Subgroups — C₁₉×#62367 #18068326

Order 4864.

1690 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3507	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3402	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3401	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3388	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3377	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3376	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3371	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3370	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3250	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3248	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3247	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3181	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3180	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#559	C₂²	1	2	yes	—
21	C₁₉×#559	C₂²	1	2	yes	—
22	C₁₉×#557	C₂²	1	2	yes	—
23	C₁₉×#557	C₂²	1	2	yes	—
24	C₁₉×#556	—	2	2	no	—
25	C₁₉×#556	—	2	2	no	—
26	C₁₉×#556	C₂²	1	2	yes	—
27	C₁₉×#556	C₂²	1	2	yes	—
28	C₁₉×#554	C₂²	1	2	yes	—
29	C₁₉×#554	C₂²	1	2	yes	—
30	C₁₉×#552	—	2	2	no	—
31	C₁₉×#552	—	2	2	no	—
32	C₁₉×#539	—	2	2	no	—
33	C₁₉×#539	—	2	2	no	—
34	C₁₉×#536	—	2	2	no	—
35	C₁₉×#533	C₂²	1	2	yes	—
36	C₁₉×#532	C₂²	1	2	yes	—
37	C₁₉×#529	C₂²	1	2	yes	—
38	C₁₉×#529	C₂²	1	2	yes	—
39	C₁₉×#529	C₂²	1	2	yes	—
40	C₁₉×#529	C₂²	1	2	yes	—
41	C₁₉×#520	—	2	2	no	—
42	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#501	C₂²	1	2	yes	—
44	C₁₉×#501	C₂²	1	2	yes	—
45	C₁₉×#499	C₂²	1	1	yes	characteristic
46	C₁₉×#499	C₂²	1	1	yes	characteristic
47	C₁₉×#497	C₂²	1	2	yes	—
48	C₁₉×#496	C₂²	1	2	yes	—
49	C₁₉×#495	C₂²	1	1	yes	characteristic
50	C₁₉×#495	C₂²	1	1	yes	characteristic
51	C₁₉×#491	C₂²	1	2	yes	—
52	C₁₉×#490	C₂²	1	2	yes	—
53	C₁₉×#489	C₂²	1	2	yes	—
54	C₁₉×#489	C₂²	1	2	yes	—
55	C₁₉×#488	C₂²	1	2	yes	—
56	C₁₉×#488	C₂²	1	2	yes	—
57	C₁₉×#479	C₂²	1	2	yes	—
58	C₁₉×#479	C₂²	1	2	yes	—
59	C₁₉×#479	C₂²	1	2	yes	—
60	C₁₉×#479	C₂²	1	2	yes	—
61	C₁₉×#478	C₂²	1	2	yes	—
62	C₁₉×#478	C₂²	1	2	yes	—
63	C₁₉×#478	C₂²	1	2	yes	—
64	C₁₉×#478	C₂²	1	2	yes	—
65	C₁₉×#477	C₂²	1	2	yes	—
66	C₁₉×#476	C₂²	1	2	yes	—
67	C₁₉×#475	C₂²	1	2	yes	—
68	C₁₉×#474	C₂²	1	2	yes	—
69	C₁₉×#467	C₂²	1	1	yes	characteristic
70	C₁₉×#467	C₂²	1	1	yes	characteristic
71	C₁₉×#467	C₂²	1	2	yes	—
72	C₁₉×#466	C₂²	1	1	yes	characteristic
73	C₁₉×#466	C₂²	1	1	yes	characteristic
74	C₁₉×#466	C₂²	1	2	yes	—
75	C₁₉×#465	C₂²	1	2	yes	—
76	C₁₉×#465	C₂²	1	2	yes	—
77	C₁₉×#465	C₂²	1	2	yes	—
78	C₁₉×#465	C₂²	1	2	yes	—
79	C₁₉×#464	C₂²	1	2	yes	—
80	C₁₉×#464	C₂²	1	2	yes	—
81	C₁₉×#464	C₂²	1	2	yes	—
82	C₁₉×#464	C₂²	1	2	yes	—
83	C₁₉×#463	C₂²	1	2	yes	—
84	C₁₉×#463	C₂²	1	2	yes	—
85	C₁₉×#463	C₂²	1	2	yes	—
86	C₁₉×#463	C₂²	1	2	yes	—
87	C₁₉×#462	C₂²	1	2	yes	—
88	C₁₉×#461	C₂²	1	2	yes	—
89	C₁₉×#460	C₂²	1	2	yes	—
90	C₁₉×#459	C₂²	1	2	yes	—
91	C₁₉×#446	C₂²	1	2	yes	—
92	C₁₉×#446	C₂²	1	1	yes	characteristic
93	C₁₉×#446	C₂²	1	1	yes	characteristic
94	C₁₉×#446	C₂²	1	2	yes	—
95	C₁₉×#446	C₂²	1	1	yes	characteristic
96	C₁₉×#446	C₂²	1	1	yes	characteristic
97	C₁₉×#442	C₂²	1	2	yes	—
98	C₁₉×#442	C₂²	1	2	yes	—
99	C₁₉×#441	C₂²	1	2	yes	—
100	C₁₉×#441	C₂²	1	2	yes	—
101	C₁₉×#440	C₂²	1	2	yes	—
102	C₁₉×#440	C₂²	1	2	yes	—
103	C₁₉×#440	C₂²	1	2	yes	—
104	C₁₉×#440	C₂²	1	2	yes	—
105	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
106	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
107	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
109	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
110	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
111	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
112	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₁₉×#97	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
115	C₂×#41×C₁₉	—	2	2	no	—
116	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
117	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
124	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₈×C₁₉	C₂³	1	2	yes	—
127	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
130	C₁₉×C₄⋊Q₈	—	2	2	no	—
131	C₁₉×C₄⋊Q₈	—	2	2	no	—
132	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₉×#127	C₂³	1	2	yes	—
136	C₁₉×#126	—	2	2	no	—
137	C₁₉×#126	—	2	2	no	—
138	C₁₉×#126	—	2	2	no	—
139	C₁₉×#126	—	2	2	no	—
140	C₁₉×#126	—	2	2	no	—
141	C₁₉×#126	—	2	2	no	—
142	C₁₉×#126	—	2	2	no	—
143	C₁₉×#126	—	2	2	no	—
144	C₁₉×#125	—	2	2	no	—
145	C₁₉×#125	—	2	2	no	—
146	C₁₉×#125	—	2	2	no	—
147	C₁₉×#125	—	2	2	no	—
148	C₁₉×#125	—	2	2	no	—
149	C₁₉×#125	C₂³	1	2	yes	—
150	C₁₉×#125	C₂³	1	2	yes	—
151	C₁₉×#125	C₂³	1	2	yes	—
152	C₁₉×#125	C₂³	1	2	yes	—
153	C₁₉×#124	—	2	2	no	—
154	C₁₉×#124	—	2	2	no	—
155	C₁₉×#124	—	2	2	no	—
156	C₁₉×#124	C₂³	1	2	yes	—
157	C₁₉×#124	C₂³	1	2	yes	—
158	C₁₉×#124	C₂³	1	2	yes	—
159	C₁₉×#124	C₂³	1	2	yes	—
160	C₁₉×#123	—	2	2	no	—
161	C₁₉×#123	—	2	2	no	—
162	C₁₉×#123	—	2	2	no	—
163	C₁₉×#123	—	2	2	no	—
164	C₁₉×#123	—	2	2	no	—
165	C₁₉×#123	—	2	2	no	—
166	C₁₉×#123	—	2	2	no	—
167	C₁₉×#123	—	2	2	no	—
168	C₁₉×C₂²⋊Q₈	—	2	2	no	—
169	C₁₉×C₂²⋊Q₈	—	2	2	no	—
170	C₁₉×C₂²⋊Q₈	—	2	2	no	—
171	C₁₉×C₂²⋊Q₈	—	2	2	no	—
172	C₁₉×C₂²⋊Q₈	—	2	2	no	—
173	C₁₉×C₂²⋊Q₈	—	2	2	no	—
174	C₁₉×C₂²⋊Q₈	—	2	2	no	—
175	C₁₉×C₂²⋊Q₈	—	2	2	no	—
176	C₁₉×C₂²⋊Q₈	—	2	2	no	—
177	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₁₉×#121	—	2	2	no	—
180	C₁₉×#121	C₂³	1	2	yes	—
181	C₁₉×#121	C₂³	1	2	yes	—
182	C₄×Q₈×C₁₉	—	2	2	no	—
183	C₄×Q₈×C₁₉	—	2	2	no	—
184	C₄×Q₈×C₁₉	—	2	2	no	—
185	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
186	C₄×Q₈×C₁₉	D₄	1	2	yes	—
187	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
188	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
189	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
190	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
191	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
193	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
194	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
195	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
196	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
197	C₄×D₄×C₁₉	—	2	2	no	—
198	C₄×D₄×C₁₉	—	2	2	no	—
199	C₄×D₄×C₁₉	—	2	2	no	—
200	C₄×D₄×C₁₉	—	2	2	no	—
201	C₄×D₄×C₁₉	—	2	2	no	—
202	C₄×D₄×C₁₉	—	2	2	no	—
203	C₄×D₄×C₁₉	—	2	2	no	—
204	C₄×D₄×C₁₉	C₂³	1	2	yes	—
205	C₄×D₄×C₁₉	C₂³	1	2	yes	—
206	C₄×D₄×C₁₉	C₂³	1	2	yes	—
207	C₄×D₄×C₁₉	C₂³	1	2	yes	—
208	C₄×D₄×C₁₉	C₂³	1	2	yes	—
209	C₄×D₄×C₁₉	C₂³	1	2	yes	—
210	C₁₉×#117	—	2	2	no	—
211	C₁₉×#117	—	2	2	no	—
212	C₁₉×#117	—	2	2	no	—
213	C₁₉×#117	—	2	2	no	—
214	C₁₉×#117	—	2	2	no	—
215	C₁₉×#117	—	2	2	no	—
216	C₁₉×#117	—	2	2	no	—
217	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
220	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
221	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
223	C₁₉×#107	C₂³	1	1	yes	characteristic
224	C₁₉×#107	C₂³	1	1	yes	characteristic
225	C₁₉×#107	C₂³	1	1	yes	characteristic
226	C₁₉×#107	C₂³	1	1	yes	characteristic
227	C₁₉×#107	C₂³	1	2	yes	—
228	C₁₉×#107	C₂³	1	2	yes	—
229	C₁₉×#106	C₂³	1	2	yes	—
230	C₁₉×#106	C₂³	1	2	yes	—
231	C₁₉×#106	C₂³	1	2	yes	—
232	C₁₉×#106	C₂³	1	2	yes	—
233	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
234	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
239	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
240	C₁₉×#103	C₂³	1	2	yes	—
241	C₁₉×#103	C₂³	1	2	yes	—
242	C₁₉×#103	C₂³	1	2	yes	—
243	C₁₉×#103	C₂³	1	2	yes	—
244	C₁₉×#103	C₂³	1	2	yes	—
245	C₁₉×#103	C₂³	1	2	yes	—
246	C₁₉×#103	C₂³	1	2	yes	—
247	C₁₉×#103	C₂³	1	2	yes	—
248	C₁₉×#102	C₂³	1	2	yes	—
249	C₁₉×#102	C₂³	1	2	yes	—
250	C₁₉×#102	C₂³	1	2	yes	—
251	C₁₉×#102	C₂³	1	2	yes	—
252	C₁₉×#102	C₂³	1	2	yes	—
253	C₁₉×#102	C₂³	1	2	yes	—
254	C₁₉×#102	C₂³	1	2	yes	—
255	C₁₉×#102	C₂³	1	2	yes	—
256	C₁₉×#97	C₂³	1	2	yes	—
257	C₁₉×#97	C₂³	1	2	yes	—
258	C₁₉×#97	C₂³	1	2	yes	—
259	C₁₉×#97	C₂³	1	2	yes	—
260	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
264	#41×C₁₉	—	4	8	no	—
265	C₂×Q₈×C₁₉	—	2	2	no	—
266	C₂×Q₈×C₁₉	—	2	2	no	—
267	C₂×Q₈×C₁₉	—	4	2	no	—
268	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
269	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
270	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
271	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
272	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
273	C₂×D₄×C₁₉	—	2	2	no	—
274	C₂×D₄×C₁₉	—	2	2	no	—
275	C₂×D₄×C₁₉	—	2	2	no	—
276	C₂×D₄×C₁₉	—	2	2	no	—
277	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
278	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₉	—	2	2	no	—
280	C₂²×C₄×C₁₉	—	2	2	no	—
281	C₂²×C₄×C₁₉	—	2	2	no	—
282	C₂²×C₄×C₁₉	—	2	2	no	—
283	C₂²×C₄×C₁₉	—	2	2	no	—
284	C₂²×C₄×C₁₉	—	2	2	no	—
285	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
290	Q₁₆×C₁₉	—	2	2	no	—
291	Q₁₆×C₁₉	—	4	1	no	—
292	Q₁₆×C₁₉	—	4	2	no	—
293	SD₁₆×C₁₉	—	2	4	no	—
294	SD₁₆×C₁₉	—	4	2	no	—
295	SD₁₆×C₁₉	—	4	2	no	—
296	SD₁₆×C₁₉	—	4	2	no	—
297	D₈×C₁₉	—	2	2	no	—
298	D₈×C₁₉	—	4	2	no	—
299	D₈×C₁₉	—	4	1	no	—
300	C₂×C₈×C₁₉	—	2	2	no	—
301	C₂×C₈×C₁₉	—	4	2	no	—
302	C₂×C₈×C₁₉	—	4	1	no	—
303	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
304	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
305	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
307	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
308	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₁₉	—	2	2	no	—
310	C₄⋊C₄×C₁₉	—	2	2	no	—
311	C₄⋊C₄×C₁₉	—	2	2	no	—
312	C₄⋊C₄×C₁₉	—	2	2	no	—
313	C₄⋊C₄×C₁₉	—	2	2	no	—
314	C₄⋊C₄×C₁₉	—	2	2	no	—
315	C₄⋊C₄×C₁₉	—	2	2	no	—
316	C₄⋊C₄×C₁₉	—	2	2	no	—
317	C₄⋊C₄×C₁₉	—	2	2	no	—
318	C₄⋊C₄×C₁₉	—	2	2	no	—
319	C₄⋊C₄×C₁₉	—	2	2	no	—
320	C₄⋊C₄×C₁₉	—	2	2	no	—
321	C₄⋊C₄×C₁₉	—	2	2	no	—
322	C₄⋊C₄×C₁₉	—	2	2	no	—
323	C₄⋊C₄×C₁₉	—	2	2	no	—
324	C₄⋊C₄×C₁₉	—	2	2	no	—
325	C₄⋊C₄×C₁₉	—	2	2	no	—
326	C₄⋊C₄×C₁₉	—	2	2	no	—
327	C₄⋊C₄×C₁₉	—	2	2	no	—
328	C₄⋊C₄×C₁₉	—	2	2	no	—
329	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
333	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
334	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
336	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
340	C₂²⋊C₄×C₁₉	—	2	2	no	—
341	C₂²⋊C₄×C₁₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	—	2	2	no	—
350	C₂²⋊C₄×C₁₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₉	—	2	2	no	—
355	C₂²⋊C₄×C₁₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₉	—	2	2	no	—
357	C₂²⋊C₄×C₁₉	—	2	2	no	—
358	C₄²×C₁₉	—	2	2	no	—
359	C₄²×C₁₉	—	2	2	no	—
360	C₄²×C₁₉	—	2	2	no	—
361	C₄²×C₁₉	—	2	2	no	—
362	C₄²×C₁₉	—	2	2	no	—
363	C₄²×C₁₉	—	2	2	no	—
364	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₁₉	C₂×D₄	1	2	yes	—
367	C₄²×C₁₉	C₂×D₄	1	2	yes	—
368	C₄²×C₁₉	C₂⁴	1	2	yes	—
369	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
370	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
371	C₄²×C₁₉	C₂⁴	1	2	yes	—
372	#62367	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
373	C₂³×C₁₉	—	2	2	no	—
374	C₂³×C₁₉	—	2	2	no	—
375	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
376	Q₈×C₁₉	—	2	2	no	—
377	Q₈×C₁₉	—	2	2	no	—
378	Q₈×C₁₉	—	2	2	no	—
379	Q₈×C₁₉	—	2	2	no	—
380	Q₈×C₁₉	—	4	1	no	—
381	Q₈×C₁₉	—	4	2	no	—
382	Q₈×C₁₉	—	4	1	no	—
383	Q₈×C₁₉	—	4	4	no	—
384	Q₈×C₁₉	—	8	2	no	—
385	D₄×C₁₉	—	2	2	no	—
386	D₄×C₁₉	—	2	2	no	—
387	D₄×C₁₉	—	2	2	no	—
388	D₄×C₁₉	—	2	2	no	—
389	D₄×C₁₉	—	4	4	no	—
390	D₄×C₁₉	—	4	4	no	—
391	D₄×C₁₉	—	4	4	no	—
392	D₄×C₁₉	—	8	2	no	—
393	C₂×C₄×C₁₉	—	2	2	no	—
394	C₂×C₄×C₁₉	—	2	4	no	—
395	C₂×C₄×C₁₉	—	2	1	no	—
396	C₂×C₄×C₁₉	—	2	1	no	—
397	C₂×C₄×C₁₉	—	2	2	no	—
398	C₂×C₄×C₁₉	—	2	2	no	—
399	C₂×C₄×C₁₉	—	2	2	no	—
400	C₂×C₄×C₁₉	—	2	2	no	—
401	C₂×C₄×C₁₉	—	2	2	no	—
402	C₂×C₄×C₁₉	—	2	2	no	—
403	C₂×C₄×C₁₉	—	4	1	no	—
404	C₂×C₄×C₁₉	—	4	2	no	—
405	C₂×C₄×C₁₉	—	4	4	no	—
406	C₂×C₄×C₁₉	—	4	4	no	—
407	C₂×C₄×C₁₉	—	8	2	no	—
408	C₂×C₄×C₁₉	—	8	2	no	—
409	C₂×C₄×C₁₉	—	8	2	no	—
410	C₂×C₄×C₁₉	—	8	2	no	—
411	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
421	C₈×C₁₉	—	2	1	no	—
422	C₈×C₁₉	—	2	2	no	—
423	C₈×C₁₉	—	2	1	no	—
424	C₈×C₁₉	—	2	1	no	—
425	C₈×C₁₉	—	2	2	no	—
426	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
427	#3507	C₂×C₁₉	1	2	yes	complemented
428	#3403	C₂×C₁₉	1	1	yes	characteristic, complemented
429	#3402	C₂×C₁₉	1	1	yes	characteristic, complemented
430	#3401	C₂×C₁₉	1	2	yes	complemented
431	#3390	C₂×C₁₉	1	1	yes	characteristic, complemented
432	#3389	C₂×C₁₉	1	1	yes	characteristic, complemented
433	#3388	C₂×C₁₉	1	2	yes	complemented
434	#3377	C₂×C₁₉	1	2	yes	complemented
435	#3376	C₂×C₁₉	1	2	yes	complemented
436	#3371	C₂×C₁₉	1	2	yes	complemented
437	#3370	C₂×C₁₉	1	2	yes	complemented
438	#3250	C₂×C₁₉	1	2	yes	complemented
439	#3248	C₂×C₁₉	1	2	yes	complemented
440	#3247	C₂×C₁₉	1	2	yes	complemented
441	#3181	C₂×C₁₉	1	2	yes	complemented
442	#3180	C₂×C₁₉	1	2	yes	complemented
443	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
444	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
445	C₂×#446	C₂×C₁₉	1	1	yes	characteristic, complemented
446	C₂²×C₁₉	—	2	1	no	—
447	C₂²×C₁₉	—	2	1	no	—
448	C₂²×C₁₉	—	4	2	no	—
449	C₂²×C₁₉	—	4	2	no	—
450	C₂²×C₁₉	—	4	2	no	—
451	C₂²×C₁₉	—	4	2	no	—
452	C₂²×C₁₉	—	4	2	no	—
453	C₂²×C₁₉	—	4	2	no	—
454	C₂²×C₁₉	#575	1	2	yes	—
455	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
456	C₄×C₁₉	—	2	1	no	—
457	C₄×C₁₉	—	2	1	no	—
458	C₄×C₁₉	—	2	2	no	—
459	C₄×C₁₉	—	2	2	no	—
460	C₄×C₁₉	—	2	1	no	—
461	C₄×C₁₉	—	2	2	no	—
462	C₄×C₁₉	—	2	2	no	—
463	C₄×C₁₉	—	2	1	no	—
464	C₄×C₁₉	—	2	1	no	—
465	C₄×C₁₉	—	4	2	no	—
466	C₄×C₁₉	—	4	2	no	—
467	C₄×C₁₉	—	4	2	no	—
468	C₄×C₁₉	—	4	2	no	—
469	C₄×C₁₉	—	4	2	no	—
470	C₄×C₁₉	—	4	2	no	—
471	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
472	C₄×C₁₉	#585	1	1	yes	characteristic
473	#559	C₂²×C₁₉	1	2	yes	—
474	#559	C₂²×C₁₉	1	2	yes	—
475	#557	C₂²×C₁₉	1	2	yes	—
476	#557	C₂²×C₁₉	1	2	yes	—
477	#556	—	2	2	no	—
478	#556	—	2	2	no	—
479	#556	C₂²×C₁₉	1	2	yes	—
480	#556	C₂²×C₁₉	1	2	yes	—
481	#554	C₂²×C₁₉	1	2	yes	—
482	#554	C₂²×C₁₉	1	2	yes	—
483	#552	—	2	2	no	—
484	#552	—	2	2	no	—
485	#539	—	2	2	no	—
486	#539	—	2	2	no	—
487	#536	—	2	2	no	—
488	#533	C₂²×C₁₉	1	2	yes	—
489	#532	C₂²×C₁₉	1	2	yes	—
490	#529	C₂²×C₁₉	1	2	yes	—
491	#529	C₂²×C₁₉	1	2	yes	—
492	#529	C₂²×C₁₉	1	2	yes	—
493	#529	C₂²×C₁₉	1	2	yes	—
494	#520	—	2	2	no	—
495	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
496	#501	C₂²×C₁₉	1	2	yes	—
497	#501	C₂²×C₁₉	1	2	yes	—
498	#499	C₂²×C₁₉	1	1	yes	characteristic
499	#499	C₂²×C₁₉	1	1	yes	characteristic
500	#497	C₂²×C₁₉	1	2	yes	—
501	#496	C₂²×C₁₉	1	2	yes	—
502	#495	C₂²×C₁₉	1	1	yes	characteristic
503	#495	C₂²×C₁₉	1	1	yes	characteristic
504	#491	C₂²×C₁₉	1	2	yes	—
505	#490	C₂²×C₁₉	1	2	yes	—
506	#489	C₂²×C₁₉	1	2	yes	—
507	#489	C₂²×C₁₉	1	2	yes	—
508	#488	C₂²×C₁₉	1	2	yes	—
509	#488	C₂²×C₁₉	1	2	yes	—
510	#479	C₂²×C₁₉	1	2	yes	—
511	#479	C₂²×C₁₉	1	2	yes	—
512	#479	C₂²×C₁₉	1	2	yes	—
513	#479	C₂²×C₁₉	1	2	yes	—
514	#478	C₂²×C₁₉	1	2	yes	—
515	#478	C₂²×C₁₉	1	2	yes	—
516	#478	C₂²×C₁₉	1	2	yes	—
517	#478	C₂²×C₁₉	1	2	yes	—
518	#477	C₂²×C₁₉	1	2	yes	—
519	#476	C₂²×C₁₉	1	2	yes	—
520	#475	C₂²×C₁₉	1	2	yes	—
521	#474	C₂²×C₁₉	1	2	yes	—
522	#467	C₂²×C₁₉	1	1	yes	characteristic
523	#467	C₂²×C₁₉	1	1	yes	characteristic
524	#467	C₂²×C₁₉	1	2	yes	—
525	#466	C₂²×C₁₉	1	1	yes	characteristic
526	#466	C₂²×C₁₉	1	1	yes	characteristic
527	#466	C₂²×C₁₉	1	2	yes	—
528	#465	C₂²×C₁₉	1	2	yes	—
529	#465	C₂²×C₁₉	1	2	yes	—
530	#465	C₂²×C₁₉	1	2	yes	—
531	#465	C₂²×C₁₉	1	2	yes	—
532	#464	C₂²×C₁₉	1	2	yes	—
533	#464	C₂²×C₁₉	1	2	yes	—
534	#464	C₂²×C₁₉	1	2	yes	—
535	#464	C₂²×C₁₉	1	2	yes	—
536	#463	C₂²×C₁₉	1	2	yes	—
537	#463	C₂²×C₁₉	1	2	yes	—
538	#463	C₂²×C₁₉	1	2	yes	—
539	#463	C₂²×C₁₉	1	2	yes	—
540	#462	C₂²×C₁₉	1	2	yes	—
541	#461	C₂²×C₁₉	1	2	yes	—
542	#460	C₂²×C₁₉	1	2	yes	—
543	#459	C₂²×C₁₉	1	2	yes	—
544	#446	C₂²×C₁₉	1	2	yes	—
545	#446	C₂²×C₁₉	1	1	yes	characteristic
546	#446	C₂²×C₁₉	1	1	yes	characteristic
547	#446	C₂²×C₁₉	1	2	yes	—
548	#446	C₂²×C₁₉	1	1	yes	characteristic
549	#446	C₂²×C₁₉	1	1	yes	characteristic
550	#442	C₂²×C₁₉	1	2	yes	—
551	#442	C₂²×C₁₉	1	2	yes	—
552	#441	C₂²×C₁₉	1	2	yes	—
553	#441	C₂²×C₁₉	1	2	yes	—
554	#440	C₂²×C₁₉	1	2	yes	—
555	#440	C₂²×C₁₉	1	2	yes	—
556	#440	C₂²×C₁₉	1	2	yes	—
557	#440	C₂²×C₁₉	1	2	yes	—
558	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
559	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
560	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
561	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
562	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
563	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
564	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
565	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
566	C₂×#97	C₂²×C₁₉	1	2	yes	—
567	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
568	C₂×C₁₉	—	2	2	no	—
569	C₂×C₁₉	—	8	2	no	—
570	C₂×C₁₉	—	8	2	no	—
571	C₂×C₁₉	#3497	1	1	yes	characteristic
572	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
573	C₂×C₁₉	#3584	1	1	yes	characteristic
574	C₂×#41	—	2	2	no	—
575	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
576	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
577	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
578	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
583	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
584	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
585	C₂×D₈	C₂³×C₁₉	1	2	yes	—
586	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
587	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
588	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
589	C₄⋊Q₈	—	2	2	no	—
590	C₄⋊Q₈	—	2	2	no	—
591	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
593	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
594	#127	C₂³×C₁₉	1	2	yes	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	C₂³×C₁₉	1	2	yes	—
609	#125	C₂³×C₁₉	1	2	yes	—
610	#125	C₂³×C₁₉	1	2	yes	—
611	#125	C₂³×C₁₉	1	2	yes	—
612	#124	—	2	2	no	—
613	#124	—	2	2	no	—
614	#124	—	2	2	no	—
615	#124	C₂³×C₁₉	1	2	yes	—
616	#124	C₂³×C₁₉	1	2	yes	—
617	#124	C₂³×C₁₉	1	2	yes	—
618	#124	C₂³×C₁₉	1	2	yes	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
637	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
638	#121	—	2	2	no	—
639	#121	C₂³×C₁₉	1	2	yes	—
640	#121	C₂³×C₁₉	1	2	yes	—
641	C₄×Q₈	—	2	2	no	—
642	C₄×Q₈	—	2	2	no	—
643	C₄×Q₈	—	2	2	no	—
644	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
645	C₄×Q₈	D₄×C₁₉	1	2	yes	—
646	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
647	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
648	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
649	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
650	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
651	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
652	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
653	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
654	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
655	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	C₂³×C₁₉	1	2	yes	—
664	C₄×D₄	C₂³×C₁₉	1	2	yes	—
665	C₄×D₄	C₂³×C₁₉	1	2	yes	—
666	C₄×D₄	C₂³×C₁₉	1	2	yes	—
667	C₄×D₄	C₂³×C₁₉	1	2	yes	—
668	C₄×D₄	C₂³×C₁₉	1	2	yes	—
669	#117	—	2	2	no	—
670	#117	—	2	2	no	—
671	#117	—	2	2	no	—
672	#117	—	2	2	no	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	C₂×C₄⋊C₄	—	2	2	no	—
677	C₂×C₄⋊C₄	—	2	2	no	—
678	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
679	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
682	#107	C₂³×C₁₉	1	1	yes	characteristic
683	#107	C₂³×C₁₉	1	1	yes	characteristic
684	#107	C₂³×C₁₉	1	1	yes	characteristic
685	#107	C₂³×C₁₉	1	1	yes	characteristic
686	#107	C₂³×C₁₉	1	2	yes	—
687	#107	C₂³×C₁₉	1	2	yes	—
688	#106	C₂³×C₁₉	1	2	yes	—
689	#106	C₂³×C₁₉	1	2	yes	—
690	#106	C₂³×C₁₉	1	2	yes	—
691	#106	C₂³×C₁₉	1	2	yes	—
692	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
693	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
694	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
695	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
696	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
697	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
698	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
699	#103	C₂³×C₁₉	1	2	yes	—
700	#103	C₂³×C₁₉	1	2	yes	—
701	#103	C₂³×C₁₉	1	2	yes	—
702	#103	C₂³×C₁₉	1	2	yes	—
703	#103	C₂³×C₁₉	1	2	yes	—
704	#103	C₂³×C₁₉	1	2	yes	—
705	#103	C₂³×C₁₉	1	2	yes	—
706	#103	C₂³×C₁₉	1	2	yes	—
707	#102	C₂³×C₁₉	1	2	yes	—
708	#102	C₂³×C₁₉	1	2	yes	—
709	#102	C₂³×C₁₉	1	2	yes	—
710	#102	C₂³×C₁₉	1	2	yes	—
711	#102	C₂³×C₁₉	1	2	yes	—
712	#102	C₂³×C₁₉	1	2	yes	—
713	#102	C₂³×C₁₉	1	2	yes	—
714	#102	C₂³×C₁₉	1	2	yes	—
715	#97	C₂³×C₁₉	1	2	yes	—
716	#97	C₂³×C₁₉	1	2	yes	—
717	#97	C₂³×C₁₉	1	2	yes	—
718	#97	C₂³×C₁₉	1	2	yes	—
719	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
720	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
721	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
722	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
723	C₁₉	#62367	1	1	yes	characteristic, direct product factor, Sylow
724	#41	—	4	8	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
729	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
730	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
731	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
732	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
738	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
746	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
748	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
750	Q₁₆	—	2	2	no	—
751	Q₁₆	—	4	1	no	—
752	Q₁₆	—	4	2	no	—
753	SD₁₆	—	2	4	no	—
754	SD₁₆	—	4	2	no	—
755	SD₁₆	—	4	2	no	—
756	SD₁₆	—	4	2	no	—
757	D₈	—	2	2	no	—
758	D₈	—	4	2	no	—
759	D₈	—	4	1	no	—
760	C₂×C₈	—	2	2	no	—
761	C₂×C₈	—	4	2	no	—
762	C₂×C₈	—	4	1	no	—
763	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
764	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
765	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
766	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
767	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
768	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
793	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
794	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
795	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
796	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
797	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
825	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
826	C₄²	C₂×D₄×C₁₉	1	2	yes	—
827	C₄²	C₂×D₄×C₁₉	1	2	yes	—
828	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
829	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
830	C₄²	C₂⁴×C₁₉	1	2	yes	—
831	C₄²	C₂⁴×C₁₉	1	2	yes	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	4	1	no	—
840	Q₈	—	4	2	no	—
841	Q₈	—	4	1	no	—
842	Q₈	—	4	4	no	—
843	Q₈	—	8	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	2	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	4	no	—
851	D₄	—	8	2	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
871	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
874	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
879	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
880	C₈	—	2	1	no	—
881	C₈	—	2	2	no	—
882	C₈	—	2	1	no	—
883	C₈	—	2	1	no	—
884	C₈	—	2	2	no	—
885	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	C₁₉×#575	1	2	yes	—
895	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
896	C₄	—	2	1	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
912	C₄	C₁₉×#585	1	1	yes	characteristic
913	C₂	—	2	2	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	C₁₉×#3497	1	1	yes	characteristic
917	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
918	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3507	C₂	semidirect
2. C₁₉×#3403	C₂	semidirect
3. C₁₉×#3402	C₂	semidirect
4. C₁₉×#3401	C₂	semidirect
5. C₁₉×#3390	C₂	semidirect
6. C₁₉×#3389	C₂	semidirect
7. C₁₉×#3388	C₂	semidirect
8. C₁₉×#3377	C₂	semidirect
9. C₁₉×#3376	C₂	semidirect
10. C₁₉×#3371	C₂	semidirect
11. C₁₉×#3370	C₂	semidirect
12. C₁₉×#3250	C₂	semidirect
13. C₁₉×#3248	C₂	semidirect
14. C₁₉×#3247	C₂	semidirect
15. C₁₉×#3181	C₂	semidirect
16. C₁₉×#3180	C₂	semidirect
17. C₁₉×#3168	C₂	semidirect
18. C₁₉×#3168	C₂	semidirect
19. C₂×C₁₉×#446	C₂	semidirect
372. #62367	C₁₉	direct (N × H)
427. #3507	C₂×C₁₉	semidirect
428. #3403	C₂×C₁₉	semidirect
429. #3402	C₂×C₁₉	semidirect
430. #3401	C₂×C₁₉	semidirect
431. #3390	C₂×C₁₉	semidirect
432. #3389	C₂×C₁₉	semidirect
433. #3388	C₂×C₁₉	semidirect
434. #3377	C₂×C₁₉	semidirect
435. #3376	C₂×C₁₉	semidirect
436. #3371	C₂×C₁₉	semidirect
437. #3370	C₂×C₁₉	semidirect
438. #3250	C₂×C₁₉	semidirect
439. #3248	C₂×C₁₉	semidirect
440. #3247	C₂×C₁₉	semidirect
441. #3181	C₂×C₁₉	semidirect
442. #3180	C₂×C₁₉	semidirect
443. #3168	C₂×C₁₉	semidirect
444. #3168	C₂×C₁₉	semidirect
445. C₂×#446	C₂×C₁₉	semidirect
723. C₁₉	#62367	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×#3507	2
C₁₉×#3403	2
C₁₉×#3402	2
C₁₉×#3401	2
C₁₉×#3390	2
C₁₉×#3389	2
C₁₉×#3388	2
C₁₉×#3377	2
C₁₉×#3376	2
C₁₉×#3371	2
C₁₉×#3370	2
C₁₉×#3250	2
C₁₉×#3248	2
C₁₉×#3247	2
C₁₉×#3181	2
C₁₉×#3180	2
C₁₉×#3168	2
C₂×C₁₉×#446	2
#62367	19

Subgroups — C19×#62367 #18068326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62367 #18068326