	—
342	Q₈×C₁₉	—	4	4	no	—
343	Q₈×C₁₉	—	4	2	no	—
344	Q₈×C₁₉	—	8	2	no	—
345	Q₈×C₁₉	—	8	2	no	—
346	Q₈×C₁₉	—	8	4	no	—
347	D₄×C₁₉	—	2	4	no	—
348	D₄×C₁₉	—	2	2	no	—
349	D₄×C₁₉	—	2	1	no	—
350	D₄×C₁₉	—	2	1	no	—
351	D₄×C₁₉	—	4	2	no	—
352	D₄×C₁₉	—	8	2	no	—
353	C₂×C₄×C₁₉	—	2	2	no	—
354	C₂×C₄×C₁₉	—	2	4	no	—
355	C₂×C₄×C₁₉	—	2	2	no	—
356	C₂×C₄×C₁₉	—	2	2	no	—
357	C₂×C₄×C₁₉	—	2	2	no	—
358	C₂×C₄×C₁₉	—	2	1	no	—
359	C₂×C₄×C₁₉	—	2	2	no	—
360	C₂×C₄×C₁₉	—	2	1	no	—
361	C₂×C₄×C₁₉	—	2	1	no	—
362	C₂×C₄×C₁₉	—	2	2	no	—
363	C₂×C₄×C₁₉	—	2	4	no	—
364	C₂×C₄×C₁₉	—	2	2	no	—
365	C₂×C₄×C₁₉	—	4	1	no	—
366	C₂×C₄×C₁₉	—	4	2	no	—
367	C₂×C₄×C₁₉	—	4	2	no	—
368	C₂×C₄×C₁₉	—	4	2	no	—
369	C₂×C₄×C₁₉	—	4	2	no	—
370	C₂×C₄×C₁₉	—	8	1	no	—
371	C₂×C₄×C₁₉	—	8	1	no	—
372	C₂×C₄×C₁₉	—	8	2	no	—
373	C₂×C₄×C₁₉	—	8	4	no	—
374	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
383	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
384	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
385	C₈×C₁₉	—	2	2	no	—
386	C₈×C₁₉	—	2	2	no	—
387	C₈×C₁₉	—	2	4	no	—
388	#3503	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#3461	C₂×C₁₉	1	1	yes	characteristic
390	#3244	C₂×C₁₉	1	4	yes	complemented
391	#3242	C₂×C₁₉	1	4	yes	complemented
392	#3239	C₂×C₁₉	1	2	yes	complemented
393	#3237	C₂×C₁₉	1	2	yes	complemented
394	#3233	C₂×C₁₉	1	2	yes	complemented
395	#3229	C₂×C₁₉	1	2	yes	complemented
396	#3163	C₂×C₁₉	1	2	yes	complemented
397	#3137	C₂×C₁₉	1	2	yes	complemented
398	#3099	C₂×C₁₉	1	2	yes	—
399	#3097	C₂×C₁₉	1	2	yes	complemented
400	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
401	#3078	C₂×C₁₉	1	1	yes	characteristic, complemented
402	#3076	C₂×C₁₉	1	1	yes	characteristic, complemented
403	C₂×#475	C₂×C₁₉	1	1	yes	characteristic, complemented
404	#2925	C₂×C₁₉	1	1	yes	characteristic, complemented
405	C₂²×C₁₉	—	2	1	no	—
406	C₂²×C₁₉	—	2	1	no	—
407	C₂²×C₁₉	—	2	2	no	—
408	C₂²×C₁₉	—	2	2	no	—
409	C₂²×C₁₉	—	2	2	no	—
410	C₂²×C₁₉	—	4	1	no	—
411	C₂²×C₁₉	—	4	1	no	—
412	C₂²×C₁₉	—	4	1	no	—
413	C₂²×C₁₉	#536	1	2	yes	—
414	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₁₉	—	2	1	no	—
416	C₄×C₁₉	—	2	1	no	—
417	C₄×C₁₉	—	2	2	no	—
418	C₄×C₁₉	—	2	2	no	—
419	C₄×C₁₉	—	2	1	no	—
420	C₄×C₁₉	—	2	2	no	—
421	C₄×C₁₉	—	4	2	no	—
422	C₄×C₁₉	—	4	1	no	—
423	C₄×C₁₉	—	4	2	no	—
424	C₄×C₁₉	—	4	1	no	—
425	C₄×C₁₉	—	4	2	no	—
426	C₄×C₁₉	—	4	1	no	—
427	C₄×C₁₉	—	4	4	no	—
428	C₄×C₁₉	—	4	2	no	—
429	C₄×C₁₉	#536	1	2	yes	—
430	C₄×C₁₉	#577	1	2	yes	—
431	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	Q₈²	—	2	1	no	—
434	#557	—	2	1	no	—
435	#554	—	2	2	no	—
436	#554	—	2	1	no	—
437	D₄×Q₈	—	2	2	no	—
438	D₄×Q₈	—	2	1	no	—
439	#544	C₂²×C₁₉	1	2	yes	—
440	#544	C₂²×C₁₉	1	1	yes	characteristic
441	#544	C₂²×C₁₉	1	4	yes	—
442	#542	—	2	1	no	—
443	#542	C₂²×C₁₉	1	2	yes	—
444	#541	—	2	1	no	—
445	#541	C₂²×C₁₉	1	2	yes	—
446	#539	—	2	2	no	—
447	#537	C₂²×C₁₉	1	1	yes	characteristic
448	#536	C₂²×C₁₉	1	1	yes	characteristic
449	#536	C₂²×C₁₉	1	1	yes	characteristic
450	#533	—	2	1	no	—
451	#533	C₂²×C₁₉	1	2	yes	—
452	#533	C₂²×C₁₉	1	1	yes	characteristic
453	#533	C₂²×C₁₉	1	2	yes	—
454	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
455	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
456	#529	—	2	2	no	—
457	#529	—	2	1	no	—
458	#529	C₂²×C₁₉	1	2	yes	—
459	#520	C₂²×C₁₉	1	2	yes	—
460	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
461	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
463	#501	C₂²×C₁₉	1	4	yes	—
464	#501	C₂²×C₁₉	1	4	yes	—
465	#499	C₂²×C₁₉	1	4	yes	—
466	#498	C₂²×C₁₉	1	4	yes	—
467	#491	C₂²×C₁₉	1	4	yes	—
468	#489	C₂²×C₁₉	1	4	yes	—
469	#488	C₂²×C₁₉	1	4	yes	—
470	#487	C₂²×C₁₉	1	4	yes	—
471	#485	C₂²×C₁₉	1	4	yes	—
472	#485	C₂²×C₁₉	1	4	yes	—
473	#485	C₂²×C₁₉	1	4	yes	—
474	#484	C₂²×C₁₉	1	4	yes	—
475	#483	C₂²×C₁₉	1	4	yes	—
476	#483	C₂²×C₁₉	1	4	yes	—
477	#482	C₂²×C₁₉	1	4	yes	—
478	#481	C₂²×C₁₉	1	4	yes	—
479	#479	C₂²×C₁₉	1	2	yes	—
480	#479	C₂²×C₁₉	1	4	yes	—
481	#478	C₂²×C₁₉	1	2	yes	—
482	#477	C₂²×C₁₉	1	1	yes	characteristic
483	#477	C₂²×C₁₉	1	2	yes	—
484	#477	C₂²×C₁₉	1	2	yes	—
485	#476	C₂²×C₁₉	1	1	yes	characteristic
486	#476	C₂²×C₁₉	1	2	yes	—
487	#475	C₂²×C₁₉	1	2	yes	—
488	#475	C₂²×C₁₉	1	2	yes	—
489	#475	C₂²×C₁₉	1	4	yes	—
490	#475	C₂²×C₁₉	1	1	yes	characteristic
491	#475	C₂²×C₁₉	1	2	yes	—
492	#475	C₂²×C₁₉	1	2	yes	—
493	#474	C₂²×C₁₉	1	1	yes	characteristic
494	#474	C₂²×C₁₉	1	2	yes	—
495	#433	C₂²×C₁₉	1	4	yes	—
496	#432	C₂²×C₁₉	1	2	yes	—
497	#431	C₂²×C₁₉	1	2	yes	—
498	#428	C₂²×C₁₉	1	2	yes	—
499	#428	C₂²×C₁₉	1	2	yes	—
500	#427	C₂²×C₁₉	1	2	yes	—
501	C₂×#106	C₂²×C₁₉	1	2	yes	—
502	#423	C₂²×C₁₉	1	1	yes	characteristic
503	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
504	#419	C₂²×C₁₉	1	2	yes	—
505	#417	C₂²×C₁₉	1	2	yes	—
506	#416	C₂²×C₁₉	1	2	yes	—
507	C₂×#103	C₂²×C₁₉	1	2	yes	—
508	#408	C₂²×C₁₉	1	2	yes	—
509	#405	C₂²×C₁₉	1	2	yes	—
510	C₂×C₁₉	—	2	2	no	—
511	C₂×C₁₉	—	4	2	no	—
512	C₂×C₁₉	—	8	1	no	—
513	C₂×C₁₉	C₂×#536	1	1	yes	characteristic
514	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
515	C₂×C₁₉	#3586	1	1	yes	characteristic
516	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
517	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
518	C₂²×Q₈	—	2	1	no	—
519	C₂²×Q₈	—	2	2	no	—
520	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
521	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
522	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	4	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
536	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	1	no	—
544	#125	—	2	2	no	—
545	#125	—	2	4	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	C₂³×C₁₉	1	2	yes	—
549	#125	C₂³×C₁₉	1	2	yes	—
550	#125	C₂³×C₁₉	1	4	yes	—
551	#124	—	2	1	no	—
552	#124	—	2	2	no	—
553	#124	C₂³×C₁₉	1	2	yes	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
572	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
574	#121	—	2	2	no	—
575	#121	—	2	1	no	—
576	#121	C₂³×C₁₉	1	2	yes	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
586	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
588	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
597	C₄×D₄	D₄×C₁₉	1	2	yes	—
598	C₄×D₄	D₄×C₁₉	1	2	yes	—
599	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
602	#117	—	2	2	no	—
603	#117	—	2	1	no	—
604	#117	—	2	2	no	—
605	#117	C₂³×C₁₉	1	1	yes	characteristic
606	#117	C₂³×C₁₉	1	2	yes	—
607	#117	C₂³×C₁₉	1	4	yes	—
608	#117	C₂³×C₁₉	1	1	yes	characteristic
609	#117	C₂³×C₁₉	1	2	yes	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
620	#107	C₂³×C₁₉	1	2	yes	—
621	#107	C₂³×C₁₉	1	2	yes	—
622	#107	C₂³×C₁₉	1	4	yes	—
623	#107	C₂³×C₁₉	1	4	yes	—
624	#106	C₂³×C₁₉	1	4	yes	—
625	#106	C₂³×C₁₉	1	4	yes	—
626	#106	C₂³×C₁₉	1	2	yes	—
627	#106	C₂³×C₁₉	1	2	yes	—
628	#106	C₂³×C₁₉	1	4	yes	—
629	#106	C₂³×C₁₉	1	4	yes	—
630	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
631	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
632	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
633	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
634	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
635	#103	C₂³×C₁₉	1	4	yes	—
636	#103	C₂³×C₁₉	1	4	yes	—
637	#103	C₂³×C₁₉	1	2	yes	—
638	#103	C₂³×C₁₉	1	2	yes	—
639	#103	C₂³×C₁₉	1	4	yes	—
640	#103	C₂³×C₁₉	1	4	yes	—
641	#103	C₂³×C₁₉	1	4	yes	—
642	#102	C₂³×C₁₉	1	2	yes	—
643	#102	C₂³×C₁₉	1	2	yes	—
644	#102	C₂³×C₁₉	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
647	#97	C₂³×C₁₉	1	4	yes	—
648	C₄×C₈	C₂³×C₁₉	1	4	yes	—
649	C₁₉	#60889	1	1	yes	characteristic, direct product factor, Sylow
650	#41	—	2	2	no	—
651	#41	—	2	2	no	—
652	#41	—	2	2	no	—
653	#41	—	2	2	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	8	2	no	—
664	C₂×Q₈	—	8	4	no	—
665	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
666	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
671	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
672	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
686	M₁₆	—	2	4	no	—
687	C₂×C₈	—	2	4	no	—
688	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
689	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
690	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
717	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
721	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
724	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
737	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
738	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	2	no	—
746	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₁₉	1	2	yes	—
748	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₁₉	1	2	yes	—
750	C₄²	C₂⁴×C₁₉	1	2	yes	—
751	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
752	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
753	C₂³	—	2	1	no	—
754	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
755	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
756	Q₈	—	2	2	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	2	no	—
765	Q₈	—	8	2	no	—
766	Q₈	—	8	4	no	—
767	Q₈	—	8	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	1	no	—
772	D₄	—	4	2	no	—
773	D₄	—	8	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	1	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	—	8	4	no	—
794	C₂×C₄	—	8	1	no	—
795	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
803	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
804	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
805	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₈	—	2	4	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	C₁₉×#536	1	2	yes	—
818	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
819	C₄	—	2	2	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	4	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	2	no	—
833	C₄	C₁₉×#536	1	2	yes	—
834	C₄	C₁₉×#577	1	2	yes	—
835	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
836	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
837	C₂	—	2	2	no	—
838	C₂	—	4	2	no	—
839	C₂	—	8	1	no	—
840	C₂	C₂×C₁₉×#536	1	1	yes	characteristic
841	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
842	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#537	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3503	C₂	semidirect
3. C₁₉×#3244	C₂	semidirect
4. C₁₉×#3242	C₂	semidirect
5. C₁₉×#3239	C₂	semidirect
6. C₁₉×#3237	C₂	semidirect
7. C₁₉×#3233	C₂	semidirect
8. C₁₉×#3229	C₂	semidirect
9. C₁₉×#3163	C₂	semidirect
10. C₁₉×#3137	C₂	semidirect
12. C₁₉×#3097	C₂	semidirect
13. C₁₉×#3079	C₂	semidirect
14. C₁₉×#3078	C₂	semidirect
15. C₁₉×#3076	C₂	semidirect
16. C₂×C₁₉×#475	C₂	semidirect
17. C₁₉×#2925	C₂	semidirect
331. #60889	C₁₉	direct (N × H)
388. #3503	C₂×C₁₉	semidirect
390. #3244	C₂×C₁₉	semidirect
391. #3242	C₂×C₁₉	semidirect
392. #3239	C₂×C₁₉	semidirect
393. #3237	C₂×C₁₉	semidirect
394. #3233	C₂×C₁₉	semidirect
395. #3229	C₂×C₁₉	semidirect
396. #3163	C₂×C₁₉	semidirect
397. #3137	C₂×C₁₉	semidirect
399. #3097	C₂×C₁₉	semidirect
400. #3079	C₂×C₁₉	semidirect
401. #3078	C₂×C₁₉	semidirect
402. #3076	C₂×C₁₉	semidirect
403. C₂×#475	C₂×C₁₉	semidirect
404. #2925	C₂×C₁₉	semidirect
649. C₁₉	#60889	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×#3503	2
C₁₉×#3461	2
C₁₉×#3244	2
C₁₉×#3242	2
C₁₉×#3239	2
C₁₉×#3237	2
C₁₉×#3233	2
C₁₉×#3229	2
C₁₉×#3163	2
C₁₉×#3137	2
C₁₉×#3099	2
C₁₉×#3097	2
C₁₉×#3079	2
C₁₉×#3078	2
C₁₉×#3076	2
C₂×C₁₉×#475	2
C₁₉×#2925	2
#60889	19

Subgroups — C19×#60889 #18066848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60889 #18066848