Subgroups — C₁₉×#62044 #18068003

Order 4864.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3546	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3323	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3317	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3278	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3222	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3121	C₂	1	2	yes	maximal, complemented
20	C₁₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3043	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#560	—	2	2	no	—
28	C₁₉×#557	—	2	1	no	—
29	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#556	—	2	1	no	—
32	C₁₉×#556	C₂²	1	1	yes	characteristic
33	C₁₉×#556	C₂²	1	1	yes	characteristic
34	C₁₉×#553	—	2	1	no	—
35	C₁₉×#552	—	2	2	no	—
36	C₁₉×#552	C₂²	1	2	yes	complemented
37	C₁₉×#550	C₂²	1	2	yes	—
38	C₁₉×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
41	C₁₉×#547	C₂²	1	1	yes	characteristic
42	C₁₉×#546	—	2	1	no	—
43	C₁₉×#546	C₂²	1	2	yes	—
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#542	C₂²	1	2	yes	—
46	C₁₉×#541	—	2	2	no	—
47	C₁₉×#541	C₂²	1	2	yes	complemented
48	C₁₉×#538	—	2	2	no	—
49	C₁₉×#537	—	2	1	no	—
50	C₁₉×#535	—	2	1	no	—
51	C₁₉×#535	C₂²	1	2	yes	—
52	C₁₉×#533	—	2	1	no	—
53	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#532	C₂²	1	1	yes	characteristic
55	C₁₉×#532	C₂²	1	1	yes	characteristic
56	C₁₉×#529	—	2	1	no	—
57	C₁₉×#529	C₂²	1	1	yes	characteristic
58	C₁₉×#519	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#497	C₂²	1	2	yes	—
61	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#492	C₂²	1	1	yes	characteristic
63	C₁₉×#492	C₂²	1	2	yes	complemented
64	C₁₉×#490	C₂²	1	2	yes	complemented
65	C₁₉×#488	C₂²	1	2	yes	—
66	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#486	C₂²	1	1	yes	characteristic
68	C₁₉×#485	C₂²	1	2	yes	complemented
69	C₁₉×#482	C₂²	1	2	yes	—
70	C₁₉×#481	C₂²	1	1	yes	characteristic
71	C₁₉×#481	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#479	C₂²	1	2	yes	complemented
73	C₁₉×#478	C₂²	1	2	yes	complemented
74	C₁₉×#477	C₂²	1	2	yes	complemented
75	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#474	C₂²	1	1	yes	characteristic
78	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#470	C₂²	1	2	yes	complemented
80	C₁₉×#468	C₂²	1	2	yes	—
81	C₁₉×#468	C₂²	1	2	yes	—
82	C₁₉×#468	C₂²	1	2	yes	complemented
83	C₁₉×#467	C₂²	1	2	yes	complemented
84	C₁₉×#465	C₂²	1	2	yes	—
85	C₁₉×#464	C₂²	1	2	yes	—
86	C₁₉×#464	C₂²	1	2	yes	—
87	C₁₉×#464	C₂²	1	2	yes	complemented
88	C₁₉×#464	C₂²	1	2	yes	complemented
89	C₁₉×#464	C₂²	1	2	yes	complemented
90	C₁₉×#464	C₂²	1	2	yes	complemented
91	C₁₉×#462	C₂²	1	2	yes	complemented
92	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
93	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
94	C₁₉×#461	C₂²	1	1	yes	characteristic
95	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
96	C₁₉×#461	C₂²	1	2	yes	complemented
97	C₁₉×#460	C₂²	1	1	yes	characteristic
98	C₁₉×#460	C₂²	1	2	yes	—
99	C₁₉×#460	C₂²	1	1	yes	characteristic
100	C₁₉×#460	C₂²	1	1	yes	characteristic
101	C₁₉×#460	C₂²	1	1	yes	characteristic
102	C₁₉×#460	C₂²	1	2	yes	complemented
103	C₁₉×#460	C₂²	1	2	yes	complemented
104	C₁₉×#452	C₂²	1	2	yes	complemented
105	C₁₉×#452	C₂²	1	2	yes	complemented
106	C₁₉×#452	C₂²	1	2	yes	complemented
107	C₁₉×#452	C₂²	1	2	yes	complemented
108	C₁₉×#451	C₂²	1	2	yes	complemented
109	C₁₉×#450	C₂²	1	2	yes	—
110	C₁₉×#450	C₂²	1	2	yes	—
111	C₁₉×#448	C₂²	1	1	yes	characteristic
112	C₁₉×#448	C₂²	1	2	yes	—
113	C₁₉×#448	C₂²	1	1	yes	characteristic, complemented
114	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
116	C₁₉×#441	C₂²	1	2	yes	complemented
117	C₁₉×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
124	C₁₉×#436	C₂²	1	1	yes	characteristic
125	C₁₉×#436	C₂²	1	2	yes	complemented
126	C₁₉×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
128	C₁₉×#433	C₂²	1	2	yes	complemented
129	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
130	C₁₉×#424	C₂²	1	2	yes	complemented
131	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
132	C₁₉×#418	C₂²	1	2	yes	—
133	C₁₉×#417	C₂²	1	2	yes	complemented
134	C₁₉×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	1	no	—
137	C₂×#41×C₁₉	C₂³	1	2	yes	—
138	C₂×#41×C₁₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₉	—	2	1	no	—
142	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
143	C₁₉×#137	—	4	4	no	—
144	C₁₉×#137	—	4	4	no	—
145	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₁₉	—	4	4	no	—
150	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
161	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
163	C₁₉×C₄⋊Q₈	—	2	1	no	—
164	C₁₉×C₄⋊Q₈	—	2	1	no	—
165	C₁₉×C₄⋊Q₈	—	2	2	no	—
166	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×#127	—	2	2	no	—
172	C₁₉×#127	C₂³	1	1	yes	characteristic
173	C₁₉×#127	C₂³	1	1	yes	characteristic
174	C₁₉×#127	C₂³	1	2	yes	—
175	C₁₉×#126	—	2	2	no	—
176	C₁₉×#126	—	2	2	no	—
177	C₁₉×#126	—	2	2	no	—
178	C₁₉×#126	—	2	2	no	—
179	C₁₉×#126	—	2	2	no	—
180	C₁₉×#126	—	2	2	no	—
181	C₁₉×#126	D₄	1	2	yes	—
182	C₁₉×#125	—	2	1	no	—
183	C₁₉×#125	—	2	2	no	—
184	C₁₉×#125	—	2	2	no	—
185	C₁₉×#125	—	2	2	no	—
186	C₁₉×#125	—	2	2	no	—
187	C₁₉×#125	—	2	2	no	—
188	C₁₉×#125	—	2	1	no	—
189	C₁₉×#125	D₄	1	1	yes	characteristic
190	C₁₉×#125	C₂³	1	2	yes	—
191	C₁₉×#124	—	2	1	no	—
192	C₁₉×#124	—	2	2	no	—
193	C₁₉×#124	—	2	1	no	—
194	C₁₉×#124	D₄	1	1	yes	characteristic
195	C₁₉×#124	C₂³	1	2	yes	—
196	C₁₉×#124	C₂³	1	2	yes	—
197	C₁₉×#123	—	2	2	no	—
198	C₁₉×#123	—	2	2	no	—
199	C₁₉×#123	—	2	2	no	—
200	C₁₉×#123	—	2	2	no	—
201	C₁₉×#123	D₄	1	2	yes	—
202	C₁₉×C₂²⋊Q₈	—	2	1	no	—
203	C₁₉×C₂²⋊Q₈	—	2	1	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	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×#121	—	2	1	no	—
214	C₁₉×#121	—	2	1	no	—
215	C₁₉×#121	—	2	1	no	—
216	C₁₉×#121	—	2	1	no	—
217	C₁₉×#121	—	2	1	no	—
218	C₁₉×#121	—	2	2	no	—
219	C₁₉×#121	—	2	2	no	—
220	C₁₉×#121	—	2	1	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	C₂³	1	2	yes	—
227	C₁₉×#121	C₂³	1	1	yes	characteristic
228	C₁₉×#121	C₂³	1	1	yes	characteristic
229	C₁₉×#120	—	2	2	no	—
230	C₁₉×#120	—	2	2	no	—
231	C₁₉×#120	—	2	2	no	—
232	C₁₉×#120	—	2	2	no	—
233	C₄×Q₈×C₁₉	—	2	1	no	—
234	C₄×Q₈×C₁₉	—	2	2	no	—
235	C₄×Q₈×C₁₉	—	2	2	no	—
236	C₄×Q₈×C₁₉	—	2	1	no	—
237	C₄×Q₈×C₁₉	—	2	1	no	—
238	C₄×Q₈×C₁₉	—	2	1	no	—
239	C₄×Q₈×C₁₉	—	2	1	no	—
240	C₄×Q₈×C₁₉	—	2	1	no	—
241	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
246	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
249	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₉	—	2	1	no	—
251	C₄×D₄×C₁₉	—	2	2	no	—
252	C₄×D₄×C₁₉	—	2	2	no	—
253	C₄×D₄×C₁₉	—	2	1	no	—
254	C₄×D₄×C₁₉	—	2	1	no	—
255	C₄×D₄×C₁₉	—	2	1	no	—
256	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₉	C₂³	1	2	yes	—
259	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₁₉	C₂³	1	2	yes	—
261	C₁₉×#117	—	2	1	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	—	2	2	no	—
264	C₁₉×#117	—	2	2	no	—
265	C₁₉×#117	—	2	2	no	—
266	C₁₉×#117	C₂³	1	2	yes	—
267	C₁₉×#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
272	C₂×C₄²×C₁₉	—	2	1	no	—
273	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
274	C₁₉×#107	C₂³	1	2	yes	—
275	C₁₉×#107	C₂³	1	2	yes	—
276	C₁₉×#106	C₂³	1	1	yes	characteristic
277	C₁₉×#106	C₂³	1	1	yes	characteristic
278	C₁₉×#106	C₂³	1	1	yes	characteristic
279	C₁₉×#106	C₂³	1	1	yes	characteristic
280	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₉×#103	C₂³	1	2	yes	—
288	C₁₉×#103	C₂³	1	2	yes	—
289	C₁₉×#103	C₂³	1	2	yes	—
290	C₁₉×#103	C₂³	1	1	yes	characteristic
291	C₁₉×#103	C₂³	1	1	yes	characteristic
292	C₁₉×#103	C₂³	1	1	yes	characteristic
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#103	C₂³	1	2	yes	—
295	C₁₉×#103	C₂³	1	2	yes	—
296	C₁₉×#103	C₂³	1	2	yes	—
297	C₁₉×#102	C₂³	1	1	yes	characteristic
298	C₁₉×#102	C₂³	1	2	yes	—
299	C₁₉×#102	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	1	yes	characteristic
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#102	C₂³	1	1	yes	characteristic
305	C₁₉×#102	C₂³	1	1	yes	characteristic
306	C₁₉×#102	C₂³	1	2	yes	—
307	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₉	C₂³	1	2	yes	—
315	C₂⁴×C₁₉	—	2	2	no	—
316	#41×C₁₉	—	4	2	no	—
317	#41×C₁₉	—	4	2	no	—
318	#41×C₁₉	—	4	2	no	—
319	#41×C₁₉	—	4	2	no	—
320	#41×C₁₉	—	8	2	no	—
321	#41×C₁₉	—	8	2	no	—
322	C₂×Q₈×C₁₉	—	2	1	no	—
323	C₂×Q₈×C₁₉	—	2	2	no	—
324	C₂×Q₈×C₁₉	—	2	1	no	—
325	C₂×Q₈×C₁₉	—	2	1	no	—
326	C₂×Q₈×C₁₉	—	2	4	no	—
327	C₂×Q₈×C₁₉	—	2	2	no	—
328	C₂×Q₈×C₁₉	—	4	2	no	—
329	C₂×Q₈×C₁₉	—	4	1	no	—
330	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₁₉	—	2	1	no	—
336	C₂×D₄×C₁₉	—	2	2	no	—
337	C₂×D₄×C₁₉	—	2	2	no	—
338	C₂×D₄×C₁₉	—	2	2	no	—
339	C₂×D₄×C₁₉	—	2	1	no	—
340	C₂×D₄×C₁₉	—	2	1	no	—
341	C₂×D₄×C₁₉	—	2	1	no	—
342	C₂×D₄×C₁₉	—	2	1	no	—
343	C₂×D₄×C₁₉	—	2	2	no	—
344	C₂×D₄×C₁₉	—	2	1	no	—
345	C₂×D₄×C₁₉	—	2	2	no	—
346	C₂×D₄×C₁₉	—	2	2	no	—
347	C₂×D₄×C₁₉	—	4	2	no	—
348	C₂×D₄×C₁₉	—	4	2	no	—
349	C₂×D₄×C₁₉	—	8	2	no	—
350	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
354	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₁₉	—	2	1	no	—
356	C₂²×C₄×C₁₉	—	2	1	no	—
357	C₂²×C₄×C₁₉	—	2	2	no	—
358	C₂²×C₄×C₁₉	—	2	1	no	—
359	C₂²×C₄×C₁₉	—	2	1	no	—
360	C₂²×C₄×C₁₉	—	2	2	no	—
361	C₂²×C₄×C₁₉	—	2	2	no	—
362	C₂²×C₄×C₁₉	—	2	2	no	—
363	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
367	Q₁₆×C₁₉	—	2	4	no	—
368	Q₁₆×C₁₉	—	4	2	no	—
369	Q₁₆×C₁₉	—	4	2	no	—
370	Q₁₆×C₁₉	—	4	2	no	—
371	SD₁₆×C₁₉	—	2	2	no	—
372	SD₁₆×C₁₉	—	2	4	no	—
373	SD₁₆×C₁₉	—	2	2	no	—
374	SD₁₆×C₁₉	—	4	2	no	—
375	SD₁₆×C₁₉	—	4	2	no	—
376	SD₁₆×C₁₉	—	4	2	no	—
377	SD₁₆×C₁₉	—	4	1	no	—
378	SD₁₆×C₁₉	—	4	1	no	—
379	SD₁₆×C₁₉	—	4	2	no	—
380	SD₁₆×C₁₉	—	4	2	no	—
381	M₁₆×C₁₉	—	4	2	no	—
382	M₁₆×C₁₉	—	4	2	no	—
383	C₂×C₈×C₁₉	—	4	2	no	—
384	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
386	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
387	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₁₉	—	2	1	no	—
391	C₄⋊C₄×C₁₉	—	2	1	no	—
392	C₄⋊C₄×C₁₉	—	2	1	no	—
393	C₄⋊C₄×C₁₉	—	2	1	no	—
394	C₄⋊C₄×C₁₉	—	2	1	no	—
395	C₄⋊C₄×C₁₉	—	2	2	no	—
396	C₄⋊C₄×C₁₉	—	2	1	no	—
397	C₄⋊C₄×C₁₉	—	2	2	no	—
398	C₄⋊C₄×C₁₉	—	2	2	no	—
399	C₄⋊C₄×C₁₉	—	2	2	no	—
400	C₄⋊C₄×C₁₉	—	2	1	no	—
401	C₄⋊C₄×C₁₉	—	2	2	no	—
402	C₄⋊C₄×C₁₉	—	2	1	no	—
403	C₄⋊C₄×C₁₉	—	2	2	no	—
404	C₄⋊C₄×C₁₉	—	2	1	no	—
405	C₄⋊C₄×C₁₉	—	2	1	no	—
406	C₄⋊C₄×C₁₉	—	2	1	no	—
407	C₄⋊C₄×C₁₉	—	2	2	no	—
408	C₄⋊C₄×C₁₉	—	2	2	no	—
409	C₄⋊C₄×C₁₉	—	2	2	no	—
410	C₄⋊C₄×C₁₉	—	2	2	no	—
411	C₄⋊C₄×C₁₉	—	2	2	no	—
412	C₄⋊C₄×C₁₉	—	2	2	no	—
413	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
430	C₂²⋊C₄×C₁₉	—	2	2	no	—
431	C₂²⋊C₄×C₁₉	—	2	2	no	—
432	C₂²⋊C₄×C₁₉	—	2	1	no	—
433	C₂²⋊C₄×C₁₉	—	2	2	no	—
434	C₂²⋊C₄×C₁₉	—	2	2	no	—
435	C₂²⋊C₄×C₁₉	—	2	2	no	—
436	C₂²⋊C₄×C₁₉	—	2	1	no	—
437	C₂²⋊C₄×C₁₉	—	2	2	no	—
438	C₂²⋊C₄×C₁₉	—	2	1	no	—
439	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
444	C₄²×C₁₉	—	2	1	no	—
445	C₄²×C₁₉	—	2	1	no	—
446	C₄²×C₁₉	—	2	1	no	—
447	C₄²×C₁₉	—	2	1	no	—
448	C₄²×C₁₉	—	2	2	no	—
449	C₄²×C₁₉	—	2	2	no	—
450	C₄²×C₁₉	—	2	2	no	—
451	C₄²×C₁₉	—	2	2	no	—
452	C₄²×C₁₉	—	2	2	no	—
453	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
456	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
457	C₄²×C₁₉	C₂⁴	1	2	yes	—
458	#62044	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₁₉	—	2	1	no	—
460	C₂³×C₁₉	—	2	2	no	—
461	C₂³×C₁₉	—	2	1	no	—
462	C₂³×C₁₉	—	8	2	no	—
463	C₂³×C₁₉	—	8	2	no	—
464	C₂³×C₁₉	—	8	2	no	—
465	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
466	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₁₉	—	2	2	no	—
468	Q₈×C₁₉	—	2	1	no	—
469	Q₈×C₁₉	—	2	2	no	—
470	Q₈×C₁₉	—	2	1	no	—
471	Q₈×C₁₉	—	2	2	no	—
472	Q₈×C₁₉	—	2	1	no	—
473	Q₈×C₁₉	—	2	2	no	—
474	Q₈×C₁₉	—	2	2	no	—
475	Q₈×C₁₉	—	4	2	no	—
476	Q₈×C₁₉	—	4	4	no	—
477	Q₈×C₁₉	—	4	2	no	—
478	Q₈×C₁₉	—	8	1	no	—
479	Q₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
480	D₄×C₁₉	—	2	2	no	—
481	D₄×C₁₉	—	2	1	no	—
482	D₄×C₁₉	—	2	2	no	—
483	D₄×C₁₉	—	2	1	no	—
484	D₄×C₁₉	—	2	1	no	—
485	D₄×C₁₉	—	2	2	no	—
486	D₄×C₁₉	—	2	1	no	—
487	D₄×C₁₉	—	4	2	no	—
488	D₄×C₁₉	—	4	2	no	—
489	D₄×C₁₉	—	8	1	no	—
490	D₄×C₁₉	—	8	1	no	—
491	D₄×C₁₉	—	8	2	no	—
492	D₄×C₁₉	—	8	2	no	—
493	D₄×C₁₉	—	8	1	no	—
494	D₄×C₁₉	—	8	2	no	—
495	D₄×C₁₉	—	8	2	no	—
496	D₄×C₁₉	—	8	2	no	—
497	D₄×C₁₉	—	8	2	no	—
498	D₄×C₁₉	—	8	1	no	—
499	D₄×C₁₉	—	8	1	no	—
500	C₂×C₄×C₁₉	—	2	1	no	—
501	C₂×C₄×C₁₉	—	2	2	no	—
502	C₂×C₄×C₁₉	—	2	2	no	—
503	C₂×C₄×C₁₉	—	2	1	no	—
504	C₂×C₄×C₁₉	—	2	2	no	—
505	C₂×C₄×C₁₉	—	2	1	no	—
506	C₂×C₄×C₁₉	—	2	1	no	—
507	C₂×C₄×C₁₉	—	2	2	no	—
508	C₂×C₄×C₁₉	—	2	1	no	—
509	C₂×C₄×C₁₉	—	2	1	no	—
510	C₂×C₄×C₁₉	—	2	1	no	—
511	C₂×C₄×C₁₉	—	2	2	no	—
512	C₂×C₄×C₁₉	—	2	2	no	—
513	C₂×C₄×C₁₉	—	2	1	no	—
514	C₂×C₄×C₁₉	—	4	1	no	—
515	C₂×C₄×C₁₉	—	4	2	no	—
516	C₂×C₄×C₁₉	—	4	4	no	—
517	C₂×C₄×C₁₉	—	4	2	no	—
518	C₂×C₄×C₁₉	—	4	2	no	—
519	C₂×C₄×C₁₉	—	4	2	no	—
520	C₂×C₄×C₁₉	—	8	2	no	—
521	C₂×C₄×C₁₉	—	8	2	no	—
522	C₂×C₄×C₁₉	—	8	2	no	—
523	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
532	C₈×C₁₉	—	2	1	no	—
533	C₈×C₁₉	—	2	2	no	—
534	C₈×C₁₉	—	2	1	no	—
535	C₈×C₁₉	—	2	2	no	—
536	C₈×C₁₉	—	2	1	no	—
537	C₈×C₁₉	—	2	1	no	—
538	#3546	C₂×C₁₉	1	1	yes	characteristic
539	#3523	C₂×C₁₉	1	1	yes	characteristic, complemented
540	#3398	C₂×C₁₉	1	1	yes	characteristic, complemented
541	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
542	#3368	C₂×C₁₉	1	1	yes	characteristic, complemented
543	#3364	C₂×C₁₉	1	1	yes	characteristic, complemented
544	#3324	C₂×C₁₉	1	1	yes	characteristic, complemented
545	#3323	C₂×C₁₉	1	2	yes	complemented
546	#3317	C₂×C₁₉	1	2	yes	complemented
547	#3302	C₂×C₁₉	1	1	yes	characteristic, complemented
548	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
549	#3278	C₂×C₁₉	1	2	yes	complemented
550	#3276	C₂×C₁₉	1	1	yes	characteristic, complemented
551	#3266	C₂×C₁₉	1	2	yes	complemented
552	#3258	C₂×C₁₉	1	2	yes	complemented
553	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
554	#3222	C₂×C₁₉	1	2	yes	complemented
555	#3210	C₂×C₁₉	1	1	yes	characteristic, complemented
556	#3121	C₂×C₁₉	1	2	yes	complemented
557	#3103	C₂×C₁₉	1	1	yes	characteristic, complemented
558	#3043	C₂×C₁₉	1	2	yes	complemented
559	#3037	C₂×C₁₉	1	1	yes	characteristic, complemented
560	#2993	C₂×C₁₉	1	1	yes	characteristic, complemented
561	C₂²×C₁₉	—	2	1	no	—
562	C₂²×C₁₉	—	2	2	no	—
563	C₂²×C₁₉	—	2	1	no	—
564	C₂²×C₁₉	—	2	2	no	—
565	C₂²×C₁₉	—	2	1	no	—
566	C₂²×C₁₉	—	2	2	no	—
567	C₂²×C₁₉	—	4	1	no	—
568	C₂²×C₁₉	—	4	2	no	—
569	C₂²×C₁₉	—	4	1	no	—
570	C₂²×C₁₉	—	4	1	no	—
571	C₂²×C₁₉	—	4	2	no	—
572	C₂²×C₁₉	—	4	1	no	—
573	C₂²×C₁₉	—	4	1	no	—
574	C₂²×C₁₉	—	4	1	no	—
575	C₂²×C₁₉	—	4	2	no	—
576	C₂²×C₁₉	—	16	4	no	—
577	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
578	C₄×C₁₉	—	2	1	no	—
579	C₄×C₁₉	—	2	1	no	—
580	C₄×C₁₉	—	2	2	no	—
581	C₄×C₁₉	—	2	1	no	—
582	C₄×C₁₉	—	2	2	no	—
583	C₄×C₁₉	—	2	2	no	—
584	C₄×C₁₉	—	2	1	no	—
585	C₄×C₁₉	—	2	2	no	—
586	C₄×C₁₉	—	4	1	no	—
587	C₄×C₁₉	—	4	1	no	—
588	C₄×C₁₉	—	4	2	no	—
589	C₄×C₁₉	—	4	1	no	—
590	C₄×C₁₉	—	4	2	no	—
591	C₄×C₁₉	—	4	1	no	—
592	C₄×C₁₉	—	4	1	no	—
593	C₄×C₁₉	—	4	2	no	—
594	C₄×C₁₉	#577	1	2	yes	—
595	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
596	C₄×C₁₉	#585	1	1	yes	characteristic
597	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
598	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
599	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
600	#560	—	2	2	no	—
601	#557	—	2	1	no	—
602	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
603	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
604	#556	—	2	1	no	—
605	#556	C₂²×C₁₉	1	1	yes	characteristic
606	#556	C₂²×C₁₉	1	1	yes	characteristic
607	#553	—	2	1	no	—
608	#552	—	2	2	no	—
609	#552	C₂²×C₁₉	1	2	yes	complemented
610	#550	C₂²×C₁₉	1	2	yes	—
611	#550	C₂²×C₁₉	1	1	yes	characteristic
612	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
613	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
614	#547	C₂²×C₁₉	1	1	yes	characteristic
615	#546	—	2	1	no	—
616	#546	C₂²×C₁₉	1	2	yes	—
617	D₄²	C₂²×C₁₉	1	1	yes	characteristic
618	#542	C₂²×C₁₉	1	2	yes	—
619	#541	—	2	2	no	—
620	#541	C₂²×C₁₉	1	2	yes	complemented
621	#538	—	2	2	no	—
622	#537	—	2	1	no	—
623	#535	—	2	1	no	—
624	#535	C₂²×C₁₉	1	2	yes	—
625	#533	—	2	1	no	—
626	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
627	#532	C₂²×C₁₉	1	1	yes	characteristic
628	#532	C₂²×C₁₉	1	1	yes	characteristic
629	#529	—	2	1	no	—
630	#529	C₂²×C₁₉	1	1	yes	characteristic
631	#519	C₂²×C₁₉	1	2	yes	complemented
632	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
633	#497	C₂²×C₁₉	1	2	yes	—
634	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
635	#492	C₂²×C₁₉	1	1	yes	characteristic
636	#492	C₂²×C₁₉	1	2	yes	complemented
637	#490	C₂²×C₁₉	1	2	yes	complemented
638	#488	C₂²×C₁₉	1	2	yes	—
639	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
640	#486	C₂²×C₁₉	1	1	yes	characteristic
641	#485	C₂²×C₁₉	1	2	yes	complemented
642	#482	C₂²×C₁₉	1	2	yes	—
643	#481	C₂²×C₁₉	1	1	yes	characteristic
644	#481	C₂²×C₁₉	1	1	yes	characteristic, complemented
645	#479	C₂²×C₁₉	1	2	yes	complemented
646	#478	C₂²×C₁₉	1	2	yes	complemented
647	#477	C₂²×C₁₉	1	2	yes	complemented
648	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
649	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
650	#474	C₂²×C₁₉	1	1	yes	characteristic
651	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
652	#470	C₂²×C₁₉	1	2	yes	complemented
653	#468	C₂²×C₁₉	1	2	yes	—
654	#468	C₂²×C₁₉	1	2	yes	—
655	#468	C₂²×C₁₉	1	2	yes	complemented
656	#467	C₂²×C₁₉	1	2	yes	complemented
657	#465	C₂²×C₁₉	1	2	yes	—
658	#464	C₂²×C₁₉	1	2	yes	—
659	#464	C₂²×C₁₉	1	2	yes	—
660	#464	C₂²×C₁₉	1	2	yes	complemented
661	#464	C₂²×C₁₉	1	2	yes	complemented
662	#464	C₂²×C₁₉	1	2	yes	complemented
663	#464	C₂²×C₁₉	1	2	yes	complemented
664	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	#462	C₂²×C₁₉	1	2	yes	complemented
666	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	#461	C₂²×C₁₉	1	1	yes	characteristic
668	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
669	#461	C₂²×C₁₉	1	2	yes	complemented
670	#460	C₂²×C₁₉	1	1	yes	characteristic
671	#460	C₂²×C₁₉	1	1	yes	characteristic
672	#460	C₂²×C₁₉	1	1	yes	characteristic
673	#460	C₂²×C₁₉	1	1	yes	characteristic
674	#460	C₂²×C₁₉	1	2	yes	—
675	#460	C₂²×C₁₉	1	2	yes	complemented
676	#460	C₂²×C₁₉	1	2	yes	complemented
677	#452	C₂²×C₁₉	1	2	yes	complemented
678	#452	C₂²×C₁₉	1	2	yes	complemented
679	#452	C₂²×C₁₉	1	2	yes	complemented
680	#452	C₂²×C₁₉	1	2	yes	complemented
681	#451	C₂²×C₁₉	1	2	yes	complemented
682	#450	C₂²×C₁₉	1	2	yes	—
683	#450	C₂²×C₁₉	1	2	yes	—
684	#448	C₂²×C₁₉	1	1	yes	characteristic
685	#448	C₂²×C₁₉	1	2	yes	—
686	#448	C₂²×C₁₉	1	1	yes	characteristic, complemented
687	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
688	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
689	#441	C₂²×C₁₉	1	2	yes	complemented
690	#440	C₂²×C₁₉	1	2	yes	complemented
691	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
694	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
695	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
696	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
697	#436	C₂²×C₁₉	1	1	yes	characteristic
698	#436	C₂²×C₁₉	1	2	yes	complemented
699	#435	C₂²×C₁₉	1	2	yes	complemented
700	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
701	#433	C₂²×C₁₉	1	2	yes	complemented
702	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
703	#424	C₂²×C₁₉	1	2	yes	complemented
704	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
705	#418	C₂²×C₁₉	1	2	yes	—
706	#417	C₂²×C₁₉	1	2	yes	complemented
707	#416	C₂²×C₁₉	1	2	yes	complemented
708	C₂×C₁₉	—	4	1	no	—
709	C₂×C₁₉	—	4	2	no	—
710	C₂×C₁₉	—	8	1	no	—
711	C₂×C₁₉	—	8	2	no	—
712	C₂×C₁₉	—	8	1	no	—
713	C₂×C₁₉	#3488	1	1	yes	characteristic
714	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
715	C₂×C₁₉	#3586	1	1	yes	characteristic
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	C₂³×C₁₉	1	2	yes	—
719	C₂×#41	C₂³×C₁₉	1	2	yes	—
720	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
721	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
724	#137	—	4	4	no	—
725	#137	—	4	4	no	—
726	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
730	C₂×SD₁₆	—	4	4	no	—
731	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
742	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
743	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	2	no	—
747	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
752	#127	—	2	2	no	—
753	#127	C₂³×C₁₉	1	1	yes	characteristic
754	#127	C₂³×C₁₉	1	1	yes	characteristic
755	#127	C₂³×C₁₉	1	2	yes	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	D₄×C₁₉	1	2	yes	—
763	#125	—	2	1	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	2	no	—
769	#125	—	2	1	no	—
770	#125	D₄×C₁₉	1	1	yes	characteristic
771	#125	C₂³×C₁₉	1	2	yes	—
772	#124	—	2	1	no	—
773	#124	—	2	2	no	—
774	#124	—	2	1	no	—
775	#124	D₄×C₁₉	1	1	yes	characteristic
776	#124	C₂³×C₁₉	1	2	yes	—
777	#124	C₂³×C₁₉	1	2	yes	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	D₄×C₁₉	1	2	yes	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
790	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	D₄×C₁₉	1	1	yes	characteristic
807	#121	C₂³×C₁₉	1	1	yes	characteristic
808	#121	C₂³×C₁₉	1	1	yes	characteristic
809	#121	C₂³×C₁₉	1	2	yes	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	#120	—	2	2	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	2	no	—
816	C₄×Q₈	—	2	2	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	—	2	1	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
827	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
828	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
829	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
830	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₁₉	1	2	yes	—
840	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₁₉	1	2	yes	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	C₂³×C₁₉	1	2	yes	—
848	#117	C₂³×C₁₉	1	2	yes	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
855	#107	C₂³×C₁₉	1	2	yes	—
856	#107	C₂³×C₁₉	1	2	yes	—
857	#106	C₂³×C₁₉	1	1	yes	characteristic
858	#106	C₂³×C₁₉	1	1	yes	characteristic
859	#106	C₂³×C₁₉	1	1	yes	characteristic
860	#106	C₂³×C₁₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
862	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
866	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
867	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
868	#103	C₂³×C₁₉	1	2	yes	—
869	#103	C₂³×C₁₉	1	2	yes	—
870	#103	C₂³×C₁₉	1	2	yes	—
871	#103	C₂³×C₁₉	1	1	yes	characteristic
872	#103	C₂³×C₁₉	1	1	yes	characteristic
873	#103	C₂³×C₁₉	1	1	yes	characteristic
874	#103	C₂³×C₁₉	1	1	yes	characteristic
875	#103	C₂³×C₁₉	1	2	yes	—
876	#103	C₂³×C₁₉	1	2	yes	—
877	#103	C₂³×C₁₉	1	2	yes	—
878	#102	C₂³×C₁₉	1	1	yes	characteristic
879	#102	C₂³×C₁₉	1	2	yes	—
880	#102	C₂³×C₁₉	1	2	yes	—
881	#102	C₂³×C₁₉	1	2	yes	—
882	#102	C₂³×C₁₉	1	1	yes	characteristic
883	#102	C₂³×C₁₉	1	2	yes	—
884	#102	C₂³×C₁₉	1	2	yes	—
885	#102	C₂³×C₁₉	1	1	yes	characteristic
886	#102	C₂³×C₁₉	1	1	yes	characteristic
887	#102	C₂³×C₁₉	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
892	#97	C₂³×C₁₉	1	2	yes	—
893	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₁₉	1	2	yes	—
896	C₁₉	#62044	1	1	yes	characteristic, direct product factor, Sylow
897	C₂⁴	—	2	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	8	2	no	—
903	#41	—	8	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	4	no	—
909	C₂×Q₈	—	2	2	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	4	1	no	—
912	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
934	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
936	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
949	Q₁₆	—	2	4	no	—
950	Q₁₆	—	4	2	no	—
951	Q₁₆	—	4	2	no	—
952	Q₁₆	—	4	2	no	—
953	SD₁₆	—	2	2	no	—
954	SD₁₆	—	2	4	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	1	no	—
960	SD₁₆	—	4	1	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	M₁₆	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
970	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
999	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1004	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₁₉	1	2	yes	—
1039	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	2	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1047	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	4	4	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	1	no	—
1060	Q₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1107	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1112	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1113	C₈	—	2	1	no	—
1114	C₈	—	2	2	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	16	4	no	—
1135	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	C₁₉×#577	1	2	yes	—
1153	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1154	C₄	C₁₉×#585	1	1	yes	characteristic
1155	C₂	—	4	2	no	—
1156	C₂	—	4	1	no	—
1157	C₂	—	8	1	no	—
1158	C₂	—	8	2	no	—
1159	C₂	—	8	1	no	—
1160	C₂	C₁₉×#3488	1	1	yes	characteristic
1161	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1162	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3523	C₂	semidirect
3. C₁₉×#3398	C₂	semidirect
4. C₁₉×#3392	C₂	semidirect
5. C₁₉×#3368	C₂	semidirect
6. C₁₉×#3364	C₂	semidirect
7. C₁₉×#3324	C₂	semidirect
8. C₁₉×#3323	C₂	semidirect
9. C₁₉×#3317	C₂	semidirect
10. C₁₉×#3302	C₂	semidirect
11. D₄×SD₁₆×C₁₉	C₂	semidirect
12. C₁₉×#3278	C₂	semidirect
13. C₁₉×#3276	C₂	semidirect
14. C₁₉×#3266	C₂	semidirect
15. C₁₉×#3258	C₂	semidirect
16. C₁₉×#3254	C₂	semidirect
17. C₁₉×#3222	C₂	semidirect
18. C₁₉×#3210	C₂	semidirect
19. C₁₉×#3121	C₂	semidirect
20. C₁₉×#3103	C₂	semidirect
21. C₁₉×#3043	C₂	semidirect
22. C₁₉×#3037	C₂	semidirect
23. C₁₉×#2993	C₂	semidirect
24. C₂×C₁₉×#137	C₂²	semidirect
25. C₂×C₁₉×#137	C₂²	semidirect
29. C₁₉×#557	C₂²	semidirect
30. C₁₉×#557	C₂²	semidirect
36. C₁₉×#552	C₂²	semidirect
40. D₄×Q₈×C₁₉	C₂²	semidirect
47. C₁₉×#541	C₂²	semidirect
53. C₁₉×#533	C₂²	semidirect
58. C₁₉×#519	C₂²	semidirect
59. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
61. C₁₉×#494	C₂²	semidirect
63. C₁₉×#492	C₂²	semidirect
64. C₁₉×#490	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
71. C₁₉×#481	C₂²	semidirect
72. C₁₉×#479	C₂²	semidirect
73. C₁₉×#478	C₂²	semidirect
74. C₁₉×#477	C₂²	semidirect
75. C₁₉×#475	C₂²	semidirect
76. C₁₉×#475	C₂²	semidirect
78. C₁₉×#474	C₂²	semidirect
79. C₁₉×#470	C₂²	semidirect
82. C₁₉×#468	C₂²	semidirect
83. C₁₉×#467	C₂²	semidirect
87. C₁₉×#464	C₂²	semidirect
88. C₁₉×#464	C₂²	semidirect
89. C₁₉×#464	C₂²	semidirect
90. C₁₉×#464	C₂²	semidirect
91. C₁₉×#462	C₂²	semidirect
92. C₁₉×#462	C₂²	semidirect
93. C₁₉×#462	C₂²	semidirect
95. C₁₉×#461	C₂²	semidirect
96. C₁₉×#461	C₂²	semidirect
102. C₁₉×#460	C₂²	semidirect
103. C₁₉×#460	C₂²	semidirect
104. C₁₉×#452	C₂²	semidirect
105. C₁₉×#452	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
107. C₁₉×#452	C₂²	semidirect
108. C₁₉×#451	C₂²	semidirect
113. C₁₉×#448	C₂²	semidirect
114. C₁₉×#446	C₂²	semidirect
115. C₈×Q₈×C₁₉	C₂²	semidirect
116. C₁₉×#441	C₂²	semidirect
117. C₁₉×#440	C₂²	semidirect
118. C₄×Q₁₆×C₁₉	C₂²	semidirect
121. C₄×SD₁₆×C₁₉	C₂²	semidirect
122. C₄×SD₁₆×C₁₉	C₂²	semidirect
123. C₄×SD₁₆×C₁₉	C₂²	semidirect
125. C₁₉×#436	C₂²	semidirect
126. C₁₉×#435	C₂²	semidirect
128. C₁₉×#433	C₂²	semidirect
129. C₁₉×#431	C₂²	semidirect
130. C₁₉×#424	C₂²	semidirect
131. C₁₉×#423	C₂²	semidirect
133. C₁₉×#417	C₂²	semidirect
134. C₁₉×#416	C₂²	semidirect
458. #62044	C₁₉	direct (N × H)
539. #3523	C₂×C₁₉	semidirect
540. #3398	C₂×C₁₉	semidirect
541. #3392	C₂×C₁₉	semidirect
542. #3368	C₂×C₁₉	semidirect
543. #3364	C₂×C₁₉	semidirect
544. #3324	C₂×C₁₉	semidirect
545. #3323	C₂×C₁₉	semidirect
546. #3317	C₂×C₁₉	semidirect
547. #3302	C₂×C₁₉	semidirect
548. D₄×SD₁₆	C₂×C₁₉	semidirect
549. #3278	C₂×C₁₉	semidirect
550. #3276	C₂×C₁₉	semidirect
551. #3266	C₂×C₁₉	semidirect
552. #3258	C₂×C₁₉	semidirect
553. #3254	C₂×C₁₉	semidirect
554. #3222	C₂×C₁₉	semidirect
555. #3210	C₂×C₁₉	semidirect
556. #3121	C₂×C₁₉	semidirect
557. #3103	C₂×C₁₉	semidirect
558. #3043	C₂×C₁₉	semidirect
559. #3037	C₂×C₁₉	semidirect
560. #2993	C₂×C₁₉	semidirect
597. C₂×#137	C₂²×C₁₉	semidirect
598. C₂×#137	C₂²×C₁₉	semidirect
602. #557	C₂²×C₁₉	semidirect
603. #557	C₂²×C₁₉	semidirect
609. #552	C₂²×C₁₉	semidirect
613. D₄×Q₈	C₂²×C₁₉	semidirect
620. #541	C₂²×C₁₉	semidirect
626. #533	C₂²×C₁₉	semidirect
631. #519	C₂²×C₁₉	semidirect
632. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
634. #494	C₂²×C₁₉	semidirect
636. #492	C₂²×C₁₉	semidirect
637. #490	C₂²×C₁₉	semidirect
639. #487	C₂²×C₁₉	semidirect
641. #485	C₂²×C₁₉	semidirect
644. #481	C₂²×C₁₉	semidirect
645. #479	C₂²×C₁₉	semidirect
646. #478	C₂²×C₁₉	semidirect
647. #477	C₂²×C₁₉	semidirect
648. #475	C₂²×C₁₉	semidirect
649. #475	C₂²×C₁₉	semidirect
651. #474	C₂²×C₁₉	semidirect
652. #470	C₂²×C₁₉	semidirect
655. #468	C₂²×C₁₉	semidirect
656. #467	C₂²×C₁₉	semidirect
660. #464	C₂²×C₁₉	semidirect
661. #464	C₂²×C₁₉	semidirect
662. #464	C₂²×C₁₉	semidirect
663. #464	C₂²×C₁₉	semidirect
664. #462	C₂²×C₁₉	semidirect
665. #462	C₂²×C₁₉	semidirect
666. #462	C₂²×C₁₉	semidirect
668. #461	C₂²×C₁₉	semidirect
669. #461	C₂²×C₁₉	semidirect
675. #460	C₂²×C₁₉	semidirect
676. #460	C₂²×C₁₉	semidirect
677. #452	C₂²×C₁₉	semidirect
678. #452	C₂²×C₁₉	semidirect
679. #452	C₂²×C₁₉	semidirect
680. #452	C₂²×C₁₉	semidirect
681. #451	C₂²×C₁₉	semidirect
686. #448	C₂²×C₁₉	semidirect
687. #446	C₂²×C₁₉	semidirect
688. C₈×Q₈	C₂²×C₁₉	semidirect
689. #441	C₂²×C₁₉	semidirect
690. #440	C₂²×C₁₉	semidirect
691. C₄×Q₁₆	C₂²×C₁₉	semidirect
694. C₄×SD₁₆	C₂²×C₁₉	semidirect
695. C₄×SD₁₆	C₂²×C₁₉	semidirect
696. C₄×SD₁₆	C₂²×C₁₉	semidirect
698. #436	C₂²×C₁₉	semidirect
699. #435	C₂²×C₁₉	semidirect
701. #433	C₂²×C₁₉	semidirect
702. #431	C₂²×C₁₉	semidirect
703. #424	C₂²×C₁₉	semidirect
704. #423	C₂²×C₁₉	semidirect
706. #417	C₂²×C₁₉	semidirect
707. #416	C₂²×C₁₉	semidirect
896. C₁₉	#62044	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×#3546	2
C₁₉×#3523	2
C₁₉×#3398	2
C₁₉×#3392	2
C₁₉×#3368	2
C₁₉×#3364	2
C₁₉×#3324	2
C₁₉×#3323	2
C₁₉×#3317	2
C₁₉×#3302	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3278	2
C₁₉×#3276	2
C₁₉×#3266	2
C₁₉×#3258	2
C₁₉×#3254	2
C₁₉×#3222	2
C₁₉×#3210	2
C₁₉×#3121	2
C₁₉×#3103	2
C₁₉×#3043	2
C₁₉×#3037	2
C₁₉×#2993	2
#62044	19

Subgroups — C19×#62044 #18068003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62044 #18068003