Subgroups — C₁₉×#62345 #18068304

Order 4864.

1834 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×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3546	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3353	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3350	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3320	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3311	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3201	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3200	C₂	1	2	yes	maximal, complemented
19	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3063	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3057	C₂	1	2	yes	maximal, complemented
23	C₁₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
26	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
27	C₁₉×#563	—	2	2	no	—
28	C₁₉×#560	—	2	2	no	—
29	C₁₉×#559	—	2	1	no	—
30	Q₈²×C₁₉	—	2	1	no	—
31	C₁₉×#556	C₂²	1	1	yes	characteristic
32	C₁₉×#556	C₂²	1	1	yes	characteristic
33	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#556	C₂²	1	2	yes	complemented
35	C₁₉×#553	C₂²	1	2	yes	—
36	C₁₉×#550	—	2	1	no	—
37	C₁₉×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
40	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, 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	—	2	1	no	—
46	C₁₉×#542	—	2	1	no	—
47	C₁₉×#542	—	2	1	no	—
48	C₁₉×#542	—	2	2	no	—
49	C₁₉×#538	—	2	2	no	—
50	C₁₉×#537	C₂²	1	2	yes	—
51	C₁₉×#536	C₂²	1	2	yes	complemented
52	C₁₉×#536	C₂²	1	2	yes	complemented
53	C₁₉×#535	—	2	1	no	—
54	C₁₉×#535	C₂²	1	2	yes	—
55	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#532	C₂²	1	1	yes	characteristic
58	C₁₉×#532	C₂²	1	1	yes	characteristic
59	C₁₉×#529	C₂²	1	1	yes	characteristic
60	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#497	C₂²	1	1	yes	characteristic
63	C₁₉×#492	C₂²	1	1	yes	characteristic
64	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#489	C₂²	1	1	yes	characteristic
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×#485	C₂²	1	2	yes	complemented
70	C₁₉×#485	C₂²	1	2	yes	complemented
71	C₁₉×#484	C₂²	1	2	yes	complemented
72	C₁₉×#483	C₂²	1	2	yes	complemented
73	C₁₉×#482	C₂²	1	2	yes	—
74	C₁₉×#482	C₂²	1	2	yes	—
75	C₁₉×#482	C₂²	1	2	yes	complemented
76	C₁₉×#479	C₂²	1	2	yes	complemented
77	C₁₉×#476	C₂²	1	2	yes	complemented
78	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
81	C₁₉×#474	C₂²	1	1	yes	characteristic
82	C₁₉×#470	C₂²	1	1	yes	characteristic, complemented
83	C₁₉×#470	C₂²	1	1	yes	characteristic, complemented
84	C₁₉×#470	C₂²	1	2	yes	complemented
85	C₁₉×#468	C₂²	1	1	yes	characteristic
86	C₁₉×#468	C₂²	1	1	yes	characteristic
87	C₁₉×#468	C₂²	1	2	yes	—
88	C₁₉×#468	C₂²	1	2	yes	—
89	C₁₉×#468	C₂²	1	2	yes	complemented
90	C₁₉×#468	C₂²	1	2	yes	complemented
91	C₁₉×#468	C₂²	1	2	yes	complemented
92	C₁₉×#467	C₂²	1	2	yes	complemented
93	C₁₉×#467	C₂²	1	2	yes	complemented
94	C₁₉×#465	C₂²	1	2	yes	—
95	C₁₉×#465	C₂²	1	2	yes	—
96	C₁₉×#465	C₂²	1	2	yes	—
97	C₁₉×#465	C₂²	1	2	yes	complemented
98	C₁₉×#465	C₂²	1	2	yes	complemented
99	C₁₉×#465	C₂²	1	2	yes	complemented
100	C₁₉×#464	C₂²	1	2	yes	—
101	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
102	C₁₉×#461	C₂²	1	1	yes	characteristic
103	C₁₉×#461	C₂²	1	2	yes	complemented
104	C₁₉×#460	C₂²	1	1	yes	characteristic
105	C₁₉×#460	C₂²	1	1	yes	characteristic
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	2	yes	—
112	C₁₉×#448	C₂²	1	2	yes	—
113	C₁₉×#448	C₂²	1	2	yes	complemented
114	C₁₉×#440	C₂²	1	2	yes	complemented
115	C₁₉×#440	C₂²	1	2	yes	complemented
116	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
120	C₁₉×#436	C₂²	1	1	yes	characteristic
121	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₉×#435	C₂²	1	2	yes	complemented
123	C₁₉×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
126	C₁₉×#428	C₂²	1	2	yes	complemented
127	C₁₉×#427	C₂²	1	2	yes	complemented
128	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
129	C₁₉×#419	C₂²	1	2	yes	complemented
130	C₁₉×#418	C₂²	1	2	yes	—
131	C₁₉×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
133	C₁₉×#408	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, 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	2	yes	—
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	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₁₉	—	4	4	no	—
148	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
155	C₁₉×#131	—	4	4	no	—
156	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
158	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
160	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
163	C₁₉×C₄⋊Q₈	—	2	2	no	—
164	C₁₉×C₄⋊Q₈	—	2	2	no	—
165	C₁₉×C₄⋊Q₈	—	2	1	no	—
166	C₁₉×C₄⋊Q₈	—	2	1	no	—
167	C₁₉×C₄⋊Q₈	—	2	2	no	—
168	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	C₁₉×#127	—	2	1	no	—
175	C₁₉×#127	—	2	2	no	—
176	C₁₉×#127	D₄	1	1	yes	characteristic
177	C₁₉×#127	C₂³	1	1	yes	characteristic
178	C₁₉×#126	—	2	2	no	—
179	C₁₉×#126	—	2	2	no	—
180	C₁₉×#126	—	2	2	no	—
181	C₁₉×#126	—	2	2	no	—
182	C₁₉×#126	—	2	2	no	—
183	C₁₉×#126	—	2	2	no	—
184	C₁₉×#126	—	2	1	no	—
185	C₁₉×#125	—	2	1	no	—
186	C₁₉×#125	—	2	1	no	—
187	C₁₉×#125	C₂³	1	1	yes	characteristic
188	C₁₉×#124	—	2	2	no	—
189	C₁₉×#124	—	2	1	no	—
190	C₁₉×#124	—	2	2	no	—
191	C₁₉×#124	—	2	2	no	—
192	C₁₉×#124	—	2	1	no	—
193	C₁₉×#124	—	2	1	no	—
194	C₁₉×#124	—	2	2	no	—
195	C₁₉×#124	—	2	1	no	—
196	C₁₉×#124	D₄	1	2	yes	—
197	C₁₉×#124	C₂³	1	1	yes	characteristic
198	C₁₉×#123	—	2	2	no	—
199	C₁₉×#123	—	2	2	no	—
200	C₁₉×#123	—	2	2	no	—
201	C₁₉×#123	—	2	2	no	—
202	C₁₉×#123	—	2	1	no	—
203	C₁₉×#123	—	2	2	no	—
204	C₁₉×#123	—	2	2	no	—
205	C₁₉×#123	—	2	2	no	—
206	C₁₉×C₂²⋊Q₈	—	2	2	no	—
207	C₁₉×C₂²⋊Q₈	—	2	1	no	—
208	C₁₉×C₂²⋊Q₈	—	2	1	no	—
209	C₁₉×C₂²⋊Q₈	—	2	1	no	—
210	C₁₉×C₂²⋊Q₈	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	—	2	2	no	—
212	C₁₉×C₂²⋊Q₈	—	2	2	no	—
213	C₁₉×C₂²⋊Q₈	—	2	2	no	—
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×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₁₉×#121	—	2	2	no	—
224	C₁₉×#121	—	2	2	no	—
225	C₁₉×#121	—	2	2	no	—
226	C₁₉×#121	—	2	2	no	—
227	C₁₉×#121	—	2	1	no	—
228	C₁₉×#121	—	2	1	no	—
229	C₁₉×#121	—	2	2	no	—
230	C₁₉×#121	—	2	2	no	—
231	C₁₉×#121	D₄	1	1	yes	characteristic
232	C₁₉×#121	D₄	1	1	yes	characteristic
233	C₁₉×#121	D₄	1	2	yes	—
234	C₁₉×#121	C₂³	1	2	yes	—
235	C₁₉×#121	C₂³	1	2	yes	—
236	C₁₉×#121	C₂³	1	2	yes	—
237	C₁₉×#121	C₂³	1	1	yes	characteristic
238	C₁₉×#121	C₂³	1	2	yes	—
239	C₁₉×#120	—	2	2	no	—
240	C₁₉×#120	—	2	2	no	—
241	C₁₉×#120	—	2	2	no	—
242	C₁₉×#120	—	2	2	no	—
243	C₄×Q₈×C₁₉	—	2	1	no	—
244	C₄×Q₈×C₁₉	—	2	1	no	—
245	C₄×Q₈×C₁₉	—	2	1	no	—
246	C₄×Q₈×C₁₉	—	2	2	no	—
247	C₄×Q₈×C₁₉	—	2	1	no	—
248	C₄×Q₈×C₁₉	—	2	1	no	—
249	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
253	C₄×D₄×C₁₉	—	2	1	no	—
254	C₄×D₄×C₁₉	—	2	1	no	—
255	C₄×D₄×C₁₉	—	2	2	no	—
256	C₄×D₄×C₁₉	—	2	1	no	—
257	C₄×D₄×C₁₉	—	2	1	no	—
258	C₄×D₄×C₁₉	—	2	2	no	—
259	C₄×D₄×C₁₉	—	2	1	no	—
260	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₁₉	C₂³	1	2	yes	—
262	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₁₉	C₂³	1	2	yes	—
265	C₁₉×#117	—	2	1	no	—
266	C₁₉×#117	—	2	1	no	—
267	C₁₉×#117	—	2	1	no	—
268	C₁₉×#117	C₂³	1	2	yes	—
269	C₁₉×#117	C₂³	1	2	yes	—
270	C₁₉×#117	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
273	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
274	C₁₉×#107	C₂³	1	1	yes	characteristic
275	C₁₉×#107	C₂³	1	2	yes	—
276	C₁₉×#107	C₂³	1	2	yes	—
277	C₁₉×#107	C₂³	1	1	yes	characteristic
278	C₁₉×#107	C₂³	1	2	yes	—
279	C₁₉×#106	C₂³	1	2	yes	—
280	C₁₉×#106	C₂³	1	2	yes	—
281	C₁₉×#106	C₂³	1	1	yes	characteristic
282	C₁₉×#106	C₂³	1	2	yes	—
283	C₁₉×#106	C₂³	1	1	yes	characteristic
284	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₉×#103	C₂³	1	1	yes	characteristic
288	C₁₉×#103	C₂³	1	2	yes	—
289	C₁₉×#103	C₂³	1	2	yes	—
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	1	yes	characteristic
292	C₁₉×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
297	C₁₉×#103	C₂³	1	1	yes	characteristic
298	C₁₉×#103	C₂³	1	1	yes	characteristic
299	C₁₉×#103	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	2	yes	—
302	C₁₉×#102	C₂³	1	1	yes	characteristic
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#102	C₂³	1	2	yes	—
305	C₁₉×#102	C₂³	1	1	yes	characteristic
306	C₁₉×#102	C₂³	1	2	yes	—
307	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₉×#97	C₂³	1	1	yes	characteristic
312	C₁₉×#97	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
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	1	no	—
324	C₂×Q₈×C₁₉	—	2	1	no	—
325	C₂×Q₈×C₁₉	—	2	2	no	—
326	C₂×Q₈×C₁₉	—	2	2	no	—
327	C₂×Q₈×C₁₉	—	4	2	no	—
328	C₂×Q₈×C₁₉	—	4	2	no	—
329	C₂×Q₈×C₁₉	—	4	2	no	—
330	C₂×Q₈×C₁₉	—	4	2	no	—
331	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
332	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₁₉	—	2	1	no	—
337	C₂×D₄×C₁₉	—	2	2	no	—
338	C₂×D₄×C₁₉	—	2	2	no	—
339	C₂×D₄×C₁₉	—	2	2	no	—
340	C₂×D₄×C₁₉	—	2	2	no	—
341	C₂×D₄×C₁₉	—	2	2	no	—
342	C₂×D₄×C₁₉	—	2	1	no	—
343	C₂×D₄×C₁₉	—	2	1	no	—
344	C₂×D₄×C₁₉	—	2	2	no	—
345	C₂×D₄×C₁₉	—	4	2	no	—
346	C₂×D₄×C₁₉	—	4	2	no	—
347	C₂×D₄×C₁₉	—	8	2	no	—
348	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₁₉	—	2	2	no	—
357	C₂²×C₄×C₁₉	—	2	2	no	—
358	C₂²×C₄×C₁₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
367	Q₁₆×C₁₉	—	2	2	no	—
368	Q₁₆×C₁₉	—	4	1	no	—
369	Q₁₆×C₁₉	—	4	2	no	—
370	SD₁₆×C₁₉	—	2	2	no	—
371	SD₁₆×C₁₉	—	2	4	no	—
372	SD₁₆×C₁₉	—	4	2	no	—
373	SD₁₆×C₁₉	—	4	2	no	—
374	SD₁₆×C₁₉	—	4	2	no	—
375	SD₁₆×C₁₉	—	4	1	no	—
376	SD₁₆×C₁₉	—	4	2	no	—
377	M₁₆×C₁₉	—	2	2	no	—
378	M₁₆×C₁₉	—	2	4	no	—
379	M₁₆×C₁₉	—	4	1	no	—
380	M₁₆×C₁₉	—	4	2	no	—
381	C₂×C₈×C₁₉	—	2	4	no	—
382	C₂×C₈×C₁₉	—	4	2	no	—
383	C₂×C₈×C₁₉	—	4	2	no	—
384	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
385	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	2	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	1	no	—
396	C₄⋊C₄×C₁₉	—	2	1	no	—
397	C₄⋊C₄×C₁₉	—	2	1	no	—
398	C₄⋊C₄×C₁₉	—	2	1	no	—
399	C₄⋊C₄×C₁₉	—	2	1	no	—
400	C₄⋊C₄×C₁₉	—	2	1	no	—
401	C₄⋊C₄×C₁₉	—	2	2	no	—
402	C₄⋊C₄×C₁₉	—	2	2	no	—
403	C₄⋊C₄×C₁₉	—	2	2	no	—
404	C₄⋊C₄×C₁₉	—	2	2	no	—
405	C₄⋊C₄×C₁₉	—	2	2	no	—
406	C₄⋊C₄×C₁₉	—	2	2	no	—
407	C₄⋊C₄×C₁₉	—	2	1	no	—
408	C₄⋊C₄×C₁₉	—	2	1	no	—
409	C₄⋊C₄×C₁₉	—	2	1	no	—
410	C₄⋊C₄×C₁₉	—	2	1	no	—
411	C₄⋊C₄×C₁₉	—	2	1	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	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	—	2	2	no	—
423	C₂²⋊C₄×C₁₉	—	2	2	no	—
424	C₂²⋊C₄×C₁₉	—	2	1	no	—
425	C₂²⋊C₄×C₁₉	—	2	1	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	2	no	—
433	C₂²⋊C₄×C₁₉	—	2	2	no	—
434	C₂²⋊C₄×C₁₉	—	2	1	no	—
435	C₂²⋊C₄×C₁₉	—	2	2	no	—
436	C₂²⋊C₄×C₁₉	—	2	1	no	—
437	C₂²⋊C₄×C₁₉	—	2	1	no	—
438	C₂²⋊C₄×C₁₉	—	2	2	no	—
439	C₂²⋊C₄×C₁₉	—	2	2	no	—
440	C₂²⋊C₄×C₁₉	—	2	2	no	—
441	C₂²⋊C₄×C₁₉	—	2	1	no	—
442	C₂²⋊C₄×C₁₉	—	2	2	no	—
443	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
447	C₄²×C₁₉	—	2	1	no	—
448	C₄²×C₁₉	—	2	2	no	—
449	C₄²×C₁₉	—	2	1	no	—
450	C₄²×C₁₉	—	2	1	no	—
451	C₄²×C₁₉	—	2	2	no	—
452	C₄²×C₁₉	—	2	2	no	—
453	C₄²×C₁₉	—	2	2	no	—
454	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
457	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
458	#62345	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	—	8	2	no	—
462	C₂³×C₁₉	—	8	2	no	—
463	C₂³×C₁₉	—	8	2	no	—
464	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
465	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
467	Q₈×C₁₉	—	2	1	no	—
468	Q₈×C₁₉	—	2	2	no	—
469	Q₈×C₁₉	—	2	1	no	—
470	Q₈×C₁₉	—	2	1	no	—
471	Q₈×C₁₉	—	2	2	no	—
472	Q₈×C₁₉	—	2	1	no	—
473	Q₈×C₁₉	—	2	1	no	—
474	Q₈×C₁₉	—	2	1	no	—
475	Q₈×C₁₉	—	4	2	no	—
476	Q₈×C₁₉	—	4	2	no	—
477	Q₈×C₁₉	—	4	2	no	—
478	Q₈×C₁₉	—	4	2	no	—
479	Q₈×C₁₉	—	8	2	no	—
480	Q₈×C₁₉	—	8	2	no	—
481	D₄×C₁₉	—	2	2	no	—
482	D₄×C₁₉	—	2	2	no	—
483	D₄×C₁₉	—	2	1	no	—
484	D₄×C₁₉	—	2	2	no	—
485	D₄×C₁₉	—	2	1	no	—
486	D₄×C₁₉	—	2	2	no	—
487	D₄×C₁₉	—	4	2	no	—
488	D₄×C₁₉	—	4	2	no	—
489	D₄×C₁₉	—	4	2	no	—
490	D₄×C₁₉	—	4	2	no	—
491	D₄×C₁₉	—	4	2	no	—
492	D₄×C₁₉	—	8	1	no	—
493	D₄×C₁₉	—	8	2	no	—
494	D₄×C₁₉	—	8	1	no	—
495	D₄×C₁₉	—	8	2	no	—
496	D₄×C₁₉	—	8	2	no	—
497	D₄×C₁₉	—	8	2	no	—
498	D₄×C₁₉	—	8	2	no	—
499	D₄×C₁₉	—	8	2	no	—
500	C₂×C₄×C₁₉	—	2	2	no	—
501	C₂×C₄×C₁₉	—	2	2	no	—
502	C₂×C₄×C₁₉	—	2	1	no	—
503	C₂×C₄×C₁₉	—	2	2	no	—
504	C₂×C₄×C₁₉	—	2	1	no	—
505	C₂×C₄×C₁₉	—	2	2	no	—
506	C₂×C₄×C₁₉	—	2	2	no	—
507	C₂×C₄×C₁₉	—	2	1	no	—
508	C₂×C₄×C₁₉	—	2	1	no	—
509	C₂×C₄×C₁₉	—	2	2	no	—
510	C₂×C₄×C₁₉	—	2	1	no	—
511	C₂×C₄×C₁₉	—	2	1	no	—
512	C₂×C₄×C₁₉	—	2	2	no	—
513	C₂×C₄×C₁₉	—	2	1	no	—
514	C₂×C₄×C₁₉	—	2	2	no	—
515	C₂×C₄×C₁₉	—	2	1	no	—
516	C₂×C₄×C₁₉	—	2	1	no	—
517	C₂×C₄×C₁₉	—	4	1	no	—
518	C₂×C₄×C₁₉	—	4	2	no	—
519	C₂×C₄×C₁₉	—	8	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	—	8	2	no	—
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	1	yes	characteristic
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	2	no	—
533	C₈×C₁₉	—	2	1	no	—
534	C₈×C₁₉	—	2	2	no	—
535	C₈×C₁₉	—	2	1	no	—
536	C₈×C₁₉	—	2	1	no	—
537	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
538	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
539	#3546	C₂×C₁₉	1	1	yes	characteristic
540	#3353	C₂×C₁₉	1	1	yes	characteristic, complemented
541	#3350	C₂×C₁₉	1	2	yes	complemented
542	#3342	C₂×C₁₉	1	1	yes	characteristic, complemented
543	#3328	C₂×C₁₉	1	1	yes	characteristic, complemented
544	#3324	C₂×C₁₉	1	1	yes	characteristic, complemented
545	#3320	C₂×C₁₉	1	2	yes	complemented
546	#3311	C₂×C₁₉	1	2	yes	complemented
547	#3304	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3298	C₂×C₁₉	1	1	yes	characteristic, complemented
549	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
550	#3278	C₂×C₁₉	1	1	yes	characteristic, complemented
551	#3266	C₂×C₁₉	1	2	yes	complemented
552	#3248	C₂×C₁₉	1	1	yes	characteristic, complemented
553	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
554	#3201	C₂×C₁₉	1	2	yes	complemented
555	#3200	C₂×C₁₉	1	2	yes	complemented
556	#3182	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
558	#3063	C₂×C₁₉	1	2	yes	complemented
559	#3057	C₂×C₁₉	1	2	yes	complemented
560	#2935	C₂×C₁₉	1	1	yes	characteristic, complemented
561	C₂²×C₁₉	—	2	1	no	—
562	C₂²×C₁₉	—	2	2	no	—
563	C₂²×C₁₉	—	2	2	no	—
564	C₂²×C₁₉	—	2	2	no	—
565	C₂²×C₁₉	—	2	2	no	—
566	C₂²×C₁₉	—	2	1	no	—
567	C₂²×C₁₉	—	2	1	no	—
568	C₂²×C₁₉	—	2	2	no	—
569	C₂²×C₁₉	—	2	2	no	—
570	C₂²×C₁₉	—	4	2	no	—
571	C₂²×C₁₉	—	4	1	no	—
572	C₂²×C₁₉	—	4	2	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	1	no	—
584	C₄×C₁₉	—	4	1	no	—
585	C₄×C₁₉	—	4	1	no	—
586	C₄×C₁₉	—	4	1	no	—
587	C₄×C₁₉	—	4	1	no	—
588	C₄×C₁₉	—	4	1	no	—
589	C₄×C₁₉	—	4	2	no	—
590	C₄×C₁₉	—	4	1	no	—
591	C₄×C₁₉	—	4	1	no	—
592	C₄×C₁₉	—	4	2	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	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
599	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
600	#563	—	2	2	no	—
601	#560	—	2	2	no	—
602	#559	—	2	1	no	—
603	Q₈²	—	2	1	no	—
604	#556	C₂²×C₁₉	1	1	yes	characteristic
605	#556	C₂²×C₁₉	1	1	yes	characteristic
606	#556	C₂²×C₁₉	1	2	yes	complemented
607	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
608	#553	C₂²×C₁₉	1	2	yes	—
609	#550	—	2	1	no	—
610	#550	C₂²×C₁₉	1	1	yes	characteristic
611	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
612	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
613	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, 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	—	2	1	no	—
619	#542	—	2	1	no	—
620	#542	—	2	1	no	—
621	#542	—	2	2	no	—
622	#538	—	2	2	no	—
623	#537	C₂²×C₁₉	1	2	yes	—
624	#536	C₂²×C₁₉	1	2	yes	complemented
625	#536	C₂²×C₁₉	1	2	yes	complemented
626	#535	—	2	1	no	—
627	#535	C₂²×C₁₉	1	2	yes	—
628	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
629	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
630	#532	C₂²×C₁₉	1	1	yes	characteristic
631	#532	C₂²×C₁₉	1	1	yes	characteristic
632	#529	C₂²×C₁₉	1	1	yes	characteristic
633	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
634	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
635	#497	C₂²×C₁₉	1	1	yes	characteristic
636	#492	C₂²×C₁₉	1	1	yes	characteristic
637	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
638	#489	C₂²×C₁₉	1	1	yes	characteristic
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	#485	C₂²×C₁₉	1	2	yes	complemented
643	#485	C₂²×C₁₉	1	2	yes	complemented
644	#484	C₂²×C₁₉	1	2	yes	complemented
645	#483	C₂²×C₁₉	1	2	yes	complemented
646	#482	C₂²×C₁₉	1	2	yes	—
647	#482	C₂²×C₁₉	1	2	yes	—
648	#482	C₂²×C₁₉	1	2	yes	complemented
649	#479	C₂²×C₁₉	1	2	yes	complemented
650	#476	C₂²×C₁₉	1	2	yes	complemented
651	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
652	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
653	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
654	#474	C₂²×C₁₉	1	1	yes	characteristic
655	#470	C₂²×C₁₉	1	2	yes	complemented
656	#470	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#470	C₂²×C₁₉	1	1	yes	characteristic, complemented
658	#468	C₂²×C₁₉	1	2	yes	—
659	#468	C₂²×C₁₉	1	1	yes	characteristic
660	#468	C₂²×C₁₉	1	1	yes	characteristic
661	#468	C₂²×C₁₉	1	2	yes	—
662	#468	C₂²×C₁₉	1	2	yes	complemented
663	#468	C₂²×C₁₉	1	2	yes	complemented
664	#468	C₂²×C₁₉	1	2	yes	complemented
665	#467	C₂²×C₁₉	1	2	yes	complemented
666	#467	C₂²×C₁₉	1	2	yes	complemented
667	#465	C₂²×C₁₉	1	2	yes	—
668	#465	C₂²×C₁₉	1	2	yes	—
669	#465	C₂²×C₁₉	1	2	yes	—
670	#465	C₂²×C₁₉	1	2	yes	complemented
671	#465	C₂²×C₁₉	1	2	yes	complemented
672	#465	C₂²×C₁₉	1	2	yes	complemented
673	#464	C₂²×C₁₉	1	2	yes	—
674	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
675	#461	C₂²×C₁₉	1	1	yes	characteristic
676	#461	C₂²×C₁₉	1	2	yes	complemented
677	#460	C₂²×C₁₉	1	1	yes	characteristic
678	#460	C₂²×C₁₉	1	1	yes	characteristic
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	2	yes	—
685	#448	C₂²×C₁₉	1	2	yes	—
686	#448	C₂²×C₁₉	1	2	yes	complemented
687	#440	C₂²×C₁₉	1	2	yes	complemented
688	#440	C₂²×C₁₉	1	2	yes	complemented
689	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
690	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
692	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
693	#436	C₂²×C₁₉	1	1	yes	characteristic
694	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
695	#435	C₂²×C₁₉	1	2	yes	complemented
696	#435	C₂²×C₁₉	1	2	yes	complemented
697	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
698	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
699	#428	C₂²×C₁₉	1	2	yes	complemented
700	#427	C₂²×C₁₉	1	2	yes	complemented
701	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
702	#419	C₂²×C₁₉	1	2	yes	complemented
703	#418	C₂²×C₁₉	1	2	yes	—
704	#416	C₂²×C₁₉	1	2	yes	complemented
705	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
706	#408	C₂²×C₁₉	1	2	yes	complemented
707	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
708	C₂×C₁₉	—	4	1	no	—
709	C₂×C₁₉	—	4	2	no	—
710	C₂×C₁₉	—	4	2	no	—
711	C₂×C₁₉	—	8	2	no	—
712	C₂×C₁₉	—	8	1	no	—
713	C₂×C₁₉	#3496	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	2	yes	—
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	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
728	C₂×SD₁₆	—	4	4	no	—
729	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
736	#131	—	4	4	no	—
737	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
739	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
740	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
741	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
742	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
743	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
744	C₄⋊Q₈	—	2	2	no	—
745	C₄⋊Q₈	—	2	2	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	—	2	2	no	—
749	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
754	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
755	#127	—	2	1	no	—
756	#127	—	2	2	no	—
757	#127	D₄×C₁₉	1	1	yes	characteristic
758	#127	C₂³×C₁₉	1	1	yes	characteristic
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	1	no	—
766	#125	—	2	1	no	—
767	#125	—	2	1	no	—
768	#125	C₂³×C₁₉	1	1	yes	characteristic
769	#124	—	2	2	no	—
770	#124	—	2	1	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	1	no	—
774	#124	—	2	1	no	—
775	#124	—	2	2	no	—
776	#124	—	2	1	no	—
777	#124	D₄×C₁₉	1	2	yes	—
778	#124	C₂³×C₁₉	1	1	yes	characteristic
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	1	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
796	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	D₄×C₁₉	1	1	yes	characteristic
813	#121	D₄×C₁₉	1	1	yes	characteristic
814	#121	D₄×C₁₉	1	2	yes	—
815	#121	C₂³×C₁₉	1	1	yes	characteristic
816	#121	C₂³×C₁₉	1	2	yes	—
817	#121	C₂³×C₁₉	1	2	yes	—
818	#121	C₂³×C₁₉	1	2	yes	—
819	#121	C₂³×C₁₉	1	2	yes	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	—	2	1	no	—
827	C₄×Q₈	—	2	2	no	—
828	C₄×Q₈	—	2	1	no	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
831	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
832	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
833	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₁₉	1	2	yes	—
843	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₁₉	1	2	yes	—
845	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
846	#117	—	2	1	no	—
847	#117	—	2	1	no	—
848	#117	—	2	1	no	—
849	#117	C₂³×C₁₉	1	2	yes	—
850	#117	C₂³×C₁₉	1	2	yes	—
851	#117	C₂³×C₁₉	1	2	yes	—
852	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
855	#107	C₂³×C₁₉	1	1	yes	characteristic
856	#107	C₂³×C₁₉	1	2	yes	—
857	#107	C₂³×C₁₉	1	2	yes	—
858	#107	C₂³×C₁₉	1	1	yes	characteristic
859	#107	C₂³×C₁₉	1	2	yes	—
860	#106	C₂³×C₁₉	1	2	yes	—
861	#106	C₂³×C₁₉	1	2	yes	—
862	#106	C₂³×C₁₉	1	1	yes	characteristic
863	#106	C₂³×C₁₉	1	2	yes	—
864	#106	C₂³×C₁₉	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
867	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
868	#103	C₂³×C₁₉	1	1	yes	characteristic
869	#103	C₂³×C₁₉	1	2	yes	—
870	#103	C₂³×C₁₉	1	2	yes	—
871	#103	C₂³×C₁₉	1	2	yes	—
872	#103	C₂³×C₁₉	1	1	yes	characteristic
873	#103	C₂³×C₁₉	1	2	yes	—
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	1	yes	characteristic
878	#103	C₂³×C₁₉	1	1	yes	characteristic
879	#103	C₂³×C₁₉	1	1	yes	characteristic
880	#103	C₂³×C₁₉	1	2	yes	—
881	#102	C₂³×C₁₉	1	2	yes	—
882	#102	C₂³×C₁₉	1	2	yes	—
883	#102	C₂³×C₁₉	1	1	yes	characteristic
884	#102	C₂³×C₁₉	1	2	yes	—
885	#102	C₂³×C₁₉	1	2	yes	—
886	#102	C₂³×C₁₉	1	1	yes	characteristic
887	#102	C₂³×C₁₉	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
892	#97	C₂³×C₁₉	1	1	yes	characteristic
893	#97	C₂³×C₁₉	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
896	C₁₉	#62345	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	1	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	—	4	2	no	—
913	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
915	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
917	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	8	2	no	—
930	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
931	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
933	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
934	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
935	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
936	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
945	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	4	1	no	—
951	Q₁₆	—	4	2	no	—
952	SD₁₆	—	2	2	no	—
953	SD₁₆	—	2	4	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	1	no	—
958	SD₁₆	—	4	2	no	—
959	M₁₆	—	2	2	no	—
960	M₁₆	—	2	4	no	—
961	M₁₆	—	4	1	no	—
962	M₁₆	—	4	2	no	—
963	C₂×C₈	—	2	4	no	—
964	C₂×C₈	—	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	2	yes	—
971	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
972	C₄⋊C₄	—	2	2	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	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	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	C₂⁴×C₁₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	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	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1037	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	2	no	—
1045	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1046	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1047	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	8	2	no	—
1061	Q₈	—	8	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	8	2	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	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	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	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
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	1	yes	characteristic
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	2	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	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	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	1	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	2	no	—
1157	C₂	—	4	1	no	—
1158	C₂	—	8	1	no	—
1159	C₂	—	8	2	no	—
1160	C₂	C₁₉×#3496	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3550	C₂	semidirect
3. C₁₉×#3353	C₂	semidirect
4. C₁₉×#3350	C₂	semidirect
5. C₁₉×#3342	C₂	semidirect
6. C₁₉×#3328	C₂	semidirect
7. C₁₉×#3324	C₂	semidirect
8. C₁₉×#3320	C₂	semidirect
9. C₁₉×#3311	C₂	semidirect
10. C₁₉×#3304	C₂	semidirect
11. C₁₉×#3298	C₂	semidirect
12. D₄×SD₁₆×C₁₉	C₂	semidirect
13. C₁₉×#3278	C₂	semidirect
14. C₁₉×#3266	C₂	semidirect
15. C₁₉×#3248	C₂	semidirect
16. C₁₉×#3246	C₂	semidirect
17. C₁₉×#3201	C₂	semidirect
18. C₁₉×#3200	C₂	semidirect
19. C₁₉×#3182	C₂	semidirect
20. C₁₉×#3172	C₂	semidirect
21. C₁₉×#3063	C₂	semidirect
22. C₁₉×#3057	C₂	semidirect
23. C₁₉×#2935	C₂	semidirect
24. C₂×C₁₉×#137	C₂²	semidirect
26. C₂×C₁₉×#131	C₂²	semidirect
33. C₁₉×#556	C₂²	semidirect
34. C₁₉×#556	C₂²	semidirect
39. D₄×Q₈×C₁₉	C₂²	semidirect
40. D₄×Q₈×C₁₉	C₂²	semidirect
51. C₁₉×#536	C₂²	semidirect
52. C₁₉×#536	C₂²	semidirect
55. C₁₉×#533	C₂²	semidirect
56. C₁₉×#533	C₂²	semidirect
60. C₁₉×#501	C₂²	semidirect
61. C₁₉×#500	C₂²	semidirect
64. C₁₉×#491	C₂²	semidirect
66. C₁₉×#487	C₂²	semidirect
68. C₁₉×#485	C₂²	semidirect
69. C₁₉×#485	C₂²	semidirect
70. C₁₉×#485	C₂²	semidirect
71. C₁₉×#484	C₂²	semidirect
72. C₁₉×#483	C₂²	semidirect
75. C₁₉×#482	C₂²	semidirect
76. C₁₉×#479	C₂²	semidirect
77. C₁₉×#476	C₂²	semidirect
78. C₁₉×#475	C₂²	semidirect
79. C₁₉×#475	C₂²	semidirect
80. C₁₉×#475	C₂²	semidirect
82. C₁₉×#470	C₂²	semidirect
83. C₁₉×#470	C₂²	semidirect
84. C₁₉×#470	C₂²	semidirect
89. C₁₉×#468	C₂²	semidirect
90. C₁₉×#468	C₂²	semidirect
91. C₁₉×#468	C₂²	semidirect
92. C₁₉×#467	C₂²	semidirect
93. C₁₉×#467	C₂²	semidirect
97. C₁₉×#465	C₂²	semidirect
98. C₁₉×#465	C₂²	semidirect
99. C₁₉×#465	C₂²	semidirect
101. C₁₉×#462	C₂²	semidirect
103. C₁₉×#461	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
107. C₁₉×#452	C₂²	semidirect
108. C₁₉×#451	C₂²	semidirect
113. C₁₉×#448	C₂²	semidirect
114. C₁₉×#440	C₂²	semidirect
115. C₁₉×#440	C₂²	semidirect
116. C₄×Q₁₆×C₁₉	C₂²	semidirect
117. C₄×Q₁₆×C₁₉	C₂²	semidirect
121. C₁₉×#436	C₂²	semidirect
122. C₁₉×#435	C₂²	semidirect
123. C₁₉×#435	C₂²	semidirect
125. C₈×D₄×C₁₉	C₂²	semidirect
126. C₁₉×#428	C₂²	semidirect
127. C₁₉×#427	C₂²	semidirect
128. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
129. C₁₉×#419	C₂²	semidirect
131. C₁₉×#416	C₂²	semidirect
132. C₂×C₁₉×#103	C₂²	semidirect
133. C₁₉×#408	C₂²	semidirect
134. C₄×M₁₆×C₁₉	C₂²	semidirect
458. #62345	C₁₉	direct (N × H)
538. #3550	C₂×C₁₉	semidirect
540. #3353	C₂×C₁₉	semidirect
541. #3350	C₂×C₁₉	semidirect
542. #3342	C₂×C₁₉	semidirect
543. #3328	C₂×C₁₉	semidirect
544. #3324	C₂×C₁₉	semidirect
545. #3320	C₂×C₁₉	semidirect
546. #3311	C₂×C₁₉	semidirect
547. #3304	C₂×C₁₉	semidirect
548. #3298	C₂×C₁₉	semidirect
549. D₄×SD₁₆	C₂×C₁₉	semidirect
550. #3278	C₂×C₁₉	semidirect
551. #3266	C₂×C₁₉	semidirect
552. #3248	C₂×C₁₉	semidirect
553. #3246	C₂×C₁₉	semidirect
554. #3201	C₂×C₁₉	semidirect
555. #3200	C₂×C₁₉	semidirect
556. #3182	C₂×C₁₉	semidirect
557. #3172	C₂×C₁₉	semidirect
558. #3063	C₂×C₁₉	semidirect
559. #3057	C₂×C₁₉	semidirect
560. #2935	C₂×C₁₉	semidirect
597. C₂×#137	C₂²×C₁₉	semidirect
599. C₂×#131	C₂²×C₁₉	semidirect
606. #556	C₂²×C₁₉	semidirect
607. #556	C₂²×C₁₉	semidirect
612. D₄×Q₈	C₂²×C₁₉	semidirect
613. D₄×Q₈	C₂²×C₁₉	semidirect
624. #536	C₂²×C₁₉	semidirect
625. #536	C₂²×C₁₉	semidirect
628. #533	C₂²×C₁₉	semidirect
629. #533	C₂²×C₁₉	semidirect
633. #501	C₂²×C₁₉	semidirect
634. #500	C₂²×C₁₉	semidirect
637. #491	C₂²×C₁₉	semidirect
639. #487	C₂²×C₁₉	semidirect
641. #485	C₂²×C₁₉	semidirect
642. #485	C₂²×C₁₉	semidirect
643. #485	C₂²×C₁₉	semidirect
644. #484	C₂²×C₁₉	semidirect
645. #483	C₂²×C₁₉	semidirect
648. #482	C₂²×C₁₉	semidirect
649. #479	C₂²×C₁₉	semidirect
650. #476	C₂²×C₁₉	semidirect
651. #475	C₂²×C₁₉	semidirect
652. #475	C₂²×C₁₉	semidirect
653. #475	C₂²×C₁₉	semidirect
655. #470	C₂²×C₁₉	semidirect
656. #470	C₂²×C₁₉	semidirect
657. #470	C₂²×C₁₉	semidirect
662. #468	C₂²×C₁₉	semidirect
663. #468	C₂²×C₁₉	semidirect
664. #468	C₂²×C₁₉	semidirect
665. #467	C₂²×C₁₉	semidirect
666. #467	C₂²×C₁₉	semidirect
670. #465	C₂²×C₁₉	semidirect
671. #465	C₂²×C₁₉	semidirect
672. #465	C₂²×C₁₉	semidirect
674. #462	C₂²×C₁₉	semidirect
676. #461	C₂²×C₁₉	semidirect
679. #452	C₂²×C₁₉	semidirect
680. #452	C₂²×C₁₉	semidirect
681. #451	C₂²×C₁₉	semidirect
686. #448	C₂²×C₁₉	semidirect
687. #440	C₂²×C₁₉	semidirect
688. #440	C₂²×C₁₉	semidirect
689. C₄×Q₁₆	C₂²×C₁₉	semidirect
690. C₄×Q₁₆	C₂²×C₁₉	semidirect
694. #436	C₂²×C₁₉	semidirect
695. #435	C₂²×C₁₉	semidirect
696. #435	C₂²×C₁₉	semidirect
698. C₈×D₄	C₂²×C₁₉	semidirect
699. #428	C₂²×C₁₉	semidirect
700. #427	C₂²×C₁₉	semidirect
701. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
702. #419	C₂²×C₁₉	semidirect
704. #416	C₂²×C₁₉	semidirect
705. C₂×#103	C₂²×C₁₉	semidirect
706. #408	C₂²×C₁₉	semidirect
707. C₄×M₁₆	C₂²×C₁₉	semidirect
896. C₁₉	#62345	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×#3550	2
C₁₉×#3546	2
C₁₉×#3353	2
C₁₉×#3350	2
C₁₉×#3342	2
C₁₉×#3328	2
C₁₉×#3324	2
C₁₉×#3320	2
C₁₉×#3311	2
C₁₉×#3304	2
C₁₉×#3298	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3278	2
C₁₉×#3266	2
C₁₉×#3248	2
C₁₉×#3246	2
C₁₉×#3201	2
C₁₉×#3200	2
C₁₉×#3182	2
C₁₉×#3172	2
C₁₉×#3063	2
C₁₉×#3057	2
C₁₉×#2935	2
#62345	19

Subgroups — C19×#62345 #18068304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62345 #18068304