Subgroups — C₁₉×#62260 #18068219

Order 4864.

1850 conjugacy classes of subgroups.

The subgroup lattice has 800 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	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3357	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3356	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3333	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3331	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3329	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3328	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3278	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3276	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3190	C₂	1	4	yes	maximal, complemented
14	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3056	C₂	1	4	yes	maximal, complemented
17	C₂×C₁₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×#137	C₂²	1	4	yes	complemented
19	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#559	—	2	2	no	—
21	C₁₉×#556	C₂²	1	2	yes	—
22	C₁₉×#555	C₂²	1	2	yes	—
23	C₁₉×#554	—	2	2	no	—
24	C₁₉×#554	—	2	2	no	—
25	C₁₉×#554	C₂²	1	2	yes	—
26	C₁₉×#554	C₂²	1	2	yes	—
27	C₁₉×#553	—	2	2	no	—
28	C₁₉×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₁₉×#547	C₂²	1	2	yes	—
32	C₁₉×#544	—	2	1	no	—
33	C₁₉×#543	—	2	2	no	—
34	C₁₉×#538	—	2	2	no	—
35	C₁₉×#535	—	2	1	no	—
36	C₁₉×#533	C₂²	1	1	yes	characteristic
37	C₁₉×#533	C₂²	1	1	yes	characteristic
38	C₁₉×#533	C₂²	1	1	yes	characteristic
39	C₁₉×#532	C₂²	1	1	yes	characteristic
40	C₁₉×#525	C₂²	1	4	yes	—
41	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
42	C₁₉×#520	—	2	1	no	—
43	C₁₉×#518	—	2	1	no	—
44	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#485	C₂²	1	4	yes	complemented
54	C₁₉×#485	C₂²	1	4	yes	complemented
55	C₁₉×#483	C₂²	1	4	yes	complemented
56	C₁₉×#480	C₂²	1	4	yes	complemented
57	C₁₉×#477	C₂²	1	2	yes	complemented
58	C₁₉×#477	C₂²	1	2	yes	complemented
59	C₁₉×#476	C₂²	1	2	yes	complemented
60	C₁₉×#475	C₂²	1	2	yes	complemented
61	C₁₉×#470	C₂²	1	4	yes	complemented
62	C₁₉×#470	C₂²	1	4	yes	complemented
63	C₁₉×#468	C₂²	1	4	yes	complemented
64	C₁₉×#468	C₂²	1	4	yes	complemented
65	C₁₉×#467	C₂²	1	2	yes	—
66	C₁₉×#467	C₂²	1	2	yes	—
67	C₁₉×#467	C₂²	1	4	yes	—
68	C₁₉×#465	C₂²	1	2	yes	—
69	C₁₉×#465	C₂²	1	2	yes	—
70	C₁₉×#465	C₂²	1	4	yes	—
71	C₁₉×#462	C₂²	1	2	yes	complemented
72	C₁₉×#462	C₂²	1	2	yes	complemented
73	C₁₉×#461	C₂²	1	2	yes	complemented
74	C₁₉×#460	C₂²	1	2	yes	complemented
75	C₁₉×#452	C₂²	1	4	yes	complemented
76	C₁₉×#452	C₂²	1	4	yes	complemented
77	C₁₉×#451	C₂²	1	4	yes	complemented
78	C₁₉×#448	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
80	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
83	C₁₉×#436	C₂²	1	2	yes	—
84	C₁₉×#436	C₂²	1	2	yes	—
85	C₁₉×#436	C₂²	1	2	yes	—
86	C₁₉×#436	C₂²	1	2	yes	—
87	C₁₉×#428	C₂²	1	4	yes	complemented
88	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₁₉×#419	C₂²	1	4	yes	complemented
90	C₁₉×#417	C₂²	1	4	yes	complemented
91	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₉	—	2	1	no	—
94	C₂×#41×C₁₉	C₂³	1	4	yes	—
95	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
98	C₁₉×#137	—	4	8	no	—
99	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
105	C₂×M₁₆×C₁₉	—	4	4	no	—
106	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
107	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
108	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
111	C₁₉×C₄⋊Q₈	—	2	2	no	—
112	C₁₉×C₄⋊Q₈	—	2	2	no	—
113	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₉×#127	—	2	2	no	—
121	C₁₉×#127	C₂³	1	1	yes	characteristic
122	C₁₉×#126	—	2	4	no	—
123	C₁₉×#125	—	2	2	no	—
124	C₁₉×#125	—	2	2	no	—
125	C₁₉×#125	—	2	1	no	—
126	C₁₉×#125	—	2	1	no	—
127	C₁₉×#125	—	2	1	no	—
128	C₁₉×#124	—	2	2	no	—
129	C₁₉×#124	—	2	4	no	—
130	C₁₉×#124	—	2	1	no	—
131	C₁₉×#123	—	2	4	no	—
132	C₁₉×#123	—	2	4	no	—
133	C₁₉×C₂²⋊Q₈	—	2	4	no	—
134	C₁₉×C₂²⋊Q₈	—	2	4	no	—
135	C₁₉×C₂²⋊Q₈	—	2	1	no	—
136	C₁₉×C₂²⋊Q₈	—	2	1	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	—	2	4	no	—
139	C₁₉×C₂²⋊Q₈	—	2	4	no	—
140	C₁₉×C₂²⋊Q₈	—	2	4	no	—
141	C₁₉×C₂²⋊Q₈	—	2	4	no	—
142	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₉×#121	—	2	2	no	—
149	C₁₉×#121	—	2	2	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	4	no	—
152	C₁₉×#121	C₂³	1	4	yes	—
153	C₁₉×#121	C₂³	1	2	yes	—
154	C₁₉×#120	—	2	4	no	—
155	C₄×Q₈×C₁₉	—	2	2	no	—
156	C₄×Q₈×C₁₉	—	2	1	no	—
157	C₄×Q₈×C₁₉	—	2	1	no	—
158	C₄×Q₈×C₁₉	—	2	1	no	—
159	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
162	C₄×D₄×C₁₉	—	2	2	no	—
163	C₄×D₄×C₁₉	—	2	2	no	—
164	C₄×D₄×C₁₉	—	2	2	no	—
165	C₄×D₄×C₁₉	—	2	2	no	—
166	C₄×D₄×C₁₉	—	2	4	no	—
167	C₄×D₄×C₁₉	—	2	4	no	—
168	C₄×D₄×C₁₉	—	2	2	no	—
169	C₄×D₄×C₁₉	—	2	1	no	—
170	C₄×D₄×C₁₉	D₄	1	2	yes	—
171	C₄×D₄×C₁₉	D₄	1	2	yes	—
172	C₄×D₄×C₁₉	C₂³	1	2	yes	—
173	C₄×D₄×C₁₉	C₂³	1	2	yes	—
174	C₄×D₄×C₁₉	C₂³	1	2	yes	—
175	C₁₉×#117	—	2	1	no	—
176	C₁₉×#117	—	2	1	no	—
177	C₁₉×#117	—	2	1	no	—
178	C₁₉×#117	—	2	2	no	—
179	C₁₉×#117	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
181	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
184	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
185	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
186	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
187	C₁₉×#107	C₂³	1	2	yes	—
188	C₁₉×#107	C₂³	1	4	yes	—
189	C₁₉×#107	C₂³	1	2	yes	—
190	C₁₉×#106	C₂³	1	2	yes	—
191	C₁₉×#106	C₂³	1	4	yes	—
192	C₁₉×#106	C₂³	1	2	yes	—
193	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
194	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₉×#103	C₂³	1	2	yes	—
196	C₁₉×#103	C₂³	1	4	yes	—
197	C₁₉×#103	C₂³	1	2	yes	—
198	C₁₉×#103	C₂³	1	2	yes	—
199	C₁₉×#103	C₂³	1	4	yes	—
200	C₁₉×#103	C₂³	1	4	yes	—
201	C₁₉×#103	C₂³	1	2	yes	—
202	C₁₉×#103	C₂³	1	2	yes	—
203	C₁₉×#103	C₂³	1	2	yes	—
204	C₁₉×#102	C₂³	1	2	yes	—
205	C₁₉×#102	C₂³	1	4	yes	—
206	C₁₉×#102	C₂³	1	2	yes	—
207	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
213	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
221	C₂×Q₈×C₁₉	—	2	4	no	—
222	C₂×Q₈×C₁₉	—	4	4	no	—
223	C₂×Q₈×C₁₉	—	4	4	no	—
224	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₉	—	2	2	no	—
228	C₂×D₄×C₁₉	—	2	4	no	—
229	C₂×D₄×C₁₉	—	2	4	no	—
230	C₂×D₄×C₁₉	—	2	4	no	—
231	C₂×D₄×C₁₉	—	2	1	no	—
232	C₂×D₄×C₁₉	—	2	1	no	—
233	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₉	—	2	4	no	—
237	C₂²×C₄×C₁₉	—	2	4	no	—
238	C₂²×C₄×C₁₉	—	2	2	no	—
239	C₂²×C₄×C₁₉	—	2	4	no	—
240	C₂²×C₄×C₁₉	—	4	2	no	—
241	C₂²×C₄×C₁₉	—	4	2	no	—
242	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
248	Q₁₆×C₁₉	—	2	4	no	—
249	Q₁₆×C₁₉	—	4	2	no	—
250	Q₁₆×C₁₉	—	4	4	no	—
251	SD₁₆×C₁₉	—	2	4	no	—
252	SD₁₆×C₁₉	—	4	2	no	—
253	SD₁₆×C₁₉	—	4	4	no	—
254	M₁₆×C₁₉	—	2	8	no	—
255	M₁₆×C₁₉	—	4	4	no	—
256	C₂×C₈×C₁₉	—	2	2	no	—
257	C₂×C₈×C₁₉	—	4	1	no	—
258	C₂×C₈×C₁₉	—	4	2	no	—
259	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
261	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₁₉	—	2	1	no	—
265	C₄⋊C₄×C₁₉	—	2	2	no	—
266	C₄⋊C₄×C₁₉	—	2	2	no	—
267	C₄⋊C₄×C₁₉	—	2	4	no	—
268	C₄⋊C₄×C₁₉	—	2	4	no	—
269	C₄⋊C₄×C₁₉	—	2	4	no	—
270	C₄⋊C₄×C₁₉	—	2	4	no	—
271	C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₄⋊C₄×C₁₉	—	2	1	no	—
273	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
280	C₄⋊C₄×C₁₉	—	2	1	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	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₁₉	—	2	2	no	—
291	C₂²⋊C₄×C₁₉	—	2	2	no	—
292	C₂²⋊C₄×C₁₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₉	—	2	2	no	—
299	C₂²⋊C₄×C₁₉	—	2	2	no	—
300	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
301	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
302	C₄²×C₁₉	—	2	4	no	—
303	C₄²×C₁₉	—	2	2	no	—
304	C₄²×C₁₉	—	2	2	no	—
305	C₄²×C₁₉	—	2	2	no	—
306	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
309	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
310	#62260	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂³×C₁₉	—	2	4	no	—
312	C₂³×C₁₉	—	2	2	no	—
313	C₂³×C₁₉	—	4	2	no	—
314	C₂³×C₁₉	—	4	2	no	—
315	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
316	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₁₉	—	2	2	no	—
318	Q₈×C₁₉	—	2	2	no	—
319	Q₈×C₁₉	—	2	2	no	—
320	Q₈×C₁₉	—	2	2	no	—
321	Q₈×C₁₉	—	2	2	no	—
322	Q₈×C₁₉	—	2	2	no	—
323	Q₈×C₁₉	—	4	2	no	—
324	Q₈×C₁₉	—	8	1	no	—
325	Q₈×C₁₉	—	8	1	no	—
326	Q₈×C₁₉	—	8	1	no	—
327	Q₈×C₁₉	—	8	4	no	—
328	D₄×C₁₉	—	2	4	no	—
329	D₄×C₁₉	—	2	4	no	—
330	D₄×C₁₉	—	2	2	no	—
331	D₄×C₁₉	—	2	2	no	—
332	D₄×C₁₉	—	4	4	no	—
333	D₄×C₁₉	—	4	2	no	—
334	D₄×C₁₉	—	8	1	no	—
335	D₄×C₁₉	—	8	4	no	—
336	D₄×C₁₉	—	8	4	no	—
337	C₂×C₄×C₁₉	—	2	1	no	—
338	C₂×C₄×C₁₉	—	2	4	no	—
339	C₂×C₄×C₁₉	—	2	1	no	—
340	C₂×C₄×C₁₉	—	2	4	no	—
341	C₂×C₄×C₁₉	—	2	2	no	—
342	C₂×C₄×C₁₉	—	2	2	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	—	4	4	no	—
349	C₂×C₄×C₁₉	—	4	2	no	—
350	C₂×C₄×C₁₉	—	4	1	no	—
351	C₂×C₄×C₁₉	—	4	4	no	—
352	C₂×C₄×C₁₉	—	8	4	no	—
353	C₂×C₄×C₁₉	—	8	4	no	—
354	C₂×C₄×C₁₉	—	8	4	no	—
355	C₂×C₄×C₁₉	#137	1	4	yes	complemented
356	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
363	C₈×C₁₉	—	2	1	no	—
364	C₈×C₁₉	—	2	4	no	—
365	C₈×C₁₉	—	2	1	no	—
366	C₈×C₁₉	—	2	1	no	—
367	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
368	#3506	C₂×C₁₉	1	1	yes	characteristic
369	#3501	C₂×C₁₉	1	1	yes	characteristic, complemented
370	#3357	C₂×C₁₉	1	2	yes	complemented
371	#3356	C₂×C₁₉	1	2	yes	complemented
372	#3333	C₂×C₁₉	1	2	yes	complemented
373	#3331	C₂×C₁₉	1	2	yes	complemented
374	#3329	C₂×C₁₉	1	2	yes	complemented
375	#3328	C₂×C₁₉	1	2	yes	complemented
376	#3278	C₂×C₁₉	1	2	yes	complemented
377	#3276	C₂×C₁₉	1	2	yes	complemented
378	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
379	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
380	#3190	C₂×C₁₉	1	4	yes	complemented
381	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
383	#3056	C₂×C₁₉	1	4	yes	complemented
384	C₂×#436	C₂×C₁₉	1	1	yes	characteristic, complemented
385	C₂²×C₁₉	—	2	1	no	—
386	C₂²×C₁₉	—	2	1	no	—
387	C₂²×C₁₉	—	2	4	no	—
388	C₂²×C₁₉	—	2	4	no	—
389	C₂²×C₁₉	—	2	4	no	—
390	C₂²×C₁₉	—	4	2	no	—
391	C₂²×C₁₉	—	4	2	no	—
392	C₂²×C₁₉	—	4	2	no	—
393	C₂²×C₁₉	—	8	4	no	—
394	C₂²×C₁₉	C₂×#137	1	2	yes	—
395	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₁₉	—	2	1	no	—
397	C₄×C₁₉	—	2	1	no	—
398	C₄×C₁₉	—	2	1	no	—
399	C₄×C₁₉	—	2	4	no	—
400	C₄×C₁₉	—	4	2	no	—
401	C₄×C₁₉	—	4	2	no	—
402	C₄×C₁₉	—	4	2	no	—
403	C₄×C₁₉	—	4	2	no	—
404	C₄×C₁₉	—	4	2	no	—
405	C₄×C₁₉	—	4	2	no	—
406	C₄×C₁₉	—	4	2	no	—
407	C₄×C₁₉	C₂×#137	1	2	yes	—
408	C₄×C₁₉	C₂×#137	1	2	yes	—
409	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₄×C₁₉	#585	1	1	yes	characteristic
411	C₂×#137	C₂²×C₁₉	1	4	yes	complemented
412	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
413	#559	—	2	2	no	—
414	#556	C₂²×C₁₉	1	2	yes	—
415	#555	C₂²×C₁₉	1	2	yes	—
416	#554	—	2	2	no	—
417	#554	—	2	2	no	—
418	#554	C₂²×C₁₉	1	2	yes	—
419	#554	C₂²×C₁₉	1	2	yes	—
420	#553	—	2	2	no	—
421	#550	C₂²×C₁₉	1	2	yes	—
422	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
423	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
424	#547	C₂²×C₁₉	1	2	yes	—
425	#544	—	2	1	no	—
426	#543	—	2	2	no	—
427	#538	—	2	2	no	—
428	#535	—	2	1	no	—
429	#533	C₂²×C₁₉	1	1	yes	characteristic
430	#533	C₂²×C₁₉	1	1	yes	characteristic
431	#533	C₂²×C₁₉	1	1	yes	characteristic
432	#532	C₂²×C₁₉	1	1	yes	characteristic
433	#525	C₂²×C₁₉	1	4	yes	—
434	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
435	#520	—	2	1	no	—
436	#518	—	2	1	no	—
437	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
438	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
439	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
440	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
441	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
442	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
443	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
444	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
445	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
446	#485	C₂²×C₁₉	1	4	yes	complemented
447	#485	C₂²×C₁₉	1	4	yes	complemented
448	#483	C₂²×C₁₉	1	4	yes	complemented
449	#480	C₂²×C₁₉	1	4	yes	complemented
450	#477	C₂²×C₁₉	1	2	yes	complemented
451	#477	C₂²×C₁₉	1	2	yes	complemented
452	#476	C₂²×C₁₉	1	2	yes	complemented
453	#475	C₂²×C₁₉	1	2	yes	complemented
454	#470	C₂²×C₁₉	1	4	yes	complemented
455	#470	C₂²×C₁₉	1	4	yes	complemented
456	#468	C₂²×C₁₉	1	4	yes	complemented
457	#468	C₂²×C₁₉	1	4	yes	complemented
458	#467	C₂²×C₁₉	1	2	yes	—
459	#467	C₂²×C₁₉	1	2	yes	—
460	#467	C₂²×C₁₉	1	4	yes	—
461	#465	C₂²×C₁₉	1	2	yes	—
462	#465	C₂²×C₁₉	1	2	yes	—
463	#465	C₂²×C₁₉	1	4	yes	—
464	#462	C₂²×C₁₉	1	2	yes	complemented
465	#462	C₂²×C₁₉	1	2	yes	complemented
466	#461	C₂²×C₁₉	1	2	yes	complemented
467	#460	C₂²×C₁₉	1	2	yes	complemented
468	#452	C₂²×C₁₉	1	4	yes	complemented
469	#452	C₂²×C₁₉	1	4	yes	complemented
470	#451	C₂²×C₁₉	1	4	yes	complemented
471	#448	C₂²×C₁₉	1	4	yes	complemented
472	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
473	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
474	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
475	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
476	#436	C₂²×C₁₉	1	2	yes	—
477	#436	C₂²×C₁₉	1	2	yes	—
478	#436	C₂²×C₁₉	1	2	yes	—
479	#436	C₂²×C₁₉	1	2	yes	—
480	#428	C₂²×C₁₉	1	4	yes	complemented
481	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
482	#419	C₂²×C₁₉	1	4	yes	complemented
483	#417	C₂²×C₁₉	1	4	yes	complemented
484	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
485	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
486	C₂×C₁₉	—	2	2	no	—
487	C₂×C₁₉	—	4	4	no	—
488	C₂×C₁₉	—	8	2	no	—
489	C₂×C₁₉	#3496	1	1	yes	characteristic
490	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
491	C₂×C₁₉	#3584	1	1	yes	characteristic
492	C₂×#41	—	2	1	no	—
493	C₂×#41	C₂³×C₁₉	1	4	yes	—
494	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
495	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
497	#137	—	4	8	no	—
498	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
499	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
500	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
501	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
502	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
504	C₂×M₁₆	—	4	4	no	—
505	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
506	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
507	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
509	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
519	#127	—	2	2	no	—
520	#127	C₂³×C₁₉	1	1	yes	characteristic
521	#126	—	2	4	no	—
522	#125	—	2	2	no	—
523	#125	—	2	2	no	—
524	#125	—	2	1	no	—
525	#125	—	2	1	no	—
526	#125	—	2	1	no	—
527	#124	—	2	2	no	—
528	#124	—	2	4	no	—
529	#124	—	2	1	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
542	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
543	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
544	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
545	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
546	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	1	no	—
550	#121	—	2	4	no	—
551	#121	C₂³×C₁₉	1	2	yes	—
552	#121	C₂³×C₁₉	1	4	yes	—
553	#120	—	2	4	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
559	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
560	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
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	4	no	—
566	C₄×D₄	—	2	4	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	D₄×C₁₉	1	2	yes	—
570	C₄×D₄	D₄×C₁₉	1	2	yes	—
571	C₄×D₄	C₂³×C₁₉	1	2	yes	—
572	C₄×D₄	C₂³×C₁₉	1	2	yes	—
573	C₄×D₄	C₂³×C₁₉	1	2	yes	—
574	#117	—	2	1	no	—
575	#117	—	2	1	no	—
576	#117	—	2	1	no	—
577	#117	—	2	2	no	—
578	#117	C₂³×C₁₉	1	4	yes	—
579	C₂×C₄⋊C₄	—	2	4	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
583	C₂×C₂²⋊C₄	—	2	4	no	—
584	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
586	#107	C₂³×C₁₉	1	2	yes	—
587	#107	C₂³×C₁₉	1	4	yes	—
588	#107	C₂³×C₁₉	1	2	yes	—
589	#106	C₂³×C₁₉	1	2	yes	—
590	#106	C₂³×C₁₉	1	4	yes	—
591	#106	C₂³×C₁₉	1	2	yes	—
592	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
593	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
594	#103	C₂³×C₁₉	1	2	yes	—
595	#103	C₂³×C₁₉	1	4	yes	—
596	#103	C₂³×C₁₉	1	2	yes	—
597	#103	C₂³×C₁₉	1	2	yes	—
598	#103	C₂³×C₁₉	1	4	yes	—
599	#103	C₂³×C₁₉	1	4	yes	—
600	#103	C₂³×C₁₉	1	2	yes	—
601	#103	C₂³×C₁₉	1	2	yes	—
602	#103	C₂³×C₁₉	1	2	yes	—
603	#102	C₂³×C₁₉	1	2	yes	—
604	#102	C₂³×C₁₉	1	4	yes	—
605	#102	C₂³×C₁₉	1	2	yes	—
606	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
607	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
608	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
609	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
610	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
611	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
612	C₁₉	#62260	1	1	yes	characteristic, direct product factor, Sylow
613	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
614	#41	—	4	4	no	—
615	#41	—	4	4	no	—
616	#41	—	4	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	4	4	no	—
623	C₂×Q₈	—	4	4	no	—
624	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
634	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
635	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
644	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
645	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
648	Q₁₆	—	2	4	no	—
649	Q₁₆	—	4	2	no	—
650	Q₁₆	—	4	4	no	—
651	SD₁₆	—	2	4	no	—
652	SD₁₆	—	4	2	no	—
653	SD₁₆	—	4	4	no	—
654	M₁₆	—	2	8	no	—
655	M₁₆	—	4	4	no	—
656	C₂×C₈	—	2	2	no	—
657	C₂×C₈	—	4	1	no	—
658	C₂×C₈	—	4	2	no	—
659	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
660	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
661	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
662	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
663	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
688	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
689	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
701	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
707	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
708	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
709	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
710	C₂³	—	2	4	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	—	4	2	no	—
714	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
715	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	8	4	no	—
724	Q₈	—	8	1	no	—
725	Q₈	—	8	1	no	—
726	Q₈	—	8	1	no	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	4	no	—
735	D₄	—	8	4	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	8	4	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	—	8	4	no	—
754	C₂×C₄	C₁₉×#137	1	4	yes	complemented
755	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
761	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
762	C₈	—	2	1	no	—
763	C₈	—	2	4	no	—
764	C₈	—	2	1	no	—
765	C₈	—	2	1	no	—
766	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	4	no	—
776	C₂²	C₂×C₁₉×#137	1	2	yes	—
777	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
778	C₄	—	2	1	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	C₂×C₁₉×#137	1	2	yes	—
790	C₄	C₂×C₁₉×#137	1	2	yes	—
791	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
792	C₄	C₁₉×#585	1	1	yes	characteristic
793	C₂	—	2	2	no	—
794	C₂	—	4	4	no	—
795	C₂	—	8	2	no	—
796	C₂	C₁₉×#3496	1	1	yes	characteristic
797	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
798	C₂	C₁₉×#3584	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. C₁₉×#3501	C₂	semidirect
3. C₁₉×#3357	C₂	semidirect
4. C₁₉×#3356	C₂	semidirect
5. C₁₉×#3333	C₂	semidirect
6. C₁₉×#3331	C₂	semidirect
7. C₁₉×#3329	C₂	semidirect
8. C₁₉×#3328	C₂	semidirect
9. C₁₉×#3278	C₂	semidirect
10. C₁₉×#3276	C₂	semidirect
11. C₁₉×#3249	C₂	semidirect
12. C₁₉×#3246	C₂	semidirect
13. C₁₉×#3190	C₂	semidirect
14. C₁₉×#3170	C₂	semidirect
15. C₁₉×#3167	C₂	semidirect
16. C₁₉×#3056	C₂	semidirect
17. C₂×C₁₉×#436	C₂	semidirect
18. C₂×C₁₉×#137	C₂²	semidirect
45. C₁₉×#500	C₂²	semidirect
46. C₁₉×#498	C₂²	semidirect
47. C₁₉×#494	C₂²	semidirect
48. C₁₉×#492	C₂²	semidirect
49. C₁₉×#487	C₂²	semidirect
50. C₁₉×#487	C₂²	semidirect
51. C₁₉×#487	C₂²	semidirect
52. C₁₉×#486	C₂²	semidirect
53. C₁₉×#485	C₂²	semidirect
54. C₁₉×#485	C₂²	semidirect
55. C₁₉×#483	C₂²	semidirect
56. C₁₉×#480	C₂²	semidirect
57. C₁₉×#477	C₂²	semidirect
58. C₁₉×#477	C₂²	semidirect
59. C₁₉×#476	C₂²	semidirect
60. C₁₉×#475	C₂²	semidirect
61. C₁₉×#470	C₂²	semidirect
62. C₁₉×#470	C₂²	semidirect
63. C₁₉×#468	C₂²	semidirect
64. C₁₉×#468	C₂²	semidirect
71. C₁₉×#462	C₂²	semidirect
72. C₁₉×#462	C₂²	semidirect
73. C₁₉×#461	C₂²	semidirect
74. C₁₉×#460	C₂²	semidirect
75. C₁₉×#452	C₂²	semidirect
76. C₁₉×#452	C₂²	semidirect
77. C₁₉×#451	C₂²	semidirect
78. C₁₉×#448	C₂²	semidirect
79. C₄×Q₁₆×C₁₉	C₂²	semidirect
80. C₄×Q₁₆×C₁₉	C₂²	semidirect
81. C₄×SD₁₆×C₁₉	C₂²	semidirect
82. C₄×SD₁₆×C₁₉	C₂²	semidirect
87. C₁₉×#428	C₂²	semidirect
89. C₁₉×#419	C₂²	semidirect
90. C₁₉×#417	C₂²	semidirect
310. #62260	C₁₉	direct (N × H)
355. C₂×C₄×C₁₉	#137	semidirect
369. #3501	C₂×C₁₉	semidirect
370. #3357	C₂×C₁₉	semidirect
371. #3356	C₂×C₁₉	semidirect
372. #3333	C₂×C₁₉	semidirect
373. #3331	C₂×C₁₉	semidirect
374. #3329	C₂×C₁₉	semidirect
375. #3328	C₂×C₁₉	semidirect
376. #3278	C₂×C₁₉	semidirect
377. #3276	C₂×C₁₉	semidirect
378. #3249	C₂×C₁₉	semidirect
379. #3246	C₂×C₁₉	semidirect
380. #3190	C₂×C₁₉	semidirect
381. #3170	C₂×C₁₉	semidirect
382. #3167	C₂×C₁₉	semidirect
383. #3056	C₂×C₁₉	semidirect
384. C₂×#436	C₂×C₁₉	semidirect
411. C₂×#137	C₂²×C₁₉	semidirect
438. #500	C₂²×C₁₉	semidirect
439. #498	C₂²×C₁₉	semidirect
440. #494	C₂²×C₁₉	semidirect
441. #492	C₂²×C₁₉	semidirect
442. #487	C₂²×C₁₉	semidirect
443. #487	C₂²×C₁₉	semidirect
444. #487	C₂²×C₁₉	semidirect
445. #486	C₂²×C₁₉	semidirect
446. #485	C₂²×C₁₉	semidirect
447. #485	C₂²×C₁₉	semidirect
448. #483	C₂²×C₁₉	semidirect
449. #480	C₂²×C₁₉	semidirect
450. #477	C₂²×C₁₉	semidirect
451. #477	C₂²×C₁₉	semidirect
452. #476	C₂²×C₁₉	semidirect
453. #475	C₂²×C₁₉	semidirect
454. #470	C₂²×C₁₉	semidirect
455. #470	C₂²×C₁₉	semidirect
456. #468	C₂²×C₁₉	semidirect
457. #468	C₂²×C₁₉	semidirect
464. #462	C₂²×C₁₉	semidirect
465. #462	C₂²×C₁₉	semidirect
466. #461	C₂²×C₁₉	semidirect
467. #460	C₂²×C₁₉	semidirect
468. #452	C₂²×C₁₉	semidirect
469. #452	C₂²×C₁₉	semidirect
470. #451	C₂²×C₁₉	semidirect
471. #448	C₂²×C₁₉	semidirect
472. C₄×Q₁₆	C₂²×C₁₉	semidirect
473. C₄×Q₁₆	C₂²×C₁₉	semidirect
474. C₄×SD₁₆	C₂²×C₁₉	semidirect
475. C₄×SD₁₆	C₂²×C₁₉	semidirect
480. #428	C₂²×C₁₉	semidirect
482. #419	C₂²×C₁₉	semidirect
483. #417	C₂²×C₁₉	semidirect
612. C₁₉	#62260	direct (N × H)
754. C₂×C₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3506	2
C₁₉×#3501	2
C₁₉×#3357	2
C₁₉×#3356	2
C₁₉×#3333	2
C₁₉×#3331	2
C₁₉×#3329	2
C₁₉×#3328	2
C₁₉×#3278	2
C₁₉×#3276	2
C₁₉×#3249	2
C₁₉×#3246	2
C₁₉×#3190	2
C₁₉×#3170	2
C₁₉×#3167	2
C₁₉×#3056	2
C₂×C₁₉×#436	2
#62260	19

Subgroups — C19×#62260 #18068219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62260 #18068219