Subgroups — C₁₉×#62267 #18068226

Order 4864.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3541	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3339	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3320	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3316	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3315	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3313	C₂	1	2	yes	maximal, complemented
10	D₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3201	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3196	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3175	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
29	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#563	—	2	2	no	—
31	C₁₉×#562	—	2	2	no	—
32	C₁₉×#556	C₂²	1	2	yes	—
33	C₁₉×#554	—	2	2	no	—
34	C₁₉×#554	C₂²	1	2	yes	—
35	C₁₉×#553	—	2	2	no	—
36	C₁₉×#553	C₂²	1	2	yes	—
37	C₁₉×#552	C₂²	1	2	yes	—
38	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
39	C₁₉×#548	C₂²	1	2	yes	—
40	C₁₉×#548	C₂²	1	2	yes	—
41	C₁₉×#547	C₂²	1	2	yes	—
42	C₁₉×#542	—	2	2	no	—
43	C₁₉×#542	C₂²	1	2	yes	—
44	C₁₉×#541	C₂²	1	2	yes	—
45	C₁₉×#539	—	2	2	no	—
46	C₁₉×#538	—	2	2	no	—
47	C₁₉×#538	—	2	2	no	—
48	C₁₉×#537	C₂²	1	2	yes	—
49	C₁₉×#536	C₂²	1	2	yes	—
50	C₁₉×#525	C₂²	1	2	yes	—
51	C₁₉×#525	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
53	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#495	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#491	C₂²	1	2	yes	complemented
58	C₁₉×#489	C₂²	1	2	yes	complemented
59	C₁₉×#485	C₂²	1	2	yes	—
60	C₁₉×#485	C₂²	1	2	yes	—
61	C₁₉×#485	C₂²	1	2	yes	complemented
62	C₁₉×#484	C₂²	1	2	yes	—
63	C₁₉×#484	C₂²	1	2	yes	complemented
64	C₁₉×#483	C₂²	1	2	yes	complemented
65	C₁₉×#482	C₂²	1	2	yes	complemented
66	C₁₉×#481	C₂²	1	2	yes	—
67	C₁₉×#479	C₂²	1	2	yes	complemented
68	C₁₉×#478	C₂²	1	2	yes	complemented
69	C₁₉×#477	C₂²	1	2	yes	complemented
70	C₁₉×#475	C₂²	1	2	yes	complemented
71	C₁₉×#470	C₂²	1	2	yes	—
72	C₁₉×#470	C₂²	1	2	yes	—
73	C₁₉×#470	C₂²	1	2	yes	complemented
74	C₁₉×#468	C₂²	1	2	yes	—
75	C₁₉×#468	C₂²	1	2	yes	—
76	C₁₉×#468	C₂²	1	2	yes	complemented
77	C₁₉×#467	C₂²	1	1	yes	characteristic
78	C₁₉×#467	C₂²	1	1	yes	characteristic
79	C₁₉×#467	C₂²	1	1	yes	characteristic
80	C₁₉×#467	C₂²	1	2	yes	—
81	C₁₉×#467	C₂²	1	1	yes	characteristic
82	C₁₉×#467	C₂²	1	1	yes	characteristic
83	C₁₉×#467	C₂²	1	1	yes	characteristic
84	C₁₉×#467	C₂²	1	2	yes	—
85	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
86	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
87	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
88	C₁₉×#466	C₂²	1	1	yes	characteristic
89	C₁₉×#466	C₂²	1	1	yes	characteristic
90	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
91	C₁₉×#465	C₂²	1	2	yes	—
92	C₁₉×#465	C₂²	1	2	yes	—
93	C₁₉×#464	C₂²	1	2	yes	complemented
94	C₁₉×#464	C₂²	1	2	yes	complemented
95	C₁₉×#462	C₂²	1	2	yes	complemented
96	C₁₉×#461	C₂²	1	2	yes	complemented
97	C₁₉×#452	C₂²	1	2	yes	—
98	C₁₉×#452	C₂²	1	2	yes	—
99	C₁₉×#452	C₂²	1	2	yes	complemented
100	C₁₉×#452	C₂²	1	2	yes	complemented
101	C₁₉×#451	C₂²	1	2	yes	—
102	C₁₉×#451	C₂²	1	2	yes	complemented
103	C₁₉×#448	C₂²	1	2	yes	—
104	C₁₉×#448	C₂²	1	2	yes	complemented
105	C₁₉×#441	C₂²	1	2	yes	complemented
106	C₁₉×#440	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
108	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
109	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
111	C₁₉×#435	C₂²	1	1	yes	characteristic
112	C₁₉×#435	C₂²	1	1	yes	characteristic
113	C₁₉×#435	C₂²	1	1	yes	characteristic
114	C₁₉×#435	C₂²	1	1	yes	characteristic
115	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
116	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
117	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
119	C₁₉×#427	C₂²	1	1	yes	characteristic
120	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
122	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
123	C₁₉×#424	C₂²	1	1	yes	characteristic
124	C₁₉×#419	C₂²	1	2	yes	complemented
125	C₁₉×#417	C₂²	1	2	yes	complemented
126	C₁₉×#416	C₂²	1	2	yes	—
127	C₂×C₁₉×#103	C₂²	1	2	yes	—
128	C₁₉×#408	C₂²	1	1	yes	characteristic
129	C₁₉×#407	C₂²	1	1	yes	characteristic
130	C₁₉×#405	C₂²	1	1	yes	characteristic
131	C₂×#41×C₁₉	C₂³	1	2	yes	—
132	C₂×#41×C₁₉	C₂³	1	2	yes	—
133	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
135	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₁₉×#135	—	4	2	no	—
138	C₁₉×#135	—	4	2	no	—
139	C₂×Q₁₆×C₁₉	—	4	2	no	—
140	C₂×Q₁₆×C₁₉	—	4	2	no	—
141	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
150	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
151	C₁₉×#131	—	4	2	no	—
152	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₁₉	—	4	2	no	—
157	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
165	C₁₉×C₄⋊Q₈	—	2	2	no	—
166	C₁₉×C₄⋊Q₈	—	2	2	no	—
167	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₁₉×#126	—	2	2	no	—
170	C₁₉×#126	—	2	2	no	—
171	C₁₉×#126	—	2	2	no	—
172	C₁₉×#126	—	2	2	no	—
173	C₁₉×#126	—	2	2	no	—
174	C₁₉×#126	—	2	2	no	—
175	C₁₉×#126	—	2	2	no	—
176	C₁₉×#125	—	2	2	no	—
177	C₁₉×#125	—	2	2	no	—
178	C₁₉×#125	—	2	2	no	—
179	C₁₉×#125	—	2	2	no	—
180	C₁₉×#125	C₂³	1	2	yes	—
181	C₁₉×#124	—	2	2	no	—
182	C₁₉×#124	—	2	2	no	—
183	C₁₉×#124	—	2	2	no	—
184	C₁₉×#124	—	2	2	no	—
185	C₁₉×#124	—	2	2	no	—
186	C₁₉×#124	C₂³	1	2	yes	—
187	C₁₉×#123	—	2	2	no	—
188	C₁₉×#123	—	2	2	no	—
189	C₁₉×#123	—	2	2	no	—
190	C₁₉×#123	—	2	2	no	—
191	C₁₉×#123	—	2	2	no	—
192	C₁₉×#123	—	2	2	no	—
193	C₁₉×#123	—	2	2	no	—
194	C₁₉×#123	—	2	2	no	—
195	C₁₉×#123	D₄	1	1	yes	characteristic
196	C₁₉×#123	D₄	1	1	yes	characteristic
197	C₁₉×C₂²⋊Q₈	—	2	2	no	—
198	C₁₉×C₂²⋊Q₈	—	2	2	no	—
199	C₁₉×C₂²⋊Q₈	—	2	2	no	—
200	C₁₉×C₂²⋊Q₈	—	2	2	no	—
201	C₁₉×C₂²⋊Q₈	—	2	2	no	—
202	C₁₉×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
208	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₉×#121	—	2	2	no	—
219	C₁₉×#121	—	2	2	no	—
220	C₁₉×#121	—	2	2	no	—
221	C₁₉×#121	—	2	2	no	—
222	C₁₉×#121	—	2	2	no	—
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	—	2	2	no	—
225	C₁₉×#121	D₄	1	1	yes	characteristic
226	C₁₉×#121	D₄	1	1	yes	characteristic
227	C₁₉×#121	C₂³	1	2	yes	—
228	C₁₉×#121	C₂³	1	2	yes	—
229	C₁₉×#121	C₂³	1	2	yes	—
230	C₁₉×#120	—	2	2	no	—
231	C₁₉×#120	D₄	1	1	yes	characteristic
232	C₁₉×#120	D₄	1	1	yes	characteristic
233	C₄×Q₈×C₁₉	—	2	2	no	—
234	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
235	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
236	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
237	C₄×D₄×C₁₉	—	2	2	no	—
238	C₄×D₄×C₁₉	—	2	2	no	—
239	C₄×D₄×C₁₉	—	2	2	no	—
240	C₄×D₄×C₁₉	—	2	2	no	—
241	C₄×D₄×C₁₉	—	2	2	no	—
242	C₄×D₄×C₁₉	—	2	2	no	—
243	C₄×D₄×C₁₉	—	2	2	no	—
244	C₄×D₄×C₁₉	C₂³	1	2	yes	—
245	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
249	C₁₉×#117	—	2	2	no	—
250	C₁₉×#117	C₂³	1	2	yes	—
251	C₁₉×#117	C₂³	1	2	yes	—
252	C₁₉×#117	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
254	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
255	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
257	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
258	C₁₉×#107	C₂³	1	1	yes	characteristic
259	C₁₉×#107	C₂³	1	1	yes	characteristic
260	C₁₉×#107	C₂³	1	2	yes	—
261	C₁₉×#107	C₂³	1	1	yes	characteristic
262	C₁₉×#107	C₂³	1	2	yes	—
263	C₁₉×#107	C₂³	1	1	yes	characteristic
264	C₁₉×#107	C₂³	1	2	yes	—
265	C₁₉×#106	C₂³	1	2	yes	—
266	C₁₉×#106	C₂³	1	2	yes	—
267	C₁₉×#106	C₂³	1	2	yes	—
268	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₁₉×#103	C₂³	1	2	yes	—
273	C₁₉×#103	C₂³	1	2	yes	—
274	C₁₉×#103	C₂³	1	2	yes	—
275	C₁₉×#103	C₂³	1	2	yes	—
276	C₁₉×#103	C₂³	1	2	yes	—
277	C₁₉×#103	C₂³	1	2	yes	—
278	C₁₉×#103	C₂³	1	2	yes	—
279	C₁₉×#103	C₂³	1	2	yes	—
280	C₁₉×#103	C₂³	1	2	yes	—
281	C₁₉×#103	C₂³	1	2	yes	—
282	C₁₉×#103	C₂³	1	2	yes	—
283	C₁₉×#103	C₂³	1	2	yes	—
284	C₁₉×#102	C₂³	1	2	yes	—
285	C₁₉×#102	C₂³	1	2	yes	—
286	C₁₉×#102	C₂³	1	2	yes	—
287	C₁₉×#102	C₂³	1	2	yes	—
288	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₁₉×#97	C₂³	1	1	yes	characteristic
297	C₁₉×#97	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
299	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
300	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
301	#41×C₁₉	—	4	1	no	—
302	#41×C₁₉	—	4	1	no	—
303	#41×C₁₉	—	4	2	no	—
304	#41×C₁₉	—	4	2	no	—
305	#41×C₁₉	—	4	2	no	—
306	#41×C₁₉	—	4	2	no	—
307	C₂×Q₈×C₁₉	—	2	2	no	—
308	C₂×Q₈×C₁₉	—	2	2	no	—
309	C₂×Q₈×C₁₉	—	2	2	no	—
310	C₂×Q₈×C₁₉	—	4	2	no	—
311	C₂×Q₈×C₁₉	—	4	2	no	—
312	C₂×Q₈×C₁₉	—	4	2	no	—
313	C₂×Q₈×C₁₉	—	4	2	no	—
314	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
315	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
316	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
317	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
318	C₂×D₄×C₁₉	—	2	2	no	—
319	C₂×D₄×C₁₉	—	2	2	no	—
320	C₂×D₄×C₁₉	—	2	2	no	—
321	C₂×D₄×C₁₉	—	2	2	no	—
322	C₂×D₄×C₁₉	—	2	2	no	—
323	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
324	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
325	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
326	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
327	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
328	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₁₉	—	2	2	no	—
332	C₂²×C₄×C₁₉	—	2	2	no	—
333	C₂²×C₄×C₁₉	—	2	2	no	—
334	C₂²×C₄×C₁₉	—	2	2	no	—
335	C₂²×C₄×C₁₉	—	2	2	no	—
336	C₂²×C₄×C₁₉	—	2	2	no	—
337	C₂²×C₄×C₁₉	—	2	2	no	—
338	C₂²×C₄×C₁₉	—	4	1	no	—
339	C₂²×C₄×C₁₉	—	4	1	no	—
340	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
348	Q₁₆×C₁₉	—	2	2	no	—
349	Q₁₆×C₁₉	—	2	2	no	—
350	Q₁₆×C₁₉	—	2	2	no	—
351	Q₁₆×C₁₉	—	4	2	no	—
352	Q₁₆×C₁₉	—	4	2	no	—
353	Q₁₆×C₁₉	—	4	2	no	—
354	SD₁₆×C₁₉	—	4	2	no	—
355	SD₁₆×C₁₉	—	4	2	no	—
356	SD₁₆×C₁₉	—	4	2	no	—
357	D₈×C₁₉	—	2	2	no	—
358	M₁₆×C₁₉	—	4	1	no	—
359	M₁₆×C₁₉	—	4	1	no	—
360	M₁₆×C₁₉	—	4	1	no	—
361	M₁₆×C₁₉	—	4	1	no	—
362	C₂×C₈×C₁₉	—	2	2	no	—
363	C₂×C₈×C₁₉	—	2	2	no	—
364	C₂×C₈×C₁₉	—	2	2	no	—
365	C₂×C₈×C₁₉	—	2	2	no	—
366	C₂×C₈×C₁₉	—	2	2	no	—
367	C₂×C₈×C₁₉	—	4	1	no	—
368	C₂×C₈×C₁₉	—	4	1	no	—
369	C₂×C₈×C₁₉	—	4	1	no	—
370	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₁₉	—	2	2	no	—
379	C₄⋊C₄×C₁₉	—	2	2	no	—
380	C₄⋊C₄×C₁₉	—	2	2	no	—
381	C₄⋊C₄×C₁₉	—	2	2	no	—
382	C₄⋊C₄×C₁₉	—	2	2	no	—
383	C₄⋊C₄×C₁₉	—	2	2	no	—
384	C₄⋊C₄×C₁₉	—	2	2	no	—
385	C₄⋊C₄×C₁₉	—	2	2	no	—
386	C₄⋊C₄×C₁₉	—	2	2	no	—
387	C₄⋊C₄×C₁₉	—	2	2	no	—
388	C₄⋊C₄×C₁₉	—	2	2	no	—
389	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
394	C₄⋊C₄×C₁₉	—	2	2	no	—
395	C₄⋊C₄×C₁₉	—	2	2	no	—
396	C₄⋊C₄×C₁₉	—	2	2	no	—
397	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₁₉	—	2	2	no	—
408	C₂²⋊C₄×C₁₉	—	2	2	no	—
409	C₂²⋊C₄×C₁₉	—	2	2	no	—
410	C₂²⋊C₄×C₁₉	—	2	2	no	—
411	C₂²⋊C₄×C₁₉	—	2	2	no	—
412	C₂²⋊C₄×C₁₉	—	2	2	no	—
413	C₂²⋊C₄×C₁₉	—	2	2	no	—
414	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
421	C₂²⋊C₄×C₁₉	—	2	2	no	—
422	C₂²⋊C₄×C₁₉	—	2	2	no	—
423	C₂²⋊C₄×C₁₉	—	2	2	no	—
424	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
425	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
426	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
427	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
428	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
429	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
430	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
431	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
432	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
433	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₁₉	—	2	2	no	—
435	C₄²×C₁₉	—	2	2	no	—
436	C₄²×C₁₉	—	2	2	no	—
437	C₄²×C₁₉	—	2	2	no	—
438	C₄²×C₁₉	—	2	2	no	—
439	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
440	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
441	#62267	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂³×C₁₉	—	2	2	no	—
443	C₂³×C₁₉	—	2	2	no	—
444	C₂³×C₁₉	—	4	1	no	—
445	C₂³×C₁₉	—	4	1	no	—
446	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
449	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₁₉	—	2	2	no	—
452	Q₈×C₁₉	—	2	2	no	—
453	Q₈×C₁₉	—	2	2	no	—
454	Q₈×C₁₉	—	2	2	no	—
455	Q₈×C₁₉	—	2	2	no	—
456	Q₈×C₁₉	—	2	2	no	—
457	Q₈×C₁₉	—	4	1	no	—
458	Q₈×C₁₉	—	8	2	no	—
459	Q₈×C₁₉	—	8	2	no	—
460	Q₈×C₁₉	—	8	2	no	—
461	D₄×C₁₉	—	2	2	no	—
462	D₄×C₁₉	—	2	2	no	—
463	D₄×C₁₉	—	2	2	no	—
464	D₄×C₁₉	—	2	2	no	—
465	D₄×C₁₉	—	4	1	no	—
466	D₄×C₁₉	—	4	1	no	—
467	D₄×C₁₉	—	4	1	no	—
468	D₄×C₁₉	—	4	1	no	—
469	D₄×C₁₉	—	4	1	no	—
470	D₄×C₁₉	—	4	4	no	—
471	D₄×C₁₉	—	8	2	no	—
472	D₄×C₁₉	—	8	2	no	—
473	D₄×C₁₉	—	8	2	no	—
474	D₄×C₁₉	—	8	2	no	—
475	C₂×C₄×C₁₉	—	2	1	no	—
476	C₂×C₄×C₁₉	—	2	1	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	1	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	2	no	—
487	C₂×C₄×C₁₉	—	2	2	no	—
488	C₂×C₄×C₁₉	—	2	2	no	—
489	C₂×C₄×C₁₉	—	2	2	no	—
490	C₂×C₄×C₁₉	—	2	2	no	—
491	C₂×C₄×C₁₉	—	2	2	no	—
492	C₂×C₄×C₁₉	—	4	1	no	—
493	C₂×C₄×C₁₉	—	4	1	no	—
494	C₂×C₄×C₁₉	—	4	1	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	—	8	2	no	—
500	C₂×C₄×C₁₉	—	8	2	no	—
501	C₂×C₄×C₁₉	—	8	2	no	—
502	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
512	C₈×C₁₉	—	2	1	no	—
513	C₈×C₁₉	—	2	1	no	—
514	C₈×C₁₉	—	2	1	no	—
515	C₈×C₁₉	—	2	1	no	—
516	C₈×C₁₉	—	2	1	no	—
517	C₈×C₁₉	—	2	1	no	—
518	C₈×C₁₉	—	2	1	no	—
519	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
520	#3541	C₂×C₁₉	1	2	yes	complemented
521	#3342	C₂×C₁₉	1	1	yes	characteristic, complemented
522	#3339	C₂×C₁₉	1	1	yes	characteristic, complemented
523	#3338	C₂×C₁₉	1	1	yes	characteristic, complemented
524	#3336	C₂×C₁₉	1	1	yes	characteristic, complemented
525	#3320	C₂×C₁₉	1	2	yes	complemented
526	#3316	C₂×C₁₉	1	2	yes	complemented
527	#3315	C₂×C₁₉	1	2	yes	complemented
528	#3313	C₂×C₁₉	1	2	yes	complemented
529	D₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
530	#3285	C₂×C₁₉	1	1	yes	characteristic, complemented
531	#3285	C₂×C₁₉	1	1	yes	characteristic, complemented
532	#3283	C₂×C₁₉	1	1	yes	characteristic, complemented
533	#3258	C₂×C₁₉	1	2	yes	complemented
534	#3201	C₂×C₁₉	1	2	yes	complemented
535	#3196	C₂×C₁₉	1	2	yes	complemented
536	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
537	#3175	C₂×C₁₉	1	1	yes	characteristic, complemented
538	#3061	C₂×C₁₉	1	1	yes	characteristic, complemented
539	#3059	C₂×C₁₉	1	1	yes	characteristic, complemented
540	#3050	C₂×C₁₉	1	1	yes	characteristic, complemented
541	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
542	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
543	C₂²×C₁₉	—	2	1	no	—
544	C₂²×C₁₉	—	2	1	no	—
545	C₂²×C₁₉	—	2	1	no	—
546	C₂²×C₁₉	—	2	1	no	—
547	C₂²×C₁₉	—	2	1	no	—
548	C₂²×C₁₉	—	2	1	no	—
549	C₂²×C₁₉	—	2	1	no	—
550	C₂²×C₁₉	—	2	1	no	—
551	C₂²×C₁₉	—	2	1	no	—
552	C₂²×C₁₉	—	2	1	no	—
553	C₂²×C₁₉	—	2	1	no	—
554	C₂²×C₁₉	—	2	1	no	—
555	C₂²×C₁₉	—	2	1	no	—
556	C₂²×C₁₉	—	2	1	no	—
557	C₂²×C₁₉	—	4	4	no	—
558	C₂²×C₁₉	—	4	2	no	—
559	C₂²×C₁₉	—	4	2	no	—
560	C₂²×C₁₉	—	4	2	no	—
561	C₂²×C₁₉	#578	1	2	yes	—
562	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
563	C₄×C₁₉	—	2	1	no	—
564	C₄×C₁₉	—	2	1	no	—
565	C₄×C₁₉	—	2	1	no	—
566	C₄×C₁₉	—	2	1	no	—
567	C₄×C₁₉	—	2	1	no	—
568	C₄×C₁₉	—	2	1	no	—
569	C₄×C₁₉	—	2	1	no	—
570	C₄×C₁₉	—	2	1	no	—
571	C₄×C₁₉	—	2	1	no	—
572	C₄×C₁₉	—	4	2	no	—
573	C₄×C₁₉	—	4	2	no	—
574	C₄×C₁₉	—	4	2	no	—
575	C₄×C₁₉	—	4	2	no	—
576	C₄×C₁₉	—	4	2	no	—
577	C₄×C₁₉	—	4	2	no	—
578	C₄×C₁₉	—	4	2	no	—
579	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₄×C₁₉	#585	1	1	yes	characteristic
581	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
582	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic, complemented
583	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
584	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
585	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
586	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
587	#563	—	2	2	no	—
588	#562	—	2	2	no	—
589	#556	C₂²×C₁₉	1	2	yes	—
590	#554	—	2	2	no	—
591	#554	C₂²×C₁₉	1	2	yes	—
592	#553	—	2	2	no	—
593	#553	C₂²×C₁₉	1	2	yes	—
594	#552	C₂²×C₁₉	1	2	yes	—
595	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
596	#548	C₂²×C₁₉	1	2	yes	—
597	#548	C₂²×C₁₉	1	2	yes	—
598	#547	C₂²×C₁₉	1	2	yes	—
599	#542	—	2	2	no	—
600	#542	C₂²×C₁₉	1	2	yes	—
601	#541	C₂²×C₁₉	1	2	yes	—
602	#539	—	2	2	no	—
603	#538	—	2	2	no	—
604	#538	—	2	2	no	—
605	#537	C₂²×C₁₉	1	2	yes	—
606	#536	C₂²×C₁₉	1	2	yes	—
607	#525	C₂²×C₁₉	1	2	yes	—
608	#525	C₂²×C₁₉	1	1	yes	characteristic
609	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
610	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
611	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
612	#495	C₂²×C₁₉	1	1	yes	characteristic, complemented
613	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
614	#491	C₂²×C₁₉	1	2	yes	complemented
615	#489	C₂²×C₁₉	1	2	yes	complemented
616	#485	C₂²×C₁₉	1	2	yes	—
617	#485	C₂²×C₁₉	1	2	yes	—
618	#485	C₂²×C₁₉	1	2	yes	complemented
619	#484	C₂²×C₁₉	1	2	yes	—
620	#484	C₂²×C₁₉	1	2	yes	complemented
621	#483	C₂²×C₁₉	1	2	yes	complemented
622	#482	C₂²×C₁₉	1	2	yes	complemented
623	#481	C₂²×C₁₉	1	2	yes	—
624	#479	C₂²×C₁₉	1	2	yes	complemented
625	#478	C₂²×C₁₉	1	2	yes	complemented
626	#477	C₂²×C₁₉	1	2	yes	complemented
627	#475	C₂²×C₁₉	1	2	yes	complemented
628	#470	C₂²×C₁₉	1	2	yes	—
629	#470	C₂²×C₁₉	1	2	yes	—
630	#470	C₂²×C₁₉	1	2	yes	complemented
631	#468	C₂²×C₁₉	1	2	yes	—
632	#468	C₂²×C₁₉	1	2	yes	—
633	#468	C₂²×C₁₉	1	2	yes	complemented
634	#467	C₂²×C₁₉	1	1	yes	characteristic
635	#467	C₂²×C₁₉	1	1	yes	characteristic
636	#467	C₂²×C₁₉	1	1	yes	characteristic
637	#467	C₂²×C₁₉	1	1	yes	characteristic
638	#467	C₂²×C₁₉	1	1	yes	characteristic
639	#467	C₂²×C₁₉	1	1	yes	characteristic
640	#467	C₂²×C₁₉	1	2	yes	—
641	#467	C₂²×C₁₉	1	2	yes	—
642	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
643	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
644	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	#466	C₂²×C₁₉	1	1	yes	characteristic
646	#466	C₂²×C₁₉	1	1	yes	characteristic
647	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
648	#465	C₂²×C₁₉	1	2	yes	—
649	#465	C₂²×C₁₉	1	2	yes	—
650	#464	C₂²×C₁₉	1	2	yes	complemented
651	#464	C₂²×C₁₉	1	2	yes	complemented
652	#462	C₂²×C₁₉	1	2	yes	complemented
653	#461	C₂²×C₁₉	1	2	yes	complemented
654	#452	C₂²×C₁₉	1	2	yes	—
655	#452	C₂²×C₁₉	1	2	yes	—
656	#452	C₂²×C₁₉	1	2	yes	complemented
657	#452	C₂²×C₁₉	1	2	yes	complemented
658	#451	C₂²×C₁₉	1	2	yes	—
659	#451	C₂²×C₁₉	1	2	yes	complemented
660	#448	C₂²×C₁₉	1	2	yes	—
661	#448	C₂²×C₁₉	1	2	yes	complemented
662	#441	C₂²×C₁₉	1	2	yes	complemented
663	#440	C₂²×C₁₉	1	2	yes	complemented
664	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	#435	C₂²×C₁₉	1	1	yes	characteristic
669	#435	C₂²×C₁₉	1	1	yes	characteristic
670	#435	C₂²×C₁₉	1	1	yes	characteristic
671	#435	C₂²×C₁₉	1	1	yes	characteristic
672	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
673	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
674	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
675	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
676	#427	C₂²×C₁₉	1	1	yes	characteristic
677	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
678	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
679	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
680	#424	C₂²×C₁₉	1	1	yes	characteristic
681	#419	C₂²×C₁₉	1	2	yes	complemented
682	#417	C₂²×C₁₉	1	2	yes	complemented
683	#416	C₂²×C₁₉	1	2	yes	—
684	C₂×#103	C₂²×C₁₉	1	2	yes	—
685	#408	C₂²×C₁₉	1	1	yes	characteristic
686	#407	C₂²×C₁₉	1	1	yes	characteristic
687	#405	C₂²×C₁₉	1	1	yes	characteristic
688	C₂×C₁₉	—	2	2	no	—
689	C₂×C₁₉	—	4	1	no	—
690	C₂×C₁₉	—	4	1	no	—
691	C₂×C₁₉	—	4	1	no	—
692	C₂×C₁₉	—	4	1	no	—
693	C₂×C₁₉	—	8	2	no	—
694	C₂×C₁₉	#3496	1	1	yes	characteristic
695	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
696	C₂×C₁₉	#3584	1	1	yes	characteristic
697	C₂×#41	C₂³×C₁₉	1	2	yes	—
698	C₂×#41	C₂³×C₁₉	1	2	yes	—
699	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
700	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
701	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
702	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
703	#135	—	4	2	no	—
704	#135	—	4	2	no	—
705	C₂×Q₁₆	—	4	2	no	—
706	C₂×Q₁₆	—	4	2	no	—
707	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
708	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
709	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
710	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
716	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
717	#131	—	4	2	no	—
718	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
719	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
721	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
722	C₂²×C₈	—	4	2	no	—
723	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
724	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
725	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
726	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
727	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
731	C₄⋊Q₈	—	2	2	no	—
732	C₄⋊Q₈	—	2	2	no	—
733	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
734	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	C₂³×C₁₉	1	2	yes	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	C₂³×C₁₉	1	2	yes	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	D₄×C₁₉	1	1	yes	characteristic
762	#123	D₄×C₁₉	1	1	yes	characteristic
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
774	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
783	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	D₄×C₁₉	1	1	yes	characteristic
792	#121	D₄×C₁₉	1	1	yes	characteristic
793	#121	C₂³×C₁₉	1	2	yes	—
794	#121	C₂³×C₁₉	1	2	yes	—
795	#121	C₂³×C₁₉	1	2	yes	—
796	#120	—	2	2	no	—
797	#120	D₄×C₁₉	1	1	yes	characteristic
798	#120	D₄×C₁₉	1	1	yes	characteristic
799	C₄×Q₈	—	2	2	no	—
800	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
801	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
802	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	C₂³×C₁₉	1	2	yes	—
811	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
815	#117	—	2	2	no	—
816	#117	C₂³×C₁₉	1	2	yes	—
817	#117	C₂³×C₁₉	1	2	yes	—
818	#117	C₂³×C₁₉	1	1	yes	characteristic
819	C₂×C₄⋊C₄	—	2	2	no	—
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	#107	C₂³×C₁₉	1	1	yes	characteristic
825	#107	C₂³×C₁₉	1	1	yes	characteristic
826	#107	C₂³×C₁₉	1	2	yes	—
827	#107	C₂³×C₁₉	1	1	yes	characteristic
828	#107	C₂³×C₁₉	1	2	yes	—
829	#107	C₂³×C₁₉	1	1	yes	characteristic
830	#107	C₂³×C₁₉	1	2	yes	—
831	#106	C₂³×C₁₉	1	2	yes	—
832	#106	C₂³×C₁₉	1	2	yes	—
833	#106	C₂³×C₁₉	1	2	yes	—
834	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
838	#103	C₂³×C₁₉	1	2	yes	—
839	#103	C₂³×C₁₉	1	2	yes	—
840	#103	C₂³×C₁₉	1	2	yes	—
841	#103	C₂³×C₁₉	1	2	yes	—
842	#103	C₂³×C₁₉	1	2	yes	—
843	#103	C₂³×C₁₉	1	2	yes	—
844	#103	C₂³×C₁₉	1	2	yes	—
845	#103	C₂³×C₁₉	1	2	yes	—
846	#103	C₂³×C₁₉	1	2	yes	—
847	#103	C₂³×C₁₉	1	2	yes	—
848	#103	C₂³×C₁₉	1	2	yes	—
849	#103	C₂³×C₁₉	1	2	yes	—
850	#102	C₂³×C₁₉	1	2	yes	—
851	#102	C₂³×C₁₉	1	2	yes	—
852	#102	C₂³×C₁₉	1	2	yes	—
853	#102	C₂³×C₁₉	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
860	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
862	#97	C₂³×C₁₉	1	1	yes	characteristic
863	#97	C₂³×C₁₉	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
866	C₁₉	#62267	1	1	yes	characteristic, direct product factor, Sylow
867	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
868	#41	—	4	1	no	—
869	#41	—	4	1	no	—
870	#41	—	4	2	no	—
871	#41	—	4	2	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	4	2	no	—
878	C₂×Q₈	—	4	2	no	—
879	C₂×Q₈	—	4	2	no	—
880	C₂×Q₈	—	4	2	no	—
881	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
883	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
884	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
891	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
892	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
893	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
894	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
895	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
896	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
897	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
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	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	4	1	no	—
906	C₂²×C₄	—	4	1	no	—
907	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
908	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
909	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
915	Q₁₆	—	2	2	no	—
916	Q₁₆	—	2	2	no	—
917	Q₁₆	—	2	2	no	—
918	Q₁₆	—	4	2	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	2	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	D₈	—	2	2	no	—
925	M₁₆	—	4	1	no	—
926	M₁₆	—	4	1	no	—
927	M₁₆	—	4	1	no	—
928	M₁₆	—	4	1	no	—
929	C₂×C₈	—	2	2	no	—
930	C₂×C₈	—	2	2	no	—
931	C₂×C₈	—	2	2	no	—
932	C₂×C₈	—	2	2	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	4	1	no	—
935	C₂×C₈	—	4	1	no	—
936	C₂×C₈	—	4	1	no	—
937	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
967	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	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	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
992	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
993	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
994	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
995	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
996	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
997	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
998	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
999	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1000	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	1	no	—
1012	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1013	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1014	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1015	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1016	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	2	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	4	1	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	—	8	2	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	4	1	no	—
1032	D₄	—	4	1	no	—
1033	D₄	—	4	1	no	—
1034	D₄	—	4	1	no	—
1035	D₄	—	4	1	no	—
1036	D₄	—	4	4	no	—
1037	D₄	—	8	2	no	—
1038	D₄	—	8	2	no	—
1039	D₄	—	8	2	no	—
1040	D₄	—	8	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	1	no	—
1060	C₂×C₄	—	4	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1077	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	4	4	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	C₁₉×#578	1	2	yes	—
1105	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1123	C₄	C₁₉×#585	1	1	yes	characteristic
1124	C₂	—	2	2	no	—
1125	C₂	—	4	1	no	—
1126	C₂	—	4	1	no	—
1127	C₂	—	4	1	no	—
1128	C₂	—	4	1	no	—
1129	C₂	—	8	2	no	—
1130	C₂	C₁₉×#3496	1	1	yes	characteristic
1131	C₂	C₂×C₁₉×#578	1	1	yes	characteristic
1132	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 ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3541	C₂	semidirect
2. C₁₉×#3342	C₂	semidirect
3. C₁₉×#3339	C₂	semidirect
4. C₁₉×#3338	C₂	semidirect
5. C₁₉×#3336	C₂	semidirect
6. C₁₉×#3320	C₂	semidirect
7. C₁₉×#3316	C₂	semidirect
8. C₁₉×#3315	C₂	semidirect
9. C₁₉×#3313	C₂	semidirect
10. D₄×Q₁₆×C₁₉	C₂	semidirect
11. C₁₉×#3285	C₂	semidirect
12. C₁₉×#3285	C₂	semidirect
13. C₁₉×#3283	C₂	semidirect
14. C₁₉×#3258	C₂	semidirect
15. C₁₉×#3201	C₂	semidirect
16. C₁₉×#3196	C₂	semidirect
17. C₁₉×#3177	C₂	semidirect
18. C₁₉×#3175	C₂	semidirect
19. C₁₉×#3061	C₂	semidirect
20. C₁₉×#3059	C₂	semidirect
21. C₁₉×#3050	C₂	semidirect
22. C₂×C₁₉×#467	C₂	semidirect
23. C₁₉×#2929	C₂	semidirect
25. C₂×C₁₉×#135	C₂²	semidirect
27. C₂²×Q₁₆×C₁₉	C₂²	semidirect
53. C₁₉×#500	C₂²	semidirect
54. C₁₉×#499	C₂²	semidirect
55. C₁₉×#495	C₂²	semidirect
56. C₁₉×#494	C₂²	semidirect
57. C₁₉×#491	C₂²	semidirect
58. C₁₉×#489	C₂²	semidirect
61. C₁₉×#485	C₂²	semidirect
63. C₁₉×#484	C₂²	semidirect
64. C₁₉×#483	C₂²	semidirect
65. C₁₉×#482	C₂²	semidirect
67. C₁₉×#479	C₂²	semidirect
68. C₁₉×#478	C₂²	semidirect
69. C₁₉×#477	C₂²	semidirect
70. C₁₉×#475	C₂²	semidirect
73. C₁₉×#470	C₂²	semidirect
76. C₁₉×#468	C₂²	semidirect
85. C₁₉×#467	C₂²	semidirect
86. C₁₉×#467	C₂²	semidirect
87. C₁₉×#467	C₂²	semidirect
90. C₁₉×#466	C₂²	semidirect
93. C₁₉×#464	C₂²	semidirect
94. C₁₉×#464	C₂²	semidirect
95. C₁₉×#462	C₂²	semidirect
96. C₁₉×#461	C₂²	semidirect
99. C₁₉×#452	C₂²	semidirect
100. C₁₉×#452	C₂²	semidirect
102. C₁₉×#451	C₂²	semidirect
104. C₁₉×#448	C₂²	semidirect
105. C₁₉×#441	C₂²	semidirect
106. C₁₉×#440	C₂²	semidirect
107. C₄×Q₁₆×C₁₉	C₂²	semidirect
108. C₄×Q₁₆×C₁₉	C₂²	semidirect
109. C₄×Q₁₆×C₁₉	C₂²	semidirect
110. C₄×D₈×C₁₉	C₂²	semidirect
120. C₁₉×#427	C₂²	semidirect
122. C₂×C₁₉×#107	C₂²	semidirect
124. C₁₉×#419	C₂²	semidirect
125. C₁₉×#417	C₂²	semidirect
441. #62267	C₁₉	direct (N × H)
520. #3541	C₂×C₁₉	semidirect
521. #3342	C₂×C₁₉	semidirect
522. #3339	C₂×C₁₉	semidirect
523. #3338	C₂×C₁₉	semidirect
524. #3336	C₂×C₁₉	semidirect
525. #3320	C₂×C₁₉	semidirect
526. #3316	C₂×C₁₉	semidirect
527. #3315	C₂×C₁₉	semidirect
528. #3313	C₂×C₁₉	semidirect
529. D₄×Q₁₆	C₂×C₁₉	semidirect
530. #3285	C₂×C₁₉	semidirect
531. #3285	C₂×C₁₉	semidirect
532. #3283	C₂×C₁₉	semidirect
533. #3258	C₂×C₁₉	semidirect
534. #3201	C₂×C₁₉	semidirect
535. #3196	C₂×C₁₉	semidirect
536. #3177	C₂×C₁₉	semidirect
537. #3175	C₂×C₁₉	semidirect
538. #3061	C₂×C₁₉	semidirect
539. #3059	C₂×C₁₉	semidirect
540. #3050	C₂×C₁₉	semidirect
541. C₂×#467	C₂×C₁₉	semidirect
542. #2929	C₂×C₁₉	semidirect
582. C₂×#135	C₂²×C₁₉	semidirect
584. C₂²×Q₁₆	C₂²×C₁₉	semidirect
610. #500	C₂²×C₁₉	semidirect
611. #499	C₂²×C₁₉	semidirect
612. #495	C₂²×C₁₉	semidirect
613. #494	C₂²×C₁₉	semidirect
614. #491	C₂²×C₁₉	semidirect
615. #489	C₂²×C₁₉	semidirect
618. #485	C₂²×C₁₉	semidirect
620. #484	C₂²×C₁₉	semidirect
621. #483	C₂²×C₁₉	semidirect
622. #482	C₂²×C₁₉	semidirect
624. #479	C₂²×C₁₉	semidirect
625. #478	C₂²×C₁₉	semidirect
626. #477	C₂²×C₁₉	semidirect
627. #475	C₂²×C₁₉	semidirect
630. #470	C₂²×C₁₉	semidirect
633. #468	C₂²×C₁₉	semidirect
642. #467	C₂²×C₁₉	semidirect
643. #467	C₂²×C₁₉	semidirect
644. #467	C₂²×C₁₉	semidirect
647. #466	C₂²×C₁₉	semidirect
650. #464	C₂²×C₁₉	semidirect
651. #464	C₂²×C₁₉	semidirect
652. #462	C₂²×C₁₉	semidirect
653. #461	C₂²×C₁₉	semidirect
656. #452	C₂²×C₁₉	semidirect
657. #452	C₂²×C₁₉	semidirect
659. #451	C₂²×C₁₉	semidirect
661. #448	C₂²×C₁₉	semidirect
662. #441	C₂²×C₁₉	semidirect
663. #440	C₂²×C₁₉	semidirect
664. C₄×Q₁₆	C₂²×C₁₉	semidirect
665. C₄×Q₁₆	C₂²×C₁₉	semidirect
666. C₄×Q₁₆	C₂²×C₁₉	semidirect
667. C₄×D₈	C₂²×C₁₉	semidirect
677. #427	C₂²×C₁₉	semidirect
679. C₂×#107	C₂²×C₁₉	semidirect
681. #419	C₂²×C₁₉	semidirect
682. #417	C₂²×C₁₉	semidirect
866. C₁₉	#62267	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×#3541	2
C₁₉×#3342	2
C₁₉×#3339	2
C₁₉×#3338	2
C₁₉×#3336	2
C₁₉×#3320	2
C₁₉×#3316	2
C₁₉×#3315	2
C₁₉×#3313	2
D₄×Q₁₆×C₁₉	2
C₁₉×#3285	2
C₁₉×#3283	2
C₁₉×#3258	2
C₁₉×#3201	2
C₁₉×#3196	2
C₁₉×#3177	2
C₁₉×#3175	2
C₁₉×#3061	2
C₁₉×#3059	2
C₁₉×#3050	2
C₂×C₁₉×#467	2
C₁₉×#2929	2
#62267	19

Subgroups — C19×#62267 #18068226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62267 #18068226