Subgroups — C₁₉×#62400 #18068359

Order 4864.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3401	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3389	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3376	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3370	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3256	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3251	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3183	C₂	1	2	yes	maximal, complemented
21	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₉×#3171	C₂	1	2	yes	maximal, complemented
23	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×#559	C₂²	1	1	yes	characteristic
25	C₁₉×#559	C₂²	1	1	yes	characteristic
26	C₁₉×#559	C₂²	1	1	yes	characteristic
27	C₁₉×#559	C₂²	1	2	yes	—
28	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#557	C₂²	1	1	yes	characteristic
30	C₁₉×#557	C₂²	1	1	yes	characteristic
31	C₁₉×#556	—	2	1	no	—
32	C₁₉×#556	—	2	1	no	—
33	C₁₉×#556	C₂²	1	2	yes	—
34	C₁₉×#554	C₂²	1	2	yes	—
35	C₁₉×#554	C₂²	1	1	yes	characteristic
36	C₁₉×#554	C₂²	1	2	yes	—
37	C₁₉×#552	—	2	2	no	—
38	C₁₉×#550	C₂²	1	1	yes	characteristic
39	C₁₉×#548	—	2	1	no	—
40	C₁₉×#547	—	2	1	no	—
41	C₁₉×#547	—	2	2	no	—
42	C₁₉×#542	—	2	2	no	—
43	C₁₉×#542	—	2	1	no	—
44	C₁₉×#539	—	2	2	no	—
45	C₁₉×#536	—	2	1	no	—
46	C₁₉×#533	C₂²	1	1	yes	characteristic
47	C₁₉×#532	C₂²	1	2	yes	—
48	C₁₉×#532	C₂²	1	1	yes	characteristic
49	C₁₉×#532	C₂²	1	1	yes	characteristic
50	C₁₉×#529	C₂²	1	2	yes	—
51	C₁₉×#529	C₂²	1	1	yes	characteristic
52	C₁₉×#529	C₂²	1	2	yes	—
53	C₁₉×#529	C₂²	1	2	yes	—
54	C₁₉×#520	—	2	1	no	—
55	C₁₉×#520	—	2	1	no	—
56	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
57	C₁₉×#501	C₂²	1	2	yes	—
58	C₁₉×#501	C₂²	1	1	yes	characteristic
59	C₁₉×#499	C₂²	1	2	yes	—
60	C₁₉×#498	C₂²	1	1	yes	characteristic
61	C₁₉×#497	C₂²	1	1	yes	characteristic
62	C₁₉×#496	C₂²	1	2	yes	—
63	C₁₉×#495	C₂²	1	2	yes	—
64	C₁₉×#493	C₂²	1	1	yes	characteristic
65	C₁₉×#491	C₂²	1	1	yes	characteristic
66	C₁₉×#490	C₂²	1	2	yes	—
67	C₁₉×#489	C₂²	1	2	yes	—
68	C₁₉×#489	C₂²	1	1	yes	characteristic
69	C₁₉×#488	C₂²	1	2	yes	—
70	C₁₉×#488	C₂²	1	2	yes	—
71	C₁₉×#486	C₂²	1	1	yes	characteristic
72	C₁₉×#486	C₂²	1	1	yes	characteristic
73	C₁₉×#479	C₂²	1	2	yes	—
74	C₁₉×#479	C₂²	1	2	yes	—
75	C₁₉×#478	C₂²	1	2	yes	—
76	C₁₉×#478	C₂²	1	2	yes	—
77	C₁₉×#478	C₂²	1	2	yes	—
78	C₁₉×#478	C₂²	1	2	yes	—
79	C₁₉×#478	C₂²	1	2	yes	—
80	C₁₉×#477	C₂²	1	1	yes	characteristic
81	C₁₉×#477	C₂²	1	1	yes	characteristic
82	C₁₉×#475	C₂²	1	1	yes	characteristic
83	C₁₉×#475	C₂²	1	2	yes	—
84	C₁₉×#474	C₂²	1	1	yes	characteristic
85	C₁₉×#474	C₂²	1	2	yes	—
86	C₁₉×#474	C₂²	1	2	yes	—
87	C₁₉×#470	C₂²	1	1	yes	characteristic
88	C₁₉×#470	C₂²	1	1	yes	characteristic
89	C₁₉×#469	C₂²	1	2	yes	—
90	C₁₉×#469	C₂²	1	2	yes	—
91	C₁₉×#469	C₂²	1	2	yes	—
92	C₁₉×#468	C₂²	1	1	yes	characteristic
93	C₁₉×#468	C₂²	1	2	yes	—
94	C₁₉×#468	C₂²	1	1	yes	characteristic
95	C₁₉×#468	C₂²	1	2	yes	—
96	C₁₉×#468	C₂²	1	2	yes	—
97	C₁₉×#464	C₂²	1	2	yes	—
98	C₁₉×#464	C₂²	1	2	yes	—
99	C₁₉×#463	C₂²	1	2	yes	—
100	C₁₉×#463	C₂²	1	2	yes	—
101	C₁₉×#463	C₂²	1	2	yes	—
102	C₁₉×#463	C₂²	1	2	yes	—
103	C₁₉×#463	C₂²	1	2	yes	—
104	C₁₉×#461	C₂²	1	2	yes	—
105	C₁₉×#460	C₂²	1	2	yes	—
106	C₁₉×#460	C₂²	1	1	yes	characteristic
107	C₁₉×#460	C₂²	1	1	yes	characteristic
108	C₁₉×#460	C₂²	1	1	yes	characteristic
109	C₁₉×#459	C₂²	1	1	yes	characteristic
110	C₁₉×#459	C₂²	1	2	yes	—
111	C₁₉×#446	C₂²	1	1	yes	characteristic
112	C₁₉×#446	C₂²	1	2	yes	—
113	C₁₉×#446	C₂²	1	1	yes	characteristic
114	C₁₉×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
117	C₁₉×#442	C₂²	1	2	yes	—
118	C₁₉×#442	C₂²	1	2	yes	—
119	C₁₉×#442	C₂²	1	2	yes	—
120	C₁₉×#441	C₂²	1	2	yes	—
121	C₁₉×#440	C₂²	1	2	yes	—
122	C₁₉×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₁₉	C₂²	1	2	yes	—
130	C₄×D₈×C₁₉	C₂²	1	2	yes	—
131	C₁₉×#423	C₂²	1	1	yes	characteristic
132	C₁₉×#423	C₂²	1	2	yes	—
133	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	1	no	—
137	C₂×#41×C₁₉	—	2	2	no	—
138	C₂×#41×C₁₉	—	2	1	no	—
139	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
140	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
147	C₂×D₈×C₁₉	C₂³	1	2	yes	—
148	C₂×D₈×C₁₉	C₂³	1	2	yes	—
149	C₂×D₈×C₁₉	C₂³	1	2	yes	—
150	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
152	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
153	C₁₉×C₄⋊Q₈	—	2	1	no	—
154	C₁₉×C₄⋊Q₈	—	2	1	no	—
155	C₁₉×C₄⋊Q₈	—	2	1	no	—
156	C₁₉×C₄⋊Q₈	—	2	2	no	—
157	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₉×#127	C₂³	1	1	yes	characteristic
163	C₁₉×#127	C₂³	1	2	yes	—
164	C₁₉×#127	C₂³	1	1	yes	characteristic
165	C₁₉×#126	—	2	2	no	—
166	C₁₉×#126	—	2	2	no	—
167	C₁₉×#126	—	2	2	no	—
168	C₁₉×#126	—	2	1	no	—
169	C₁₉×#126	—	2	2	no	—
170	C₁₉×#126	—	2	2	no	—
171	C₁₉×#125	—	2	2	no	—
172	C₁₉×#125	—	2	2	no	—
173	C₁₉×#125	—	2	1	no	—
174	C₁₉×#125	C₂³	1	2	yes	—
175	C₁₉×#125	C₂³	1	1	yes	characteristic
176	C₁₉×#125	C₂³	1	2	yes	—
177	C₁₉×#125	C₂³	1	2	yes	—
178	C₁₉×#124	—	2	1	no	—
179	C₁₉×#124	—	2	1	no	—
180	C₁₉×#124	—	2	1	no	—
181	C₁₉×#124	—	2	2	no	—
182	C₁₉×#124	—	2	2	no	—
183	C₁₉×#124	—	2	1	no	—
184	C₁₉×#124	—	2	1	no	—
185	C₁₉×#124	C₂³	1	2	yes	—
186	C₁₉×#124	C₂³	1	1	yes	characteristic
187	C₁₉×#124	C₂³	1	2	yes	—
188	C₁₉×#124	C₂³	1	2	yes	—
189	C₁₉×#123	—	2	2	no	—
190	C₁₉×#123	—	2	2	no	—
191	C₁₉×#123	—	2	2	no	—
192	C₁₉×#123	—	2	1	no	—
193	C₁₉×#123	—	2	2	no	—
194	C₁₉×#123	—	2	2	no	—
195	C₁₉×#123	—	2	2	no	—
196	C₁₉×#123	—	2	2	no	—
197	C₁₉×#123	—	2	2	no	—
198	C₁₉×C₂²⋊Q₈	—	2	2	no	—
199	C₁₉×C₂²⋊Q₈	—	2	2	no	—
200	C₁₉×C₂²⋊Q₈	—	2	1	no	—
201	C₁₉×C₂²⋊Q₈	—	2	2	no	—
202	C₁₉×C₂²⋊Q₈	—	2	1	no	—
203	C₁₉×C₂²⋊Q₈	—	2	2	no	—
204	C₁₉×C₂²⋊Q₈	—	2	2	no	—
205	C₁₉×C₂²⋊Q₈	—	2	2	no	—
206	C₁₉×C₂²⋊Q₈	—	2	2	no	—
207	C₁₉×C₂²⋊Q₈	—	2	2	no	—
208	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₁₉×#121	—	2	1	no	—
212	C₁₉×#121	—	2	1	no	—
213	C₁₉×#121	—	2	2	no	—
214	C₁₉×#121	—	2	1	no	—
215	C₁₉×#121	—	2	2	no	—
216	C₁₉×#121	C₂³	1	1	yes	characteristic
217	C₁₉×#121	C₂³	1	2	yes	—
218	C₁₉×#121	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₉	—	2	1	no	—
220	C₄×Q₈×C₁₉	—	2	1	no	—
221	C₄×Q₈×C₁₉	—	2	1	no	—
222	C₄×Q₈×C₁₉	—	2	1	no	—
223	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
224	C₄×Q₈×C₁₉	D₄	1	2	yes	—
225	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
227	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
231	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
232	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
235	C₄×D₄×C₁₉	—	2	2	no	—
236	C₄×D₄×C₁₉	—	2	2	no	—
237	C₄×D₄×C₁₉	—	2	1	no	—
238	C₄×D₄×C₁₉	—	2	2	no	—
239	C₄×D₄×C₁₉	—	2	1	no	—
240	C₄×D₄×C₁₉	—	2	2	no	—
241	C₄×D₄×C₁₉	—	2	1	no	—
242	C₄×D₄×C₁₉	—	2	1	no	—
243	C₄×D₄×C₁₉	—	2	2	no	—
244	C₄×D₄×C₁₉	—	2	1	no	—
245	C₄×D₄×C₁₉	—	2	1	no	—
246	C₄×D₄×C₁₉	C₂³	1	2	yes	—
247	C₄×D₄×C₁₉	C₂³	1	2	yes	—
248	C₄×D₄×C₁₉	C₂³	1	2	yes	—
249	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₉	C₂³	1	2	yes	—
251	C₄×D₄×C₁₉	C₂³	1	2	yes	—
252	C₄×D₄×C₁₉	C₂³	1	2	yes	—
253	C₄×D₄×C₁₉	C₂³	1	2	yes	—
254	C₁₉×#117	—	2	1	no	—
255	C₁₉×#117	—	2	2	no	—
256	C₁₉×#117	—	2	2	no	—
257	C₁₉×#117	—	2	1	no	—
258	C₁₉×#117	—	2	2	no	—
259	C₁₉×#117	—	2	2	no	—
260	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
262	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
263	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
265	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
266	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
267	C₁₉×#107	C₂³	1	1	yes	characteristic
268	C₁₉×#107	C₂³	1	2	yes	—
269	C₁₉×#107	C₂³	1	1	yes	characteristic
270	C₁₉×#107	C₂³	1	2	yes	—
271	C₁₉×#107	C₂³	1	2	yes	—
272	C₁₉×#106	C₂³	1	2	yes	—
273	C₁₉×#106	C₂³	1	1	yes	characteristic
274	C₁₉×#106	C₂³	1	2	yes	—
275	C₁₉×#106	C₂³	1	1	yes	characteristic
276	C₁₉×#106	C₂³	1	2	yes	—
277	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₉×#103	C₂³	1	1	yes	characteristic
285	C₁₉×#103	C₂³	1	1	yes	characteristic
286	C₁₉×#103	C₂³	1	2	yes	—
287	C₁₉×#103	C₂³	1	1	yes	characteristic
288	C₁₉×#103	C₂³	1	1	yes	characteristic
289	C₁₉×#103	C₂³	1	1	yes	characteristic
290	C₁₉×#103	C₂³	1	1	yes	characteristic
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#102	C₂³	1	1	yes	characteristic
294	C₁₉×#102	C₂³	1	2	yes	—
295	C₁₉×#102	C₂³	1	2	yes	—
296	C₁₉×#102	C₂³	1	2	yes	—
297	C₁₉×#102	C₂³	1	2	yes	—
298	C₁₉×#102	C₂³	1	1	yes	characteristic
299	C₁₉×#102	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	2	yes	—
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#97	C₂³	1	2	yes	—
305	C₁₉×#97	C₂³	1	2	yes	—
306	C₁₉×#97	C₂³	1	1	yes	characteristic
307	C₁₉×#97	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₁₉	C₂³	1	2	yes	—
309	C₄×C₈×C₁₉	C₂³	1	2	yes	—
310	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
312	#41×C₁₉	—	4	4	no	—
313	#41×C₁₉	—	4	4	no	—
314	#41×C₁₉	—	8	4	no	—
315	#41×C₁₉	—	8	2	no	—
316	C₂×Q₈×C₁₉	—	2	1	no	—
317	C₂×Q₈×C₁₉	—	2	1	no	—
318	C₂×Q₈×C₁₉	—	2	2	no	—
319	C₂×Q₈×C₁₉	—	2	1	no	—
320	C₂×Q₈×C₁₉	—	4	2	no	—
321	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₁₉	—	2	2	no	—
328	C₂×D₄×C₁₉	—	2	1	no	—
329	C₂×D₄×C₁₉	—	2	2	no	—
330	C₂×D₄×C₁₉	—	2	2	no	—
331	C₂×D₄×C₁₉	—	2	1	no	—
332	C₂×D₄×C₁₉	—	2	1	no	—
333	C₂×D₄×C₁₉	—	2	1	no	—
334	C₂×D₄×C₁₉	—	2	2	no	—
335	C₂×D₄×C₁₉	—	2	1	no	—
336	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
337	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
338	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₉	—	2	2	no	—
340	C₂²×C₄×C₁₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
352	Q₁₆×C₁₉	—	2	2	no	—
353	Q₁₆×C₁₉	—	4	1	no	—
354	SD₁₆×C₁₉	—	2	2	no	—
355	SD₁₆×C₁₉	—	4	2	no	—
356	SD₁₆×C₁₉	—	4	2	no	—
357	SD₁₆×C₁₉	—	4	2	no	—
358	SD₁₆×C₁₉	—	4	1	no	—
359	D₈×C₁₉	—	2	4	no	—
360	D₈×C₁₉	—	4	2	no	—
361	D₈×C₁₉	—	4	2	no	—
362	M₁₆×C₁₉	—	2	2	no	—
363	M₁₆×C₁₉	—	4	1	no	—
364	M₁₆×C₁₉	—	4	2	no	—
365	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
367	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
368	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₁₉	—	2	2	no	—
372	C₄⋊C₄×C₁₉	—	2	1	no	—
373	C₄⋊C₄×C₁₉	—	2	1	no	—
374	C₄⋊C₄×C₁₉	—	2	2	no	—
375	C₄⋊C₄×C₁₉	—	2	1	no	—
376	C₄⋊C₄×C₁₉	—	2	2	no	—
377	C₄⋊C₄×C₁₉	—	2	2	no	—
378	C₄⋊C₄×C₁₉	—	2	1	no	—
379	C₄⋊C₄×C₁₉	—	2	1	no	—
380	C₄⋊C₄×C₁₉	—	2	1	no	—
381	C₄⋊C₄×C₁₉	—	2	1	no	—
382	C₄⋊C₄×C₁₉	—	2	2	no	—
383	C₄⋊C₄×C₁₉	—	2	2	no	—
384	C₄⋊C₄×C₁₉	—	2	1	no	—
385	C₄⋊C₄×C₁₉	—	2	2	no	—
386	C₄⋊C₄×C₁₉	—	2	1	no	—
387	C₄⋊C₄×C₁₉	—	2	1	no	—
388	C₄⋊C₄×C₁₉	—	2	1	no	—
389	C₄⋊C₄×C₁₉	—	2	1	no	—
390	C₄⋊C₄×C₁₉	—	2	2	no	—
391	C₄⋊C₄×C₁₉	—	2	2	no	—
392	C₄⋊C₄×C₁₉	—	2	2	no	—
393	C₄⋊C₄×C₁₉	—	2	1	no	—
394	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₁₉	—	2	1	no	—
408	C₂²⋊C₄×C₁₉	—	2	1	no	—
409	C₂²⋊C₄×C₁₉	—	2	1	no	—
410	C₂²⋊C₄×C₁₉	—	2	2	no	—
411	C₂²⋊C₄×C₁₉	—	2	2	no	—
412	C₂²⋊C₄×C₁₉	—	2	1	no	—
413	C₂²⋊C₄×C₁₉	—	2	2	no	—
414	C₂²⋊C₄×C₁₉	—	2	1	no	—
415	C₂²⋊C₄×C₁₉	—	2	2	no	—
416	C₂²⋊C₄×C₁₉	—	2	2	no	—
417	C₂²⋊C₄×C₁₉	—	2	2	no	—
418	C₂²⋊C₄×C₁₉	—	2	2	no	—
419	C₂²⋊C₄×C₁₉	—	2	2	no	—
420	C₂²⋊C₄×C₁₉	—	2	1	no	—
421	C₂²⋊C₄×C₁₉	—	2	2	no	—
422	C₂²⋊C₄×C₁₉	—	2	1	no	—
423	C₂²⋊C₄×C₁₉	—	2	2	no	—
424	C₂²⋊C₄×C₁₉	—	2	2	no	—
425	C₂²⋊C₄×C₁₉	—	2	2	no	—
426	C₂²⋊C₄×C₁₉	—	2	2	no	—
427	C₂²⋊C₄×C₁₉	—	2	2	no	—
428	C₂²⋊C₄×C₁₉	—	2	2	no	—
429	C₄²×C₁₉	—	2	2	no	—
430	C₄²×C₁₉	—	2	2	no	—
431	C₄²×C₁₉	—	2	2	no	—
432	C₄²×C₁₉	—	2	1	no	—
433	C₄²×C₁₉	—	2	1	no	—
434	C₄²×C₁₉	—	2	1	no	—
435	C₄²×C₁₉	C₂×D₄	1	2	yes	—
436	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₁₉	C₂×D₄	1	2	yes	—
438	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
440	C₄²×C₁₉	C₂⁴	1	2	yes	—
441	C₄²×C₁₉	C₂⁴	1	2	yes	—
442	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
443	#62400	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₁₉	—	2	2	no	—
445	C₂³×C₁₉	—	2	2	no	—
446	C₂³×C₁₉	—	2	1	no	—
447	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₁₉	—	2	2	no	—
449	Q₈×C₁₉	—	2	2	no	—
450	Q₈×C₁₉	—	2	1	no	—
451	Q₈×C₁₉	—	2	1	no	—
452	Q₈×C₁₉	—	2	1	no	—
453	Q₈×C₁₉	—	2	1	no	—
454	Q₈×C₁₉	—	2	1	no	—
455	Q₈×C₁₉	—	2	1	no	—
456	Q₈×C₁₉	—	4	2	no	—
457	Q₈×C₁₉	—	4	2	no	—
458	Q₈×C₁₉	—	8	1	no	—
459	Q₈×C₁₉	—	8	2	no	—
460	Q₈×C₁₉	—	8	1	no	—
461	D₄×C₁₉	—	2	2	no	—
462	D₄×C₁₉	—	2	2	no	—
463	D₄×C₁₉	—	2	1	no	—
464	D₄×C₁₉	—	2	2	no	—
465	D₄×C₁₉	—	2	1	no	—
466	D₄×C₁₉	—	2	2	no	—
467	D₄×C₁₉	—	4	4	no	—
468	D₄×C₁₉	—	4	4	no	—
469	D₄×C₁₉	—	4	2	no	—
470	D₄×C₁₉	—	4	4	no	—
471	D₄×C₁₉	—	4	2	no	—
472	D₄×C₁₉	—	4	2	no	—
473	D₄×C₁₉	—	8	1	no	—
474	D₄×C₁₉	—	8	2	no	—
475	D₄×C₁₉	—	8	1	no	—
476	C₂×C₄×C₁₉	—	2	2	no	—
477	C₂×C₄×C₁₉	—	2	1	no	—
478	C₂×C₄×C₁₉	—	2	1	no	—
479	C₂×C₄×C₁₉	—	2	1	no	—
480	C₂×C₄×C₁₉	—	2	1	no	—
481	C₂×C₄×C₁₉	—	2	1	no	—
482	C₂×C₄×C₁₉	—	2	2	no	—
483	C₂×C₄×C₁₉	—	2	1	no	—
484	C₂×C₄×C₁₉	—	2	1	no	—
485	C₂×C₄×C₁₉	—	2	2	no	—
486	C₂×C₄×C₁₉	—	2	1	no	—
487	C₂×C₄×C₁₉	—	2	1	no	—
488	C₂×C₄×C₁₉	—	4	2	no	—
489	C₂×C₄×C₁₉	—	4	2	no	—
490	C₂×C₄×C₁₉	—	4	1	no	—
491	C₂×C₄×C₁₉	—	4	4	no	—
492	C₂×C₄×C₁₉	—	4	4	no	—
493	C₂×C₄×C₁₉	—	4	2	no	—
494	C₂×C₄×C₁₉	—	8	2	no	—
495	C₂×C₄×C₁₉	—	8	2	no	—
496	C₂×C₄×C₁₉	—	8	2	no	—
497	C₂×C₄×C₁₉	—	8	2	no	—
498	C₂×C₄×C₁₉	—	8	2	no	—
499	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
509	C₈×C₁₉	—	2	1	no	—
510	C₈×C₁₉	—	2	1	no	—
511	C₈×C₁₉	—	2	2	no	—
512	C₈×C₁₉	—	2	2	no	—
513	C₈×C₁₉	—	2	1	no	—
514	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
515	#3522	C₂×C₁₉	1	1	yes	characteristic, complemented
516	#3507	C₂×C₁₉	1	1	yes	characteristic, complemented
517	#3401	C₂×C₁₉	1	2	yes	complemented
518	#3399	C₂×C₁₉	1	1	yes	characteristic, complemented
519	#3396	C₂×C₁₉	1	1	yes	characteristic, complemented
520	#3389	C₂×C₁₉	1	2	yes	complemented
521	#3387	C₂×C₁₉	1	1	yes	characteristic, complemented
522	#3381	C₂×C₁₉	1	1	yes	characteristic, complemented
523	#3376	C₂×C₁₉	1	2	yes	complemented
524	#3375	C₂×C₁₉	1	1	yes	characteristic, complemented
525	#3370	C₂×C₁₉	1	2	yes	complemented
526	#3368	C₂×C₁₉	1	1	yes	characteristic, complemented
527	#3365	C₂×C₁₉	1	1	yes	characteristic, complemented
528	#3361	C₂×C₁₉	1	1	yes	characteristic, complemented
529	#3256	C₂×C₁₉	1	2	yes	complemented
530	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
531	#3251	C₂×C₁₉	1	1	yes	characteristic, complemented
532	#3251	C₂×C₁₉	1	2	yes	complemented
533	#3184	C₂×C₁₉	1	1	yes	characteristic, complemented
534	#3183	C₂×C₁₉	1	2	yes	complemented
535	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
536	#3171	C₂×C₁₉	1	2	yes	complemented
537	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
538	C₂²×C₁₉	—	2	1	no	—
539	C₂²×C₁₉	—	2	1	no	—
540	C₂²×C₁₉	—	2	1	no	—
541	C₂²×C₁₉	—	4	1	no	—
542	C₂²×C₁₉	—	4	2	no	—
543	C₂²×C₁₉	—	4	2	no	—
544	C₂²×C₁₉	—	4	2	no	—
545	C₂²×C₁₉	—	4	2	no	—
546	C₂²×C₁₉	—	4	1	no	—
547	C₂²×C₁₉	—	4	2	no	—
548	C₂²×C₁₉	—	4	2	no	—
549	C₂²×C₁₉	—	4	1	no	—
550	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₁₉	—	2	2	no	—
552	C₄×C₁₉	—	2	1	no	—
553	C₄×C₁₉	—	2	2	no	—
554	C₄×C₁₉	—	2	1	no	—
555	C₄×C₁₉	—	2	1	no	—
556	C₄×C₁₉	—	2	1	no	—
557	C₄×C₁₉	—	2	2	no	—
558	C₄×C₁₉	—	2	2	no	—
559	C₄×C₁₉	—	4	1	no	—
560	C₄×C₁₉	—	4	2	no	—
561	C₄×C₁₉	—	4	1	no	—
562	C₄×C₁₉	—	4	1	no	—
563	C₄×C₁₉	—	4	1	no	—
564	C₄×C₁₉	—	4	1	no	—
565	C₄×C₁₉	—	4	1	no	—
566	C₄×C₁₉	—	4	1	no	—
567	C₄×C₁₉	—	4	2	no	—
568	C₄×C₁₉	#575	1	2	yes	—
569	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
570	C₄×C₁₉	#585	1	1	yes	characteristic
571	#559	C₂²×C₁₉	1	1	yes	characteristic
572	#559	C₂²×C₁₉	1	1	yes	characteristic
573	#559	C₂²×C₁₉	1	2	yes	—
574	#559	C₂²×C₁₉	1	1	yes	characteristic
575	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
576	#557	C₂²×C₁₉	1	1	yes	characteristic
577	#557	C₂²×C₁₉	1	1	yes	characteristic
578	#556	—	2	1	no	—
579	#556	—	2	1	no	—
580	#556	C₂²×C₁₉	1	2	yes	—
581	#554	C₂²×C₁₉	1	1	yes	characteristic
582	#554	C₂²×C₁₉	1	2	yes	—
583	#554	C₂²×C₁₉	1	2	yes	—
584	#552	—	2	2	no	—
585	#550	C₂²×C₁₉	1	1	yes	characteristic
586	#548	—	2	1	no	—
587	#547	—	2	1	no	—
588	#547	—	2	2	no	—
589	#542	—	2	2	no	—
590	#542	—	2	1	no	—
591	#539	—	2	2	no	—
592	#536	—	2	1	no	—
593	#533	C₂²×C₁₉	1	1	yes	characteristic
594	#532	C₂²×C₁₉	1	2	yes	—
595	#532	C₂²×C₁₉	1	1	yes	characteristic
596	#532	C₂²×C₁₉	1	1	yes	characteristic
597	#529	C₂²×C₁₉	1	2	yes	—
598	#529	C₂²×C₁₉	1	1	yes	characteristic
599	#529	C₂²×C₁₉	1	2	yes	—
600	#529	C₂²×C₁₉	1	2	yes	—
601	#520	—	2	1	no	—
602	#520	—	2	1	no	—
603	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
604	#501	C₂²×C₁₉	1	2	yes	—
605	#501	C₂²×C₁₉	1	1	yes	characteristic
606	#499	C₂²×C₁₉	1	2	yes	—
607	#498	C₂²×C₁₉	1	1	yes	characteristic
608	#497	C₂²×C₁₉	1	1	yes	characteristic
609	#496	C₂²×C₁₉	1	2	yes	—
610	#495	C₂²×C₁₉	1	2	yes	—
611	#493	C₂²×C₁₉	1	1	yes	characteristic
612	#491	C₂²×C₁₉	1	1	yes	characteristic
613	#490	C₂²×C₁₉	1	2	yes	—
614	#489	C₂²×C₁₉	1	1	yes	characteristic
615	#489	C₂²×C₁₉	1	2	yes	—
616	#488	C₂²×C₁₉	1	2	yes	—
617	#488	C₂²×C₁₉	1	2	yes	—
618	#486	C₂²×C₁₉	1	1	yes	characteristic
619	#486	C₂²×C₁₉	1	1	yes	characteristic
620	#479	C₂²×C₁₉	1	2	yes	—
621	#479	C₂²×C₁₉	1	2	yes	—
622	#478	C₂²×C₁₉	1	2	yes	—
623	#478	C₂²×C₁₉	1	2	yes	—
624	#478	C₂²×C₁₉	1	2	yes	—
625	#478	C₂²×C₁₉	1	2	yes	—
626	#478	C₂²×C₁₉	1	2	yes	—
627	#477	C₂²×C₁₉	1	1	yes	characteristic
628	#477	C₂²×C₁₉	1	1	yes	characteristic
629	#475	C₂²×C₁₉	1	1	yes	characteristic
630	#475	C₂²×C₁₉	1	2	yes	—
631	#474	C₂²×C₁₉	1	1	yes	characteristic
632	#474	C₂²×C₁₉	1	2	yes	—
633	#474	C₂²×C₁₉	1	2	yes	—
634	#470	C₂²×C₁₉	1	1	yes	characteristic
635	#470	C₂²×C₁₉	1	1	yes	characteristic
636	#469	C₂²×C₁₉	1	2	yes	—
637	#469	C₂²×C₁₉	1	2	yes	—
638	#469	C₂²×C₁₉	1	2	yes	—
639	#468	C₂²×C₁₉	1	1	yes	characteristic
640	#468	C₂²×C₁₉	1	2	yes	—
641	#468	C₂²×C₁₉	1	1	yes	characteristic
642	#468	C₂²×C₁₉	1	2	yes	—
643	#468	C₂²×C₁₉	1	2	yes	—
644	#464	C₂²×C₁₉	1	2	yes	—
645	#464	C₂²×C₁₉	1	2	yes	—
646	#463	C₂²×C₁₉	1	2	yes	—
647	#463	C₂²×C₁₉	1	2	yes	—
648	#463	C₂²×C₁₉	1	2	yes	—
649	#463	C₂²×C₁₉	1	2	yes	—
650	#463	C₂²×C₁₉	1	2	yes	—
651	#461	C₂²×C₁₉	1	2	yes	—
652	#460	C₂²×C₁₉	1	1	yes	characteristic
653	#460	C₂²×C₁₉	1	1	yes	characteristic
654	#460	C₂²×C₁₉	1	2	yes	—
655	#460	C₂²×C₁₉	1	1	yes	characteristic
656	#459	C₂²×C₁₉	1	1	yes	characteristic
657	#459	C₂²×C₁₉	1	2	yes	—
658	#446	C₂²×C₁₉	1	1	yes	characteristic
659	#446	C₂²×C₁₉	1	2	yes	—
660	#446	C₂²×C₁₉	1	1	yes	characteristic
661	#446	C₂²×C₁₉	1	2	yes	—
662	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
663	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
664	#442	C₂²×C₁₉	1	2	yes	—
665	#442	C₂²×C₁₉	1	2	yes	—
666	#442	C₂²×C₁₉	1	2	yes	—
667	#441	C₂²×C₁₉	1	2	yes	—
668	#440	C₂²×C₁₉	1	2	yes	—
669	#440	C₂²×C₁₉	1	2	yes	—
670	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
671	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
674	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
676	C₄×D₈	C₂²×C₁₉	1	2	yes	—
677	C₄×D₈	C₂²×C₁₉	1	2	yes	—
678	#423	C₂²×C₁₉	1	1	yes	characteristic
679	#423	C₂²×C₁₉	1	2	yes	—
680	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
681	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
682	C₂×C₁₉	—	4	1	no	—
683	C₂×C₁₉	—	8	2	no	—
684	C₂×C₁₉	—	8	1	no	—
685	C₂×C₁₉	—	8	2	no	—
686	C₂×C₁₉	#3497	1	1	yes	characteristic
687	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
688	C₂×C₁₉	#3585	1	1	yes	characteristic
689	C₂×#41	—	2	1	no	—
690	C₂×#41	—	2	1	no	—
691	C₂×#41	—	2	2	no	—
692	C₂×#41	—	2	1	no	—
693	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
694	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
695	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
698	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
701	C₂×D₈	C₂³×C₁₉	1	2	yes	—
702	C₂×D₈	C₂³×C₁₉	1	2	yes	—
703	C₂×D₈	C₂³×C₁₉	1	2	yes	—
704	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
705	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
706	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	2	1	no	—
710	C₄⋊Q₈	—	2	2	no	—
711	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
714	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
716	#127	C₂³×C₁₉	1	2	yes	—
717	#127	C₂³×C₁₉	1	1	yes	characteristic
718	#127	C₂³×C₁₉	1	1	yes	characteristic
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	1	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	C₂³×C₁₉	1	1	yes	characteristic
729	#125	C₂³×C₁₉	1	2	yes	—
730	#125	C₂³×C₁₉	1	2	yes	—
731	#125	C₂³×C₁₉	1	2	yes	—
732	#124	—	2	1	no	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	—	2	1	no	—
738	#124	—	2	1	no	—
739	#124	C₂³×C₁₉	1	2	yes	—
740	#124	C₂³×C₁₉	1	2	yes	—
741	#124	C₂³×C₁₉	1	1	yes	characteristic
742	#124	C₂³×C₁₉	1	2	yes	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
764	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	C₂³×C₁₉	1	2	yes	—
771	#121	C₂³×C₁₉	1	1	yes	characteristic
772	#121	C₂³×C₁₉	1	2	yes	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
778	C₄×Q₈	D₄×C₁₉	1	2	yes	—
779	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
781	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
782	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
784	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
788	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₁₉	1	2	yes	—
802	C₄×D₄	C₂³×C₁₉	1	2	yes	—
803	C₄×D₄	C₂³×C₁₉	1	2	yes	—
804	C₄×D₄	C₂³×C₁₉	1	2	yes	—
805	C₄×D₄	C₂³×C₁₉	1	2	yes	—
806	C₄×D₄	C₂³×C₁₉	1	2	yes	—
807	C₄×D₄	C₂³×C₁₉	1	2	yes	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	—	2	2	no	—
813	#117	—	2	2	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
818	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
819	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
820	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
821	#107	C₂³×C₁₉	1	1	yes	characteristic
822	#107	C₂³×C₁₉	1	2	yes	—
823	#107	C₂³×C₁₉	1	1	yes	characteristic
824	#107	C₂³×C₁₉	1	2	yes	—
825	#107	C₂³×C₁₉	1	2	yes	—
826	#106	C₂³×C₁₉	1	2	yes	—
827	#106	C₂³×C₁₉	1	1	yes	characteristic
828	#106	C₂³×C₁₉	1	2	yes	—
829	#106	C₂³×C₁₉	1	1	yes	characteristic
830	#106	C₂³×C₁₉	1	2	yes	—
831	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
834	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
835	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
836	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
837	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
838	#103	C₂³×C₁₉	1	1	yes	characteristic
839	#103	C₂³×C₁₉	1	1	yes	characteristic
840	#103	C₂³×C₁₉	1	2	yes	—
841	#103	C₂³×C₁₉	1	1	yes	characteristic
842	#103	C₂³×C₁₉	1	1	yes	characteristic
843	#103	C₂³×C₁₉	1	1	yes	characteristic
844	#103	C₂³×C₁₉	1	1	yes	characteristic
845	#103	C₂³×C₁₉	1	2	yes	—
846	#103	C₂³×C₁₉	1	2	yes	—
847	#102	C₂³×C₁₉	1	1	yes	characteristic
848	#102	C₂³×C₁₉	1	2	yes	—
849	#102	C₂³×C₁₉	1	2	yes	—
850	#102	C₂³×C₁₉	1	2	yes	—
851	#102	C₂³×C₁₉	1	2	yes	—
852	#102	C₂³×C₁₉	1	1	yes	characteristic
853	#102	C₂³×C₁₉	1	2	yes	—
854	#102	C₂³×C₁₉	1	2	yes	—
855	#102	C₂³×C₁₉	1	2	yes	—
856	#102	C₂³×C₁₉	1	2	yes	—
857	#102	C₂³×C₁₉	1	2	yes	—
858	#97	C₂³×C₁₉	1	2	yes	—
859	#97	C₂³×C₁₉	1	2	yes	—
860	#97	C₂³×C₁₉	1	1	yes	characteristic
861	#97	C₂³×C₁₉	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₁₉	1	2	yes	—
863	C₄×C₈	C₂³×C₁₉	1	2	yes	—
864	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
866	C₁₉	#62400	1	1	yes	characteristic, direct product factor, Sylow
867	#41	—	4	4	no	—
868	#41	—	4	4	no	—
869	#41	—	8	4	no	—
870	#41	—	8	2	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	4	2	no	—
876	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
877	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
878	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
879	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
880	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
881	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
892	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
893	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
904	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
905	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
907	Q₁₆	—	2	2	no	—
908	Q₁₆	—	4	1	no	—
909	SD₁₆	—	2	2	no	—
910	SD₁₆	—	4	2	no	—
911	SD₁₆	—	4	2	no	—
912	SD₁₆	—	4	2	no	—
913	SD₁₆	—	4	1	no	—
914	D₈	—	2	4	no	—
915	D₈	—	4	2	no	—
916	D₈	—	4	2	no	—
917	M₁₆	—	2	2	no	—
918	M₁₆	—	4	1	no	—
919	M₁₆	—	4	2	no	—
920	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
923	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
924	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
950	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
951	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
952	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
953	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
955	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
957	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	C₂×D₄×C₁₉	1	2	yes	—
991	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
992	C₄²	C₂×D₄×C₁₉	1	2	yes	—
993	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
994	C₄²	C₂⁴×C₁₉	1	2	yes	—
995	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
996	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
997	C₄²	C₂⁴×C₁₉	1	2	yes	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1002	Q₈	—	2	2	no	—
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	8	2	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	1	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	2	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	4	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	4	2	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	8	2	no	—
1028	D₄	—	8	1	no	—
1029	D₄	—	8	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1054	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1055	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1057	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1059	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1060	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1062	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	2	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	1	no	—
1068	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1082	C₄	—	2	1	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	C₁₉×#575	1	2	yes	—
1100	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
1101	C₄	C₁₉×#585	1	1	yes	characteristic
1102	C₂	—	4	1	no	—
1103	C₂	—	8	2	no	—
1104	C₂	—	8	1	no	—
1105	C₂	—	8	2	no	—
1106	C₂	C₁₉×#3497	1	1	yes	characteristic
1107	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
1108	C₂	C₁₉×#3585	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×#3522	C₂	semidirect
2. C₁₉×#3507	C₂	semidirect
3. C₁₉×#3401	C₂	semidirect
4. C₁₉×#3399	C₂	semidirect
5. C₁₉×#3396	C₂	semidirect
6. C₁₉×#3389	C₂	semidirect
7. C₁₉×#3387	C₂	semidirect
8. C₁₉×#3381	C₂	semidirect
9. C₁₉×#3376	C₂	semidirect
10. C₁₉×#3375	C₂	semidirect
11. C₁₉×#3370	C₂	semidirect
12. C₁₉×#3368	C₂	semidirect
13. C₁₉×#3365	C₂	semidirect
14. C₁₉×#3361	C₂	semidirect
15. C₁₉×#3256	C₂	semidirect
16. C₁₉×#3254	C₂	semidirect
17. C₁₉×#3251	C₂	semidirect
18. C₁₉×#3251	C₂	semidirect
19. C₁₉×#3184	C₂	semidirect
20. C₁₉×#3183	C₂	semidirect
21. C₁₉×#3172	C₂	semidirect
22. C₁₉×#3171	C₂	semidirect
23. Q₈×M₁₆×C₁₉	C₂	semidirect
443. #62400	C₁₉	direct (N × H)
515. #3522	C₂×C₁₉	semidirect
516. #3507	C₂×C₁₉	semidirect
517. #3401	C₂×C₁₉	semidirect
518. #3399	C₂×C₁₉	semidirect
519. #3396	C₂×C₁₉	semidirect
520. #3389	C₂×C₁₉	semidirect
521. #3387	C₂×C₁₉	semidirect
522. #3381	C₂×C₁₉	semidirect
523. #3376	C₂×C₁₉	semidirect
524. #3375	C₂×C₁₉	semidirect
525. #3370	C₂×C₁₉	semidirect
526. #3368	C₂×C₁₉	semidirect
527. #3365	C₂×C₁₉	semidirect
528. #3361	C₂×C₁₉	semidirect
529. #3256	C₂×C₁₉	semidirect
530. #3254	C₂×C₁₉	semidirect
531. #3251	C₂×C₁₉	semidirect
532. #3251	C₂×C₁₉	semidirect
533. #3184	C₂×C₁₉	semidirect
534. #3183	C₂×C₁₉	semidirect
535. #3172	C₂×C₁₉	semidirect
536. #3171	C₂×C₁₉	semidirect
537. Q₈×M₁₆	C₂×C₁₉	semidirect
866. C₁₉	#62400	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×#3522	2
C₁₉×#3507	2
C₁₉×#3401	2
C₁₉×#3399	2
C₁₉×#3396	2
C₁₉×#3389	2
C₁₉×#3387	2
C₁₉×#3381	2
C₁₉×#3376	2
C₁₉×#3375	2
C₁₉×#3370	2
C₁₉×#3368	2
C₁₉×#3365	2
C₁₉×#3361	2
C₁₉×#3256	2
C₁₉×#3254	2
C₁₉×#3251	2
C₁₉×#3184	2
C₁₉×#3183	2
C₁₉×#3172	2
C₁₉×#3171	2
Q₈×M₁₆×C₁₉	2
#62400	19

Subgroups — C19×#62400 #18068359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62400 #18068359