Subgroups — C₁₉×#61711 #18067670

Order 4864.

1762 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3349	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3348	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3317	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3315	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3196	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3190	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3092	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3091	C₂	1	2	yes	maximal, complemented
15	C₁₉×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	—	2	2	no	—
17	C₁₉×#556	C₂²	1	2	yes	—
18	C₁₉×#555	C₂²	1	2	yes	—
19	C₁₉×#553	—	2	2	no	—
20	C₁₉×#552	—	2	2	no	—
21	C₁₉×#552	—	2	2	no	—
22	C₁₉×#552	C₂²	1	4	yes	—
23	C₁₉×#552	C₂²	1	4	yes	—
24	C₁₉×#550	C₂²	1	2	yes	—
25	C₁₉×#547	C₂²	1	2	yes	—
26	C₁₉×#538	—	2	1	no	—
27	C₁₉×#538	—	2	1	no	—
28	C₁₉×#535	—	2	1	no	—
29	C₁₉×#533	C₂²	1	1	yes	characteristic
30	C₁₉×#532	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#126	—	2	1	no	—
32	C₂×C₁₉×#125	—	2	1	no	—
33	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
34	C₁₉×#525	C₂²	1	2	yes	—
35	C₁₉×#525	C₂²	1	2	yes	—
36	C₂×C₁₉×#123	—	2	1	no	—
37	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₁₉×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#117	—	2	1	no	—
43	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#501	C₂²	1	2	yes	complemented
46	C₁₉×#501	C₂²	1	2	yes	complemented
47	C₁₉×#491	C₂²	1	2	yes	complemented
48	C₁₉×#490	C₂²	1	2	yes	complemented
49	C₁₉×#485	C₂²	1	4	yes	complemented
50	C₁₉×#485	C₂²	1	4	yes	complemented
51	C₁₉×#485	C₂²	1	4	yes	complemented
52	C₁₉×#484	C₂²	1	2	yes	—
53	C₁₉×#484	C₂²	1	4	yes	complemented
54	C₁₉×#483	C₂²	1	2	yes	—
55	C₁₉×#483	C₂²	1	2	yes	—
56	C₁₉×#482	C₂²	1	4	yes	complemented
57	C₁₉×#481	C₂²	1	2	yes	—
58	C₁₉×#481	C₂²	1	4	yes	complemented
59	C₁₉×#480	C₂²	1	2	yes	—
60	C₁₉×#480	C₂²	1	2	yes	—
61	C₁₉×#479	C₂²	1	4	yes	complemented
62	C₁₉×#478	C₂²	1	4	yes	complemented
63	C₁₉×#477	C₂²	1	2	yes	complemented
64	C₁₉×#475	C₂²	1	2	yes	complemented
65	C₁₉×#470	C₂²	1	4	yes	complemented
66	C₁₉×#468	C₂²	1	4	yes	complemented
67	C₁₉×#467	C₂²	1	4	yes	complemented
68	C₁₉×#465	C₂²	1	4	yes	complemented
69	C₁₉×#462	C₂²	1	2	yes	complemented
70	C₁₉×#460	C₂²	1	2	yes	complemented
71	C₁₉×#452	C₂²	1	4	yes	complemented
72	C₁₉×#452	C₂²	1	4	yes	complemented
73	C₁₉×#451	C₂²	1	2	yes	—
74	C₁₉×#448	C₂²	1	2	yes	—
75	C₁₉×#441	C₂²	1	4	yes	complemented
76	C₁₉×#440	C₂²	1	4	yes	complemented
77	C₁₉×#435	C₂²	1	4	yes	—
78	C₁₉×#435	C₂²	1	4	yes	—
79	C₁₉×#432	C₂²	1	1	yes	characteristic
80	C₁₉×#432	C₂²	1	1	yes	characteristic
81	C₁₉×#428	C₂²	1	4	yes	complemented
82	C₁₉×#427	C₂²	1	4	yes	complemented
83	C₁₉×#417	C₂²	1	4	yes	complemented
84	C₁₉×#416	C₂²	1	4	yes	complemented
85	C₁₉×#407	C₂²	1	2	yes	—
86	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
87	C₂×#41×C₁₉	—	2	1	no	—
88	C₂×#41×C₁₉	C₂³	1	2	yes	—
89	C₂×#41×C₁₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₁₉	—	2	1	no	—
93	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
97	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
98	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
99	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₁₉×#127	—	2	2	no	—
103	C₁₉×#127	C₂³	1	1	yes	characteristic
104	C₁₉×#126	—	2	4	no	—
105	C₁₉×#126	—	2	4	no	—
106	C₁₉×#126	—	2	2	no	—
107	C₁₉×#126	—	2	2	no	—
108	C₁₉×#125	—	2	4	no	—
109	C₁₉×#125	—	2	4	no	—
110	C₁₉×#125	—	2	1	no	—
111	C₁₉×#125	—	2	1	no	—
112	C₁₉×#125	—	2	1	no	—
113	C₁₉×#125	C₂³	1	2	yes	—
114	C₁₉×#125	C₂³	1	2	yes	—
115	C₁₉×#124	—	2	2	no	—
116	C₁₉×#124	—	2	2	no	—
117	C₁₉×#124	—	2	2	no	—
118	C₁₉×#124	—	2	1	no	—
119	C₁₉×#123	—	2	4	no	—
120	C₁₉×#123	—	2	4	no	—
121	C₁₉×#123	—	2	2	no	—
122	C₁₉×#123	—	2	2	no	—
123	C₁₉×#123	—	2	2	no	—
124	C₁₉×#123	—	2	2	no	—
125	C₁₉×C₂²⋊Q₈	—	2	2	no	—
126	C₁₉×C₂²⋊Q₈	—	2	2	no	—
127	C₁₉×C₂²⋊Q₈	—	2	1	no	—
128	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₁₉×#121	—	2	2	no	—
134	C₁₉×#121	—	2	2	no	—
135	C₁₉×#121	—	2	1	no	—
136	C₁₉×#121	—	2	2	no	—
137	C₁₉×#121	—	2	2	no	—
138	C₁₉×#121	C₂³	1	2	yes	—
139	C₁₉×#121	C₂³	1	2	yes	—
140	C₁₉×#121	C₂³	1	2	yes	—
141	C₁₉×#120	—	2	2	no	—
142	C₁₉×#120	—	2	2	no	—
143	C₄×Q₈×C₁₉	—	2	2	no	—
144	C₄×Q₈×C₁₉	—	2	1	no	—
145	C₄×Q₈×C₁₉	—	2	1	no	—
146	C₄×Q₈×C₁₉	—	2	1	no	—
147	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
148	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
149	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
150	C₄×D₄×C₁₉	—	2	2	no	—
151	C₄×D₄×C₁₉	—	2	2	no	—
152	C₄×D₄×C₁₉	—	2	2	no	—
153	C₄×D₄×C₁₉	—	2	2	no	—
154	C₄×D₄×C₁₉	—	2	2	no	—
155	C₄×D₄×C₁₉	—	2	1	no	—
156	C₄×D₄×C₁₉	D₄	1	2	yes	—
157	C₄×D₄×C₁₉	D₄	1	2	yes	—
158	C₄×D₄×C₁₉	C₂³	1	2	yes	—
159	C₄×D₄×C₁₉	C₂³	1	2	yes	—
160	C₄×D₄×C₁₉	C₂³	1	2	yes	—
161	C₁₉×#117	—	2	2	no	—
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	—	2	2	no	—
164	C₁₉×#117	—	2	4	no	—
165	C₁₉×#117	—	2	4	no	—
166	C₁₉×#117	C₂³	1	4	yes	—
167	C₁₉×#117	C₂³	1	2	yes	—
168	C₁₉×#117	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
179	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₁₉	—	2	1	no	—
188	C₂×C₄²×C₁₉	—	2	1	no	—
189	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
190	C₁₉×#107	C₂³	1	4	yes	—
191	C₁₉×#107	C₂³	1	4	yes	—
192	C₁₉×#107	C₂³	1	4	yes	—
193	C₁₉×#106	C₂³	1	4	yes	—
194	C₁₉×#106	C₂³	1	4	yes	—
195	C₁₉×#106	C₂³	1	4	yes	—
196	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
197	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
198	C₁₉×#103	C₂³	1	4	yes	—
199	C₁₉×#103	C₂³	1	4	yes	—
200	C₁₉×#103	C₂³	1	4	yes	—
201	C₁₉×#103	C₂³	1	4	yes	—
202	C₁₉×#103	C₂³	1	4	yes	—
203	C₁₉×#102	C₂³	1	4	yes	—
204	C₁₉×#102	C₂³	1	4	yes	—
205	C₁₉×#102	C₂³	1	4	yes	—
206	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₁₉×#97	C₂³	1	2	yes	—
211	C₁₉×#97	C₂³	1	2	yes	—
212	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
214	#41×C₁₉	—	4	4	no	—
215	#41×C₁₉	—	4	4	no	—
216	#41×C₁₉	—	4	4	no	—
217	C₂×Q₈×C₁₉	—	2	1	no	—
218	C₂×Q₈×C₁₉	—	2	1	no	—
219	C₂×Q₈×C₁₉	—	2	1	no	—
220	C₂×Q₈×C₁₉	—	4	2	no	—
221	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
222	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
223	C₂×D₄×C₁₉	—	2	2	no	—
224	C₂×D₄×C₁₉	—	2	2	no	—
225	C₂×D₄×C₁₉	—	2	2	no	—
226	C₂×D₄×C₁₉	—	2	2	no	—
227	C₂×D₄×C₁₉	—	2	2	no	—
228	C₂×D₄×C₁₉	—	2	1	no	—
229	C₂×D₄×C₁₉	—	2	1	no	—
230	C₂×D₄×C₁₉	—	4	2	no	—
231	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₉	—	2	1	no	—
235	C₂²×C₄×C₁₉	—	2	1	no	—
236	C₂²×C₄×C₁₉	—	2	1	no	—
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	2	4	no	—
239	C₂²×C₄×C₁₉	—	2	2	no	—
240	C₂²×C₄×C₁₉	—	2	2	no	—
241	C₂²×C₄×C₁₉	—	2	2	no	—
242	C₂²×C₄×C₁₉	—	4	2	no	—
243	C₂²×C₄×C₁₉	—	4	2	no	—
244	C₂²×C₄×C₁₉	—	4	4	no	—
245	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
254	Q₁₆×C₁₉	—	4	4	no	—
255	SD₁₆×C₁₉	—	4	4	no	—
256	M₁₆×C₁₉	—	4	4	no	—
257	C₂×C₈×C₁₉	—	4	4	no	—
258	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
259	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
260	C₄⋊C₄×C₁₉	—	2	1	no	—
261	C₄⋊C₄×C₁₉	—	2	1	no	—
262	C₄⋊C₄×C₁₉	—	2	4	no	—
263	C₄⋊C₄×C₁₉	—	2	1	no	—
264	C₄⋊C₄×C₁₉	—	2	4	no	—
265	C₄⋊C₄×C₁₉	—	2	2	no	—
266	C₄⋊C₄×C₁₉	—	2	2	no	—
267	C₄⋊C₄×C₁₉	—	2	2	no	—
268	C₄⋊C₄×C₁₉	—	2	2	no	—
269	C₄⋊C₄×C₁₉	—	2	2	no	—
270	C₄⋊C₄×C₁₉	—	2	2	no	—
271	C₄⋊C₄×C₁₉	—	2	4	no	—
272	C₄⋊C₄×C₁₉	—	2	2	no	—
273	C₄⋊C₄×C₁₉	—	2	2	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
280	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₁₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₉	—	2	2	no	—
291	C₂²⋊C₄×C₁₉	—	2	2	no	—
292	C₂²⋊C₄×C₁₉	—	2	2	no	—
293	C₂²⋊C₄×C₁₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	2	no	—
296	C₂²⋊C₄×C₁₉	—	2	2	no	—
297	C₂²⋊C₄×C₁₉	—	2	2	no	—
298	C₂²⋊C₄×C₁₉	—	2	2	no	—
299	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
300	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
301	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
302	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
303	C₄²×C₁₉	—	2	4	no	—
304	C₄²×C₁₉	—	2	2	no	—
305	C₄²×C₁₉	—	2	2	no	—
306	C₄²×C₁₉	—	2	2	no	—
307	C₄²×C₁₉	—	2	2	no	—
308	C₄²×C₁₉	—	2	2	no	—
309	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
312	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
313	#61711	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂³×C₁₉	—	2	2	no	—
315	C₂³×C₁₉	—	2	2	no	—
316	C₂³×C₁₉	—	2	2	no	—
317	C₂³×C₁₉	—	4	1	no	—
318	C₂³×C₁₉	—	4	1	no	—
319	C₂³×C₁₉	—	4	1	no	—
320	C₂³×C₁₉	—	4	1	no	—
321	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
322	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
323	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₁₉	—	2	2	no	—
325	Q₈×C₁₉	—	2	2	no	—
326	Q₈×C₁₉	—	2	4	no	—
327	Q₈×C₁₉	—	4	2	no	—
328	Q₈×C₁₉	—	4	2	no	—
329	Q₈×C₁₉	—	8	1	no	—
330	D₄×C₁₉	—	2	4	no	—
331	D₄×C₁₉	—	4	2	no	—
332	D₄×C₁₉	—	4	2	no	—
333	D₄×C₁₉	—	4	2	no	—
334	D₄×C₁₉	—	4	4	no	—
335	D₄×C₁₉	—	8	1	no	—
336	D₄×C₁₉	—	8	2	no	—
337	D₄×C₁₉	—	8	2	no	—
338	D₄×C₁₉	—	8	2	no	—
339	D₄×C₁₉	—	8	2	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	4	no	—
342	C₂×C₄×C₁₉	—	2	4	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	2	2	no	—
345	C₂×C₄×C₁₉	—	2	2	no	—
346	C₂×C₄×C₁₉	—	2	2	no	—
347	C₂×C₄×C₁₉	—	2	2	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	2	2	no	—
350	C₂×C₄×C₁₉	—	2	2	no	—
351	C₂×C₄×C₁₉	—	4	2	no	—
352	C₂×C₄×C₁₉	—	4	2	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	4	4	no	—
357	C₂×C₄×C₁₉	—	4	2	no	—
358	C₂×C₄×C₁₉	—	4	8	no	—
359	C₂×C₄×C₁₉	—	4	2	no	—
360	C₂×C₄×C₁₉	—	4	2	no	—
361	C₂×C₄×C₁₉	—	4	2	no	—
362	C₂×C₄×C₁₉	—	8	2	no	—
363	C₂×C₄×C₁₉	—	8	2	no	—
364	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
372	C₈×C₁₉	—	2	4	no	—
373	C₈×C₁₉	—	2	4	no	—
374	#3506	C₂×C₁₉	1	1	yes	characteristic
375	C₂×#552	C₂×C₁₉	1	1	yes	characteristic, complemented
376	#3349	C₂×C₁₉	1	4	yes	complemented
377	#3348	C₂×C₁₉	1	4	yes	complemented
378	#3317	C₂×C₁₉	1	4	yes	complemented
379	#3315	C₂×C₁₉	1	4	yes	complemented
380	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#3234	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#3196	C₂×C₁₉	1	2	yes	complemented
383	#3190	C₂×C₁₉	1	2	yes	complemented
384	#3113	C₂×C₁₉	1	1	yes	characteristic, complemented
385	#3112	C₂×C₁₉	1	1	yes	characteristic, complemented
386	#3092	C₂×C₁₉	1	2	yes	complemented
387	#3091	C₂×C₁₉	1	2	yes	complemented
388	#2973	C₂×C₁₉	1	1	yes	characteristic, complemented
389	C₂²×C₁₉	—	2	1	no	—
390	C₂²×C₁₉	—	2	1	no	—
391	C₂²×C₁₉	—	2	2	no	—
392	C₂²×C₁₉	—	2	2	no	—
393	C₂²×C₁₉	—	2	2	no	—
394	C₂²×C₁₉	—	2	2	no	—
395	C₂²×C₁₉	—	2	2	no	—
396	C₂²×C₁₉	—	2	2	no	—
397	C₂²×C₁₉	—	4	4	no	—
398	C₂²×C₁₉	—	4	2	no	—
399	C₂²×C₁₉	—	4	2	no	—
400	C₂²×C₁₉	—	4	2	no	—
401	C₂²×C₁₉	—	8	2	no	—
402	C₂²×C₁₉	#575	1	2	yes	—
403	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₁₉	—	2	1	no	—
405	C₄×C₁₉	—	2	1	no	—
406	C₄×C₁₉	—	2	1	no	—
407	C₄×C₁₉	—	2	2	no	—
408	C₄×C₁₉	—	2	2	no	—
409	C₄×C₁₉	—	2	1	no	—
410	C₄×C₁₉	—	2	1	no	—
411	C₄×C₁₉	—	4	2	no	—
412	C₄×C₁₉	—	4	2	no	—
413	C₄×C₁₉	—	4	2	no	—
414	C₄×C₁₉	—	4	2	no	—
415	C₄×C₁₉	—	4	2	no	—
416	C₄×C₁₉	—	4	2	no	—
417	C₄×C₁₉	—	4	2	no	—
418	C₄×C₁₉	#585	1	2	yes	—
419	#559	—	2	2	no	—
420	#556	C₂²×C₁₉	1	2	yes	—
421	#555	C₂²×C₁₉	1	2	yes	—
422	#553	—	2	2	no	—
423	#552	—	2	2	no	—
424	#552	—	2	2	no	—
425	#552	C₂²×C₁₉	1	4	yes	—
426	#552	C₂²×C₁₉	1	4	yes	—
427	#550	C₂²×C₁₉	1	2	yes	—
428	#547	C₂²×C₁₉	1	2	yes	—
429	#538	—	2	1	no	—
430	#538	—	2	1	no	—
431	#535	—	2	1	no	—
432	#533	C₂²×C₁₉	1	1	yes	characteristic
433	#532	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×#126	—	2	1	no	—
435	C₂×#125	—	2	1	no	—
436	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
437	#525	C₂²×C₁₉	1	2	yes	—
438	#525	C₂²×C₁₉	1	2	yes	—
439	C₂×#123	—	2	1	no	—
440	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
441	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
442	#520	—	2	1	no	—
443	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×#117	—	2	1	no	—
446	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
447	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
448	#501	C₂²×C₁₉	1	2	yes	complemented
449	#501	C₂²×C₁₉	1	2	yes	complemented
450	#491	C₂²×C₁₉	1	2	yes	complemented
451	#490	C₂²×C₁₉	1	2	yes	complemented
452	#485	C₂²×C₁₉	1	4	yes	complemented
453	#485	C₂²×C₁₉	1	4	yes	complemented
454	#485	C₂²×C₁₉	1	4	yes	complemented
455	#484	C₂²×C₁₉	1	2	yes	—
456	#484	C₂²×C₁₉	1	4	yes	complemented
457	#483	C₂²×C₁₉	1	2	yes	—
458	#483	C₂²×C₁₉	1	2	yes	—
459	#482	C₂²×C₁₉	1	4	yes	complemented
460	#481	C₂²×C₁₉	1	2	yes	—
461	#481	C₂²×C₁₉	1	4	yes	complemented
462	#480	C₂²×C₁₉	1	2	yes	—
463	#480	C₂²×C₁₉	1	2	yes	—
464	#479	C₂²×C₁₉	1	4	yes	complemented
465	#478	C₂²×C₁₉	1	4	yes	complemented
466	#477	C₂²×C₁₉	1	2	yes	complemented
467	#475	C₂²×C₁₉	1	2	yes	complemented
468	#470	C₂²×C₁₉	1	4	yes	complemented
469	#468	C₂²×C₁₉	1	4	yes	complemented
470	#467	C₂²×C₁₉	1	4	yes	complemented
471	#465	C₂²×C₁₉	1	4	yes	complemented
472	#462	C₂²×C₁₉	1	2	yes	complemented
473	#460	C₂²×C₁₉	1	2	yes	complemented
474	#452	C₂²×C₁₉	1	4	yes	complemented
475	#452	C₂²×C₁₉	1	4	yes	complemented
476	#451	C₂²×C₁₉	1	2	yes	—
477	#448	C₂²×C₁₉	1	2	yes	—
478	#441	C₂²×C₁₉	1	4	yes	complemented
479	#440	C₂²×C₁₉	1	4	yes	complemented
480	#435	C₂²×C₁₉	1	4	yes	—
481	#435	C₂²×C₁₉	1	4	yes	—
482	#432	C₂²×C₁₉	1	1	yes	characteristic
483	#432	C₂²×C₁₉	1	1	yes	characteristic
484	#428	C₂²×C₁₉	1	4	yes	complemented
485	#427	C₂²×C₁₉	1	4	yes	complemented
486	#417	C₂²×C₁₉	1	4	yes	complemented
487	#416	C₂²×C₁₉	1	4	yes	complemented
488	#407	C₂²×C₁₉	1	2	yes	—
489	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
490	C₂×C₁₉	—	2	2	no	—
491	C₂×C₁₉	—	4	2	no	—
492	C₂×C₁₉	—	4	2	no	—
493	C₂×C₁₉	—	8	2	no	—
494	C₂×C₁₉	#3485	1	1	yes	characteristic
495	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
496	C₂×C₁₉	#3586	1	1	yes	characteristic
497	C₂×#41	—	2	1	no	—
498	C₂×#41	C₂³×C₁₉	1	2	yes	—
499	C₂×#41	C₂³×C₁₉	1	2	yes	—
500	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
501	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
505	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
506	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
507	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
508	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
509	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
512	#127	—	2	2	no	—
513	#127	C₂³×C₁₉	1	1	yes	characteristic
514	#126	—	2	4	no	—
515	#126	—	2	4	no	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#125	—	2	4	no	—
519	#125	—	2	4	no	—
520	#125	—	2	1	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#125	C₂³×C₁₉	1	2	yes	—
524	#125	C₂³×C₁₉	1	2	yes	—
525	#124	—	2	2	no	—
526	#124	—	2	2	no	—
527	#124	—	2	2	no	—
528	#124	—	2	1	no	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
539	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
540	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
541	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
542	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	1	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	C₂³×C₁₉	1	2	yes	—
549	#121	C₂³×C₁₉	1	2	yes	—
550	#121	C₂³×C₁₉	1	2	yes	—
551	#120	—	2	2	no	—
552	#120	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
558	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
559	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	D₄×C₁₉	1	2	yes	—
567	C₄×D₄	D₄×C₁₉	1	2	yes	—
568	C₄×D₄	C₂³×C₁₉	1	2	yes	—
569	C₄×D₄	C₂³×C₁₉	1	2	yes	—
570	C₄×D₄	C₂³×C₁₉	1	2	yes	—
571	#117	—	2	2	no	—
572	#117	—	2	1	no	—
573	#117	—	2	2	no	—
574	#117	—	2	4	no	—
575	#117	—	2	4	no	—
576	#117	C₂³×C₁₉	1	4	yes	—
577	#117	C₂³×C₁₉	1	2	yes	—
578	#117	C₂³×C₁₉	1	2	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
597	C₂×C₄²	—	2	1	no	—
598	C₂×C₄²	—	2	1	no	—
599	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
600	#107	C₂³×C₁₉	1	4	yes	—
601	#107	C₂³×C₁₉	1	4	yes	—
602	#107	C₂³×C₁₉	1	4	yes	—
603	#106	C₂³×C₁₉	1	4	yes	—
604	#106	C₂³×C₁₉	1	4	yes	—
605	#106	C₂³×C₁₉	1	4	yes	—
606	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
607	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
608	#103	C₂³×C₁₉	1	4	yes	—
609	#103	C₂³×C₁₉	1	4	yes	—
610	#103	C₂³×C₁₉	1	4	yes	—
611	#103	C₂³×C₁₉	1	4	yes	—
612	#103	C₂³×C₁₉	1	4	yes	—
613	#102	C₂³×C₁₉	1	4	yes	—
614	#102	C₂³×C₁₉	1	4	yes	—
615	#102	C₂³×C₁₉	1	4	yes	—
616	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
617	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
618	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
619	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
620	#97	C₂³×C₁₉	1	2	yes	—
621	#97	C₂³×C₁₉	1	2	yes	—
622	C₁₉	#61711	1	1	yes	characteristic, direct product factor, Sylow
623	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
624	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
625	#41	—	4	4	no	—
626	#41	—	4	4	no	—
627	#41	—	4	4	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	4	2	no	—
632	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
643	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
644	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
661	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
665	Q₁₆	—	4	4	no	—
666	SD₁₆	—	4	4	no	—
667	M₁₆	—	4	4	no	—
668	C₂×C₈	—	4	4	no	—
669	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
670	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
692	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
711	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
712	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
713	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	2	no	—
720	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
721	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
722	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
723	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
732	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
733	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
734	Q₈	—	2	2	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	4	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	8	1	no	—
740	D₄	—	2	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	4	no	—
745	D₄	—	8	1	no	—
746	D₄	—	8	2	no	—
747	D₄	—	8	2	no	—
748	D₄	—	8	2	no	—
749	D₄	—	8	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	8	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
775	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
781	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
782	C₈	—	2	4	no	—
783	C₈	—	2	4	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	8	2	no	—
797	C₂²	C₁₉×#575	1	2	yes	—
798	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
799	C₄	—	2	1	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	C₁₉×#585	1	2	yes	—
814	C₂	—	2	2	no	—
815	C₂	—	4	2	no	—
816	C₂	—	4	2	no	—
817	C₂	—	8	2	no	—
818	C₂	C₁₉×#3485	1	1	yes	characteristic
819	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
820	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×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#552	C₂	semidirect
3. C₁₉×#3349	C₂	semidirect
4. C₁₉×#3348	C₂	semidirect
5. C₁₉×#3317	C₂	semidirect
6. C₁₉×#3315	C₂	semidirect
7. C₁₉×#3236	C₂	semidirect
8. C₁₉×#3234	C₂	semidirect
9. C₁₉×#3196	C₂	semidirect
10. C₁₉×#3190	C₂	semidirect
11. C₁₉×#3113	C₂	semidirect
12. C₁₉×#3112	C₂	semidirect
13. C₁₉×#3092	C₂	semidirect
14. C₁₉×#3091	C₂	semidirect
15. C₁₉×#2973	C₂	semidirect
45. C₁₉×#501	C₂²	semidirect
46. C₁₉×#501	C₂²	semidirect
47. C₁₉×#491	C₂²	semidirect
48. C₁₉×#490	C₂²	semidirect
49. C₁₉×#485	C₂²	semidirect
50. C₁₉×#485	C₂²	semidirect
51. C₁₉×#485	C₂²	semidirect
53. C₁₉×#484	C₂²	semidirect
56. C₁₉×#482	C₂²	semidirect
58. C₁₉×#481	C₂²	semidirect
61. C₁₉×#479	C₂²	semidirect
62. C₁₉×#478	C₂²	semidirect
63. C₁₉×#477	C₂²	semidirect
64. C₁₉×#475	C₂²	semidirect
65. C₁₉×#470	C₂²	semidirect
66. C₁₉×#468	C₂²	semidirect
67. C₁₉×#467	C₂²	semidirect
68. C₁₉×#465	C₂²	semidirect
69. C₁₉×#462	C₂²	semidirect
70. C₁₉×#460	C₂²	semidirect
71. C₁₉×#452	C₂²	semidirect
72. C₁₉×#452	C₂²	semidirect
75. C₁₉×#441	C₂²	semidirect
76. C₁₉×#440	C₂²	semidirect
81. C₁₉×#428	C₂²	semidirect
82. C₁₉×#427	C₂²	semidirect
83. C₁₉×#417	C₂²	semidirect
84. C₁₉×#416	C₂²	semidirect
313. #61711	C₁₉	direct (N × H)
375. C₂×#552	C₂×C₁₉	semidirect
376. #3349	C₂×C₁₉	semidirect
377. #3348	C₂×C₁₉	semidirect
378. #3317	C₂×C₁₉	semidirect
379. #3315	C₂×C₁₉	semidirect
380. #3236	C₂×C₁₉	semidirect
381. #3234	C₂×C₁₉	semidirect
382. #3196	C₂×C₁₉	semidirect
383. #3190	C₂×C₁₉	semidirect
384. #3113	C₂×C₁₉	semidirect
385. #3112	C₂×C₁₉	semidirect
386. #3092	C₂×C₁₉	semidirect
387. #3091	C₂×C₁₉	semidirect
388. #2973	C₂×C₁₉	semidirect
448. #501	C₂²×C₁₉	semidirect
449. #501	C₂²×C₁₉	semidirect
450. #491	C₂²×C₁₉	semidirect
451. #490	C₂²×C₁₉	semidirect
452. #485	C₂²×C₁₉	semidirect
453. #485	C₂²×C₁₉	semidirect
454. #485	C₂²×C₁₉	semidirect
456. #484	C₂²×C₁₉	semidirect
459. #482	C₂²×C₁₉	semidirect
461. #481	C₂²×C₁₉	semidirect
464. #479	C₂²×C₁₉	semidirect
465. #478	C₂²×C₁₉	semidirect
466. #477	C₂²×C₁₉	semidirect
467. #475	C₂²×C₁₉	semidirect
468. #470	C₂²×C₁₉	semidirect
469. #468	C₂²×C₁₉	semidirect
470. #467	C₂²×C₁₉	semidirect
471. #465	C₂²×C₁₉	semidirect
472. #462	C₂²×C₁₉	semidirect
473. #460	C₂²×C₁₉	semidirect
474. #452	C₂²×C₁₉	semidirect
475. #452	C₂²×C₁₉	semidirect
478. #441	C₂²×C₁₉	semidirect
479. #440	C₂²×C₁₉	semidirect
484. #428	C₂²×C₁₉	semidirect
485. #427	C₂²×C₁₉	semidirect
486. #417	C₂²×C₁₉	semidirect
487. #416	C₂²×C₁₉	semidirect
622. C₁₉	#61711	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×#3506	2
C₂×C₁₉×#552	2
C₁₉×#3349	2
C₁₉×#3348	2
C₁₉×#3317	2
C₁₉×#3315	2
C₁₉×#3236	2
C₁₉×#3234	2
C₁₉×#3196	2
C₁₉×#3190	2
C₁₉×#3113	2
C₁₉×#3112	2
C₁₉×#3092	2
C₁₉×#3091	2
C₁₉×#2973	2
#61711	19

Subgroups — C19×#61711 #18067670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61711 #18067670