Subgroups — C₁₉×#62266 #18068225

Order 4864.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3542	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3341	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3339	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3336	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3319	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3310	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3309	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3306	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3280	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3257	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3198	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3194	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3176	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×#3058	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₁₉×#466	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, complemented
25	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#562	—	2	2	no	—
31	C₁₉×#560	—	2	2	no	—
32	C₁₉×#555	C₂²	1	2	yes	complemented
33	C₁₉×#553	C₂²	1	2	yes	complemented
34	C₁₉×#552	C₂²	1	2	yes	—
35	C₁₉×#551	—	2	2	no	—
36	C₁₉×#550	C₂²	1	2	yes	complemented
37	C₁₉×#547	C₂²	1	2	yes	complemented
38	C₁₉×#546	—	2	2	no	—
39	C₁₉×#546	C₂²	1	2	yes	complemented
40	C₁₉×#546	C₂²	1	2	yes	complemented
41	D₄²×C₁₉	C₂²	1	2	yes	—
42	C₁₉×#542	C₂²	1	2	yes	complemented
43	C₁₉×#540	—	2	2	no	—
44	C₁₉×#540	C₂²	1	2	yes	complemented
45	C₁₉×#538	—	2	2	no	—
46	C₁₉×#537	C₂²	1	2	yes	complemented
47	C₁₉×#535	—	2	2	no	—
48	C₁₉×#535	C₂²	1	2	yes	complemented
49	C₁₉×#534	—	2	2	no	—
50	C₁₉×#525	C₂²	1	1	yes	characteristic
51	C₁₉×#525	C₂²	1	2	yes	complemented
52	C₂×C₁₉×#121	C₂²	1	2	yes	complemented
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×#493	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#490	C₂²	1	2	yes	complemented
58	C₁₉×#489	C₂²	1	2	yes	complemented
59	C₁₉×#485	C₂²	1	2	yes	complemented
60	C₁₉×#483	C₂²	1	2	yes	complemented
61	C₁₉×#482	C₂²	1	2	yes	complemented
62	C₁₉×#482	C₂²	1	2	yes	complemented
63	C₁₉×#482	C₂²	1	2	yes	complemented
64	C₁₉×#481	C₂²	1	2	yes	complemented
65	C₁₉×#480	C₂²	1	2	yes	complemented
66	C₁₉×#480	C₂²	1	2	yes	complemented
67	C₁₉×#479	C₂²	1	2	yes	complemented
68	C₁₉×#478	C₂²	1	2	yes	complemented
69	C₁₉×#476	C₂²	1	2	yes	complemented
70	C₁₉×#474	C₂²	1	2	yes	complemented
71	C₁₉×#469	C₂²	1	2	yes	complemented
72	C₁₉×#469	C₂²	1	2	yes	complemented
73	C₁₉×#469	C₂²	1	2	yes	complemented
74	C₁₉×#468	C₂²	1	2	yes	complemented
75	C₁₉×#468	C₂²	1	2	yes	complemented
76	C₁₉×#468	C₂²	1	2	yes	complemented
77	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#466	C₂²	1	1	yes	characteristic
81	C₁₉×#466	C₂²	1	1	yes	characteristic
82	C₁₉×#466	C₂²	1	1	yes	characteristic
83	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
84	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
85	C₁₉×#466	C₂²	1	2	yes	complemented
86	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
87	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
88	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
89	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
90	C₁₉×#466	C₂²	1	2	yes	complemented
91	C₁₉×#465	C₂²	1	2	yes	complemented
92	C₁₉×#465	C₂²	1	2	yes	complemented
93	C₁₉×#463	C₂²	1	2	yes	complemented
94	C₁₉×#463	C₂²	1	2	yes	complemented
95	C₁₉×#460	C₂²	1	2	yes	complemented
96	C₁₉×#459	C₂²	1	2	yes	complemented
97	C₁₉×#450	C₂²	1	2	yes	complemented
98	C₁₉×#450	C₂²	1	2	yes	complemented
99	C₁₉×#449	C₂²	1	2	yes	complemented
100	C₁₉×#449	C₂²	1	2	yes	complemented
101	C₁₉×#449	C₂²	1	2	yes	complemented
102	C₁₉×#449	C₂²	1	2	yes	complemented
103	C₁₉×#447	C₂²	1	2	yes	—
104	C₁₉×#447	C₂²	1	2	yes	complemented
105	C₁₉×#442	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×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₈×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, complemented
113	C₁₉×#435	C₂²	1	1	yes	characteristic, complemented
114	C₁₉×#435	C₂²	1	1	yes	characteristic, complemented
115	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
116	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
117	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
119	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
120	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
123	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
124	C₁₉×#418	C₂²	1	2	yes	complemented
125	C₁₉×#417	C₂²	1	2	yes	complemented
126	C₁₉×#416	C₂²	1	2	yes	complemented
127	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
128	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
129	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
130	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41×C₁₉	—	2	2	no	—
132	C₂×#41×C₁₉	C₂³	1	2	yes	—
133	C₂×#41×C₁₉	C₂³	1	2	yes	—
134	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₁₉	—	2	2	no	—
136	C₂²×D₄×C₁₉	—	2	2	no	—
137	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
140	C₁₉×#135	—	4	2	no	—
141	C₁₉×#135	—	4	2	no	—
142	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×D₈×C₁₉	—	4	2	no	—
147	C₂×D₈×C₁₉	—	4	2	no	—
148	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
151	C₂×D₈×C₁₉	C₂³	1	2	yes	—
152	C₂×D₈×C₁₉	C₂³	1	2	yes	—
153	C₂×D₈×C₁₉	C₂³	1	2	yes	—
154	C₁₉×#131	—	4	2	no	—
155	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₁₉	—	4	2	no	—
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	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
168	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₁₉×#127	—	2	2	no	—
170	C₁₉×#127	—	2	2	no	—
171	C₁₉×#127	C₂³	1	2	yes	—
172	C₁₉×#126	—	2	2	no	—
173	C₁₉×#126	—	2	2	no	—
174	C₁₉×#126	—	2	2	no	—
175	C₁₉×#125	—	2	2	no	—
176	C₁₉×#125	C₂³	1	2	yes	—
177	C₁₉×#124	—	2	2	no	—
178	C₁₉×#124	—	2	2	no	—
179	C₁₉×#124	—	2	2	no	—
180	C₁₉×#124	—	2	2	no	—
181	C₁₉×#124	C₂³	1	2	yes	—
182	C₁₉×#123	—	2	2	no	—
183	C₁₉×#123	—	2	2	no	—
184	C₁₉×#123	—	2	2	no	—
185	C₁₉×#123	—	2	2	no	—
186	C₁₉×#123	—	2	2	no	—
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	D₄	1	1	yes	characteristic
193	C₁₉×#123	D₄	1	1	yes	characteristic
194	C₁₉×C₂²⋊Q₈	—	2	2	no	—
195	C₁₉×C₂²⋊Q₈	—	2	2	no	—
196	C₁₉×C₂²⋊Q₈	—	2	2	no	—
197	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
198	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
199	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₉×#121	—	2	2	no	—
203	C₁₉×#121	—	2	2	no	—
204	C₁₉×#121	—	2	2	no	—
205	C₁₉×#121	—	2	2	no	—
206	C₁₉×#121	—	2	2	no	—
207	C₁₉×#121	—	2	2	no	—
208	C₁₉×#121	—	2	2	no	—
209	C₁₉×#121	—	2	2	no	—
210	C₁₉×#121	—	2	2	no	—
211	C₁₉×#121	—	2	2	no	—
212	C₁₉×#121	—	2	2	no	—
213	C₁₉×#121	—	2	2	no	—
214	C₁₉×#121	—	2	2	no	—
215	C₁₉×#121	—	2	2	no	—
216	C₁₉×#121	D₄	1	1	yes	characteristic
217	C₁₉×#121	D₄	1	1	yes	characteristic
218	C₁₉×#121	C₂³	1	2	yes	—
219	C₁₉×#121	C₂³	1	2	yes	—
220	C₁₉×#121	C₂³	1	2	yes	—
221	C₁₉×#121	C₂³	1	2	yes	—
222	C₁₉×#121	C₂³	1	2	yes	—
223	C₁₉×#121	C₂³	1	2	yes	—
224	C₁₉×#121	C₂³	1	2	yes	—
225	C₁₉×#121	C₂³	1	2	yes	—
226	C₁₉×#121	C₂³	1	2	yes	—
227	C₁₉×#120	—	2	2	no	—
228	C₁₉×#120	—	2	2	no	—
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	C₁₉×#120	—	2	2	no	—
234	C₁₉×#120	D₄	1	1	yes	characteristic
235	C₁₉×#120	D₄	1	1	yes	characteristic
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	C₂³	1	2	yes	—
242	C₄×D₄×C₁₉	C₂³	1	2	yes	—
243	C₄×D₄×C₁₉	C₂³	1	2	yes	—
244	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×#117	—	2	2	no	—
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	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
255	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
256	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
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	1	yes	characteristic
261	C₁₉×#107	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
277	C₁₉×#102	C₂³	1	2	yes	—
278	C₁₉×#102	C₂³	1	2	yes	—
279	C₁₉×#102	C₂³	1	2	yes	—
280	C₁₉×#102	C₂³	1	2	yes	—
281	C₁₉×#102	C₂³	1	2	yes	—
282	C₁₉×#102	C₂³	1	2	yes	—
283	C₁₉×#102	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	—	2	2	no	—
301	C₂⁴×C₁₉	—	2	2	no	—
302	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
303	#41×C₁₉	—	4	1	no	—
304	#41×C₁₉	—	4	1	no	—
305	#41×C₁₉	—	4	2	no	—
306	#41×C₁₉	—	4	2	no	—
307	#41×C₁₉	—	4	2	no	—
308	#41×C₁₉	—	4	2	no	—
309	#41×C₁₉	—	8	4	no	—
310	C₂×Q₈×C₁₉	—	2	2	no	—
311	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
312	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
313	C₂×D₄×C₁₉	—	2	2	no	—
314	C₂×D₄×C₁₉	—	2	2	no	—
315	C₂×D₄×C₁₉	—	2	2	no	—
316	C₂×D₄×C₁₉	—	2	2	no	—
317	C₂×D₄×C₁₉	—	2	2	no	—
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	—	2	2	no	—
324	C₂×D₄×C₁₉	—	2	2	no	—
325	C₂×D₄×C₁₉	—	2	2	no	—
326	C₂×D₄×C₁₉	—	2	2	no	—
327	C₂×D₄×C₁₉	—	2	2	no	—
328	C₂×D₄×C₁₉	—	4	2	no	—
329	C₂×D₄×C₁₉	—	4	2	no	—
330	C₂×D₄×C₁₉	—	4	2	no	—
331	C₂×D₄×C₁₉	—	4	2	no	—
332	C₂×D₄×C₁₉	—	8	4	no	—
333	C₂×D₄×C₁₉	—	8	4	no	—
334	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
342	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
343	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₁₉	—	2	2	no	—
345	C₂²×C₄×C₁₉	—	2	2	no	—
346	C₂²×C₄×C₁₉	—	2	2	no	—
347	C₂²×C₄×C₁₉	—	2	2	no	—
348	C₂²×C₄×C₁₉	—	2	2	no	—
349	C₂²×C₄×C₁₉	—	2	2	no	—
350	C₂²×C₄×C₁₉	—	2	2	no	—
351	C₂²×C₄×C₁₉	—	4	1	no	—
352	C₂²×C₄×C₁₉	—	4	1	no	—
353	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₁₉	—	2	2	no	—
362	SD₁₆×C₁₉	—	4	2	no	—
363	SD₁₆×C₁₉	—	4	2	no	—
364	SD₁₆×C₁₉	—	4	2	no	—
365	D₈×C₁₉	—	2	2	no	—
366	D₈×C₁₉	—	2	2	no	—
367	D₈×C₁₉	—	2	2	no	—
368	D₈×C₁₉	—	4	2	no	—
369	D₈×C₁₉	—	4	2	no	—
370	D₈×C₁₉	—	4	2	no	—
371	M₁₆×C₁₉	—	4	1	no	—
372	M₁₆×C₁₉	—	4	1	no	—
373	M₁₆×C₁₉	—	4	1	no	—
374	M₁₆×C₁₉	—	4	1	no	—
375	C₂×C₈×C₁₉	—	2	2	no	—
376	C₂×C₈×C₁₉	—	2	2	no	—
377	C₂×C₈×C₁₉	—	2	2	no	—
378	C₂×C₈×C₁₉	—	2	2	no	—
379	C₂×C₈×C₁₉	—	2	2	no	—
380	C₂×C₈×C₁₉	—	4	1	no	—
381	C₂×C₈×C₁₉	—	4	1	no	—
382	C₂×C₈×C₁₉	—	4	1	no	—
383	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
398	C₄⋊C₄×C₁₉	—	2	2	no	—
399	C₄⋊C₄×C₁₉	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
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	—	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	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	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
435	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
438	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₁₉	—	2	2	no	—
440	C₄²×C₁₉	—	2	2	no	—
441	C₄²×C₁₉	—	2	2	no	—
442	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
443	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
444	#62266	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂³×C₁₉	—	2	2	no	—
446	C₂³×C₁₉	—	2	2	no	—
447	C₂³×C₁₉	—	2	2	no	—
448	C₂³×C₁₉	—	2	2	no	—
449	C₂³×C₁₉	—	4	1	no	—
450	C₂³×C₁₉	—	4	1	no	—
451	C₂³×C₁₉	—	4	4	no	—
452	C₂³×C₁₉	—	8	2	no	—
453	C₂³×C₁₉	—	8	2	no	—
454	C₂³×C₁₉	—	8	2	no	—
455	C₂³×C₁₉	—	8	2	no	—
456	C₂³×C₁₉	—	8	2	no	—
457	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₁₉	—	2	2	no	—
463	Q₈×C₁₉	—	2	2	no	—
464	Q₈×C₁₉	—	4	1	no	—
465	Q₈×C₁₉	—	8	2	no	—
466	D₄×C₁₉	—	2	2	no	—
467	D₄×C₁₉	—	2	2	no	—
468	D₄×C₁₉	—	2	2	no	—
469	D₄×C₁₉	—	2	2	no	—
470	D₄×C₁₉	—	2	2	no	—
471	D₄×C₁₉	—	2	2	no	—
472	D₄×C₁₉	—	2	2	no	—
473	D₄×C₁₉	—	2	2	no	—
474	D₄×C₁₉	—	4	1	no	—
475	D₄×C₁₉	—	4	1	no	—
476	D₄×C₁₉	—	4	1	no	—
477	D₄×C₁₉	—	4	1	no	—
478	D₄×C₁₉	—	4	1	no	—
479	D₄×C₁₉	—	4	4	no	—
480	D₄×C₁₉	—	8	2	no	—
481	D₄×C₁₉	—	8	2	no	—
482	D₄×C₁₉	—	8	2	no	—
483	D₄×C₁₉	—	8	2	no	—
484	D₄×C₁₉	—	8	2	no	—
485	D₄×C₁₉	—	8	2	no	—
486	D₄×C₁₉	—	8	2	no	—
487	D₄×C₁₉	—	8	2	no	—
488	D₄×C₁₉	—	8	2	no	—
489	D₄×C₁₉	—	8	2	no	—
490	D₄×C₁₉	—	8	2	no	—
491	D₄×C₁₉	—	8	2	no	—
492	D₄×C₁₉	—	8	2	no	—
493	D₄×C₁₉	—	8	2	no	—
494	C₂×C₄×C₁₉	—	2	1	no	—
495	C₂×C₄×C₁₉	—	2	1	no	—
496	C₂×C₄×C₁₉	—	2	1	no	—
497	C₂×C₄×C₁₉	—	2	1	no	—
498	C₂×C₄×C₁₉	—	2	1	no	—
499	C₂×C₄×C₁₉	—	2	1	no	—
500	C₂×C₄×C₁₉	—	2	1	no	—
501	C₂×C₄×C₁₉	—	2	1	no	—
502	C₂×C₄×C₁₉	—	2	1	no	—
503	C₂×C₄×C₁₉	—	2	1	no	—
504	C₂×C₄×C₁₉	—	2	2	no	—
505	C₂×C₄×C₁₉	—	2	2	no	—
506	C₂×C₄×C₁₉	—	2	2	no	—
507	C₂×C₄×C₁₉	—	2	2	no	—
508	C₂×C₄×C₁₉	—	2	2	no	—
509	C₂×C₄×C₁₉	—	4	1	no	—
510	C₂×C₄×C₁₉	—	4	1	no	—
511	C₂×C₄×C₁₉	—	4	1	no	—
512	C₂×C₄×C₁₉	—	4	4	no	—
513	C₂×C₄×C₁₉	—	8	2	no	—
514	C₂×C₄×C₁₉	—	8	2	no	—
515	C₂×C₄×C₁₉	—	8	2	no	—
516	C₂×C₄×C₁₉	—	8	2	no	—
517	C₂×C₄×C₁₉	—	8	2	no	—
518	C₂×C₄×C₁₉	—	8	2	no	—
519	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
526	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
529	C₈×C₁₉	—	2	1	no	—
530	C₈×C₁₉	—	2	1	no	—
531	C₈×C₁₉	—	2	1	no	—
532	C₈×C₁₉	—	2	1	no	—
533	C₈×C₁₉	—	2	1	no	—
534	C₈×C₁₉	—	2	1	no	—
535	C₈×C₁₉	—	2	1	no	—
536	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
537	#3542	C₂×C₁₉	1	2	yes	complemented
538	#3341	C₂×C₁₉	1	1	yes	characteristic, complemented
539	#3339	C₂×C₁₉	1	1	yes	characteristic, complemented
540	#3336	C₂×C₁₉	1	1	yes	characteristic, complemented
541	#3334	C₂×C₁₉	1	1	yes	characteristic, complemented
542	#3319	C₂×C₁₉	1	2	yes	complemented
543	#3310	C₂×C₁₉	1	2	yes	complemented
544	#3309	C₂×C₁₉	1	2	yes	complemented
545	#3306	C₂×C₁₉	1	2	yes	complemented
546	#3287	C₂×C₁₉	1	1	yes	characteristic, complemented
547	#3280	C₂×C₁₉	1	1	yes	characteristic, complemented
548	#3280	C₂×C₁₉	1	1	yes	characteristic, complemented
549	D₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
550	#3257	C₂×C₁₉	1	2	yes	complemented
551	#3198	C₂×C₁₉	1	2	yes	complemented
552	#3194	C₂×C₁₉	1	2	yes	complemented
553	#3176	C₂×C₁₉	1	1	yes	characteristic, complemented
554	#3175	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3061	C₂×C₁₉	1	1	yes	characteristic, complemented
556	#3058	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#3050	C₂×C₁₉	1	1	yes	characteristic, complemented
558	C₂×#466	C₂×C₁₉	1	1	yes	characteristic, complemented
559	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
560	C₂²×C₁₉	—	2	1	no	—
561	C₂²×C₁₉	—	2	1	no	—
562	C₂²×C₁₉	—	2	1	no	—
563	C₂²×C₁₉	—	2	1	no	—
564	C₂²×C₁₉	—	2	1	no	—
565	C₂²×C₁₉	—	2	1	no	—
566	C₂²×C₁₉	—	2	1	no	—
567	C₂²×C₁₉	—	2	1	no	—
568	C₂²×C₁₉	—	2	1	no	—
569	C₂²×C₁₉	—	2	1	no	—
570	C₂²×C₁₉	—	2	1	no	—
571	C₂²×C₁₉	—	2	1	no	—
572	C₂²×C₁₉	—	2	1	no	—
573	C₂²×C₁₉	—	2	1	no	—
574	C₂²×C₁₉	—	4	4	no	—
575	C₂²×C₁₉	—	4	2	no	—
576	C₂²×C₁₉	—	4	2	no	—
577	C₂²×C₁₉	—	4	2	no	—
578	C₂²×C₁₉	—	4	2	no	—
579	C₂²×C₁₉	—	4	2	no	—
580	C₂²×C₁₉	—	4	2	no	—
581	C₂²×C₁₉	—	4	2	no	—
582	C₂²×C₁₉	—	4	2	no	—
583	C₂²×C₁₉	—	4	2	no	—
584	C₂²×C₁₉	—	16	4	no	—
585	C₂²×C₁₉	—	16	4	no	—
586	C₂²×C₁₉	#576	1	2	yes	—
587	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₁₉	—	2	1	no	—
589	C₄×C₁₉	—	2	1	no	—
590	C₄×C₁₉	—	2	1	no	—
591	C₄×C₁₉	—	2	1	no	—
592	C₄×C₁₉	—	2	1	no	—
593	C₄×C₁₉	—	2	1	no	—
594	C₄×C₁₉	—	2	1	no	—
595	C₄×C₁₉	—	2	1	no	—
596	C₄×C₁₉	—	2	1	no	—
597	C₄×C₁₉	—	4	2	no	—
598	C₄×C₁₉	—	4	2	no	—
599	C₄×C₁₉	—	4	2	no	—
600	C₄×C₁₉	—	4	2	no	—
601	C₄×C₁₉	—	4	2	no	—
602	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	C₄×C₁₉	#585	1	1	yes	characteristic
604	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic, complemented
605	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic, complemented
606	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
607	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
608	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
609	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
610	#562	—	2	2	no	—
611	#560	—	2	2	no	—
612	#555	C₂²×C₁₉	1	2	yes	complemented
613	#553	C₂²×C₁₉	1	2	yes	complemented
614	#552	C₂²×C₁₉	1	2	yes	—
615	#551	—	2	2	no	—
616	#550	C₂²×C₁₉	1	2	yes	complemented
617	#547	C₂²×C₁₉	1	2	yes	complemented
618	#546	—	2	2	no	—
619	#546	C₂²×C₁₉	1	2	yes	complemented
620	#546	C₂²×C₁₉	1	2	yes	complemented
621	D₄²	C₂²×C₁₉	1	2	yes	—
622	#542	C₂²×C₁₉	1	2	yes	complemented
623	#540	—	2	2	no	—
624	#540	C₂²×C₁₉	1	2	yes	complemented
625	#538	—	2	2	no	—
626	#537	C₂²×C₁₉	1	2	yes	complemented
627	#535	—	2	2	no	—
628	#535	C₂²×C₁₉	1	2	yes	complemented
629	#534	—	2	2	no	—
630	#525	C₂²×C₁₉	1	1	yes	characteristic
631	#525	C₂²×C₁₉	1	2	yes	complemented
632	C₂×#121	C₂²×C₁₉	1	2	yes	complemented
633	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
634	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
635	#495	C₂²×C₁₉	1	1	yes	characteristic, complemented
636	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
637	#490	C₂²×C₁₉	1	2	yes	complemented
638	#489	C₂²×C₁₉	1	2	yes	complemented
639	#485	C₂²×C₁₉	1	2	yes	complemented
640	#483	C₂²×C₁₉	1	2	yes	complemented
641	#482	C₂²×C₁₉	1	2	yes	complemented
642	#482	C₂²×C₁₉	1	2	yes	complemented
643	#482	C₂²×C₁₉	1	2	yes	complemented
644	#481	C₂²×C₁₉	1	2	yes	complemented
645	#480	C₂²×C₁₉	1	2	yes	complemented
646	#480	C₂²×C₁₉	1	2	yes	complemented
647	#479	C₂²×C₁₉	1	2	yes	complemented
648	#478	C₂²×C₁₉	1	2	yes	complemented
649	#476	C₂²×C₁₉	1	2	yes	complemented
650	#474	C₂²×C₁₉	1	2	yes	complemented
651	#469	C₂²×C₁₉	1	2	yes	complemented
652	#469	C₂²×C₁₉	1	2	yes	complemented
653	#469	C₂²×C₁₉	1	2	yes	complemented
654	#468	C₂²×C₁₉	1	2	yes	complemented
655	#468	C₂²×C₁₉	1	2	yes	complemented
656	#468	C₂²×C₁₉	1	2	yes	complemented
657	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
658	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
659	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
660	#466	C₂²×C₁₉	1	1	yes	characteristic
661	#466	C₂²×C₁₉	1	1	yes	characteristic
662	#466	C₂²×C₁₉	1	1	yes	characteristic
663	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
664	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
669	#466	C₂²×C₁₉	1	2	yes	complemented
670	#466	C₂²×C₁₉	1	2	yes	complemented
671	#465	C₂²×C₁₉	1	2	yes	complemented
672	#465	C₂²×C₁₉	1	2	yes	complemented
673	#463	C₂²×C₁₉	1	2	yes	complemented
674	#463	C₂²×C₁₉	1	2	yes	complemented
675	#460	C₂²×C₁₉	1	2	yes	complemented
676	#459	C₂²×C₁₉	1	2	yes	complemented
677	#450	C₂²×C₁₉	1	2	yes	complemented
678	#450	C₂²×C₁₉	1	2	yes	complemented
679	#449	C₂²×C₁₉	1	2	yes	complemented
680	#449	C₂²×C₁₉	1	2	yes	complemented
681	#449	C₂²×C₁₉	1	2	yes	complemented
682	#449	C₂²×C₁₉	1	2	yes	complemented
683	#447	C₂²×C₁₉	1	2	yes	—
684	#447	C₂²×C₁₉	1	2	yes	complemented
685	#442	C₂²×C₁₉	1	2	yes	complemented
686	#440	C₂²×C₁₉	1	2	yes	complemented
687	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
688	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
689	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
690	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
691	#435	C₂²×C₁₉	1	1	yes	characteristic
692	#435	C₂²×C₁₉	1	1	yes	characteristic, complemented
693	#435	C₂²×C₁₉	1	1	yes	characteristic, complemented
694	#435	C₂²×C₁₉	1	1	yes	characteristic, complemented
695	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
696	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
697	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
698	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
699	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
700	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
701	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
702	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
703	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
704	#418	C₂²×C₁₉	1	2	yes	complemented
705	#417	C₂²×C₁₉	1	2	yes	complemented
706	#416	C₂²×C₁₉	1	2	yes	complemented
707	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
708	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
709	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
710	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
711	C₂×C₁₉	—	2	2	no	—
712	C₂×C₁₉	—	4	1	no	—
713	C₂×C₁₉	—	4	1	no	—
714	C₂×C₁₉	—	4	1	no	—
715	C₂×C₁₉	—	4	1	no	—
716	C₂×C₁₉	—	8	2	no	—
717	C₂×C₁₉	—	8	2	no	—
718	C₂×C₁₉	—	8	2	no	—
719	C₂×C₁₉	#3496	1	1	yes	characteristic
720	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
721	C₂×C₁₉	#3584	1	1	yes	characteristic
722	C₂×#41	—	2	2	no	—
723	C₂×#41	C₂³×C₁₉	1	2	yes	—
724	C₂×#41	C₂³×C₁₉	1	2	yes	—
725	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	—	2	2	no	—
728	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
729	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
730	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
731	#135	—	4	2	no	—
732	#135	—	4	2	no	—
733	C₂×Q₁₆	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×D₈	—	4	2	no	—
738	C₂×D₈	—	4	2	no	—
739	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
741	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
742	C₂×D₈	C₂³×C₁₉	1	2	yes	—
743	C₂×D₈	C₂³×C₁₉	1	2	yes	—
744	C₂×D₈	C₂³×C₁₉	1	2	yes	—
745	#131	—	4	2	no	—
746	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
749	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
750	C₂²×C₈	—	4	2	no	—
751	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
753	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
754	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
757	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
758	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
760	#127	—	2	2	no	—
761	#127	—	2	2	no	—
762	#127	C₂³×C₁₉	1	2	yes	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	C₂³×C₁₉	1	2	yes	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	C₂³×C₁₉	1	2	yes	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	D₄×C₁₉	1	1	yes	characteristic
784	#123	D₄×C₁₉	1	1	yes	characteristic
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
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	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	D₄×C₁₉	1	1	yes	characteristic
808	#121	D₄×C₁₉	1	1	yes	characteristic
809	#121	C₂³×C₁₉	1	2	yes	—
810	#121	C₂³×C₁₉	1	2	yes	—
811	#121	C₂³×C₁₉	1	2	yes	—
812	#121	C₂³×C₁₉	1	2	yes	—
813	#121	C₂³×C₁₉	1	2	yes	—
814	#121	C₂³×C₁₉	1	2	yes	—
815	#121	C₂³×C₁₉	1	2	yes	—
816	#121	C₂³×C₁₉	1	2	yes	—
817	#121	C₂³×C₁₉	1	2	yes	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	D₄×C₁₉	1	1	yes	characteristic
826	#120	D₄×C₁₉	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	C₂³×C₁₉	1	2	yes	—
833	C₄×D₄	C₂³×C₁₉	1	2	yes	—
834	C₄×D₄	C₂³×C₁₉	1	2	yes	—
835	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
839	#117	—	2	2	no	—
840	#117	—	2	2	no	—
841	#117	C₂³×C₁₉	1	2	yes	—
842	#117	C₂³×C₁₉	1	2	yes	—
843	#117	C₂³×C₁₉	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
845	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	#107	C₂³×C₁₉	1	1	yes	characteristic
850	#107	C₂³×C₁₉	1	1	yes	characteristic
851	#107	C₂³×C₁₉	1	1	yes	characteristic
852	#107	C₂³×C₁₉	1	2	yes	—
853	#107	C₂³×C₁₉	1	2	yes	—
854	#107	C₂³×C₁₉	1	1	yes	characteristic
855	#107	C₂³×C₁₉	1	2	yes	—
856	#106	C₂³×C₁₉	1	2	yes	—
857	#106	C₂³×C₁₉	1	2	yes	—
858	#106	C₂³×C₁₉	1	2	yes	—
859	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
863	#103	C₂³×C₁₉	1	2	yes	—
864	#103	C₂³×C₁₉	1	2	yes	—
865	#103	C₂³×C₁₉	1	2	yes	—
866	#103	C₂³×C₁₉	1	2	yes	—
867	#102	C₂³×C₁₉	1	2	yes	—
868	#102	C₂³×C₁₉	1	2	yes	—
869	#102	C₂³×C₁₉	1	2	yes	—
870	#102	C₂³×C₁₉	1	2	yes	—
871	#102	C₂³×C₁₉	1	2	yes	—
872	#102	C₂³×C₁₉	1	2	yes	—
873	#102	C₂³×C₁₉	1	2	yes	—
874	#102	C₂³×C₁₉	1	2	yes	—
875	#102	C₂³×C₁₉	1	2	yes	—
876	#102	C₂³×C₁₉	1	2	yes	—
877	#102	C₂³×C₁₉	1	2	yes	—
878	#102	C₂³×C₁₉	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
887	#97	C₂³×C₁₉	1	1	yes	characteristic
888	#97	C₂³×C₁₉	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
891	C₁₉	#62266	1	1	yes	characteristic, direct product factor, Sylow
892	C₂⁴	—	2	2	no	—
893	C₂⁴	—	2	2	no	—
894	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
895	#41	—	4	1	no	—
896	#41	—	4	1	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	8	4	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	8	4	no	—
925	C₂×D₄	—	8	4	no	—
926	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
927	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
928	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
929	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
934	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
935	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	4	1	no	—
944	C₂²×C₄	—	4	1	no	—
945	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
947	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
953	Q₁₆	—	2	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	2	2	no	—
958	D₈	—	2	2	no	—
959	D₈	—	2	2	no	—
960	D₈	—	4	2	no	—
961	D₈	—	4	2	no	—
962	D₈	—	4	2	no	—
963	M₁₆	—	4	1	no	—
964	M₁₆	—	4	1	no	—
965	M₁₆	—	4	1	no	—
966	M₁₆	—	4	1	no	—
967	C₂×C₈	—	2	2	no	—
968	C₂×C₈	—	2	2	no	—
969	C₂×C₈	—	2	2	no	—
970	C₂×C₈	—	2	2	no	—
971	C₂×C₈	—	2	2	no	—
972	C₂×C₈	—	4	1	no	—
973	C₂×C₈	—	4	1	no	—
974	C₂×C₈	—	4	1	no	—
975	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
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	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
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	2	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	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1022	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1023	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1025	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1026	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1027	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1028	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1029	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1030	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	4	4	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	2	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1049	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1050	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1051	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1052	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	4	1	no	—
1056	Q₈	—	8	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	4	1	no	—
1066	D₄	—	4	1	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	1	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	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	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	4	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1119	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1120	C₈	—	2	1	no	—
1121	C₈	—	2	1	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	4	4	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	16	4	no	—
1153	C₂²	—	16	4	no	—
1154	C₂²	C₁₉×#576	1	2	yes	—
1155	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	2	no	—
1170	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1171	C₄	C₁₉×#585	1	1	yes	characteristic
1172	C₂	—	2	2	no	—
1173	C₂	—	4	1	no	—
1174	C₂	—	4	1	no	—
1175	C₂	—	4	1	no	—
1176	C₂	—	4	1	no	—
1177	C₂	—	8	2	no	—
1178	C₂	—	8	2	no	—
1179	C₂	—	8	2	no	—
1180	C₂	C₁₉×#3496	1	1	yes	characteristic
1181	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
1182	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×#3542	C₂	semidirect
2. C₁₉×#3341	C₂	semidirect
3. C₁₉×#3339	C₂	semidirect
4. C₁₉×#3336	C₂	semidirect
5. C₁₉×#3334	C₂	semidirect
6. C₁₉×#3319	C₂	semidirect
7. C₁₉×#3310	C₂	semidirect
8. C₁₉×#3309	C₂	semidirect
9. C₁₉×#3306	C₂	semidirect
10. C₁₉×#3287	C₂	semidirect
11. C₁₉×#3280	C₂	semidirect
12. C₁₉×#3280	C₂	semidirect
13. D₄×D₈×C₁₉	C₂	semidirect
14. C₁₉×#3257	C₂	semidirect
15. C₁₉×#3198	C₂	semidirect
16. C₁₉×#3194	C₂	semidirect
17. C₁₉×#3176	C₂	semidirect
18. C₁₉×#3175	C₂	semidirect
19. C₁₉×#3061	C₂	semidirect
20. C₁₉×#3058	C₂	semidirect
21. C₁₉×#3050	C₂	semidirect
22. C₂×C₁₉×#466	C₂	semidirect
23. C₁₉×#2929	C₂	semidirect
24. C₂×C₁₉×#135	C₂²	semidirect
25. C₂×C₁₉×#135	C₂²	semidirect
27. C₂²×D₈×C₁₉	C₂²	semidirect
28. C₂×C₁₉×#131	C₂²	semidirect
29. C₂³×C₈×C₁₉	C₂²	semidirect
32. C₁₉×#555	C₂²	semidirect
33. C₁₉×#553	C₂²	semidirect
36. C₁₉×#550	C₂²	semidirect
37. C₁₉×#547	C₂²	semidirect
39. C₁₉×#546	C₂²	semidirect
40. C₁₉×#546	C₂²	semidirect
42. C₁₉×#542	C₂²	semidirect
44. C₁₉×#540	C₂²	semidirect
46. C₁₉×#537	C₂²	semidirect
48. C₁₉×#535	C₂²	semidirect
51. C₁₉×#525	C₂²	semidirect
52. C₂×C₁₉×#121	C₂²	semidirect
53. C₁₉×#500	C₂²	semidirect
54. C₁₉×#499	C₂²	semidirect
55. C₁₉×#495	C₂²	semidirect
56. C₁₉×#493	C₂²	semidirect
57. C₁₉×#490	C₂²	semidirect
58. C₁₉×#489	C₂²	semidirect
59. C₁₉×#485	C₂²	semidirect
60. C₁₉×#483	C₂²	semidirect
61. C₁₉×#482	C₂²	semidirect
62. C₁₉×#482	C₂²	semidirect
63. C₁₉×#482	C₂²	semidirect
64. C₁₉×#481	C₂²	semidirect
65. C₁₉×#480	C₂²	semidirect
66. C₁₉×#480	C₂²	semidirect
67. C₁₉×#479	C₂²	semidirect
68. C₁₉×#478	C₂²	semidirect
69. C₁₉×#476	C₂²	semidirect
70. C₁₉×#474	C₂²	semidirect
71. C₁₉×#469	C₂²	semidirect
72. C₁₉×#469	C₂²	semidirect
73. C₁₉×#469	C₂²	semidirect
74. C₁₉×#468	C₂²	semidirect
75. C₁₉×#468	C₂²	semidirect
76. C₁₉×#468	C₂²	semidirect
77. C₁₉×#467	C₂²	semidirect
78. C₁₉×#467	C₂²	semidirect
79. C₁₉×#467	C₂²	semidirect
83. C₁₉×#466	C₂²	semidirect
84. C₁₉×#466	C₂²	semidirect
85. C₁₉×#466	C₂²	semidirect
86. C₁₉×#466	C₂²	semidirect
87. C₁₉×#466	C₂²	semidirect
88. C₁₉×#466	C₂²	semidirect
89. C₁₉×#466	C₂²	semidirect
90. C₁₉×#466	C₂²	semidirect
91. C₁₉×#465	C₂²	semidirect
92. C₁₉×#465	C₂²	semidirect
93. C₁₉×#463	C₂²	semidirect
94. C₁₉×#463	C₂²	semidirect
95. C₁₉×#460	C₂²	semidirect
96. C₁₉×#459	C₂²	semidirect
97. C₁₉×#450	C₂²	semidirect
98. C₁₉×#450	C₂²	semidirect
99. C₁₉×#449	C₂²	semidirect
100. C₁₉×#449	C₂²	semidirect
101. C₁₉×#449	C₂²	semidirect
102. C₁₉×#449	C₂²	semidirect
104. C₁₉×#447	C₂²	semidirect
105. C₁₉×#442	C₂²	semidirect
106. C₁₉×#440	C₂²	semidirect
107. C₄×Q₁₆×C₁₉	C₂²	semidirect
108. C₄×D₈×C₁₉	C₂²	semidirect
109. C₄×D₈×C₁₉	C₂²	semidirect
110. C₄×D₈×C₁₉	C₂²	semidirect
112. C₁₉×#435	C₂²	semidirect
113. C₁₉×#435	C₂²	semidirect
114. C₁₉×#435	C₂²	semidirect
116. C₈×D₄×C₁₉	C₂²	semidirect
117. C₈×D₄×C₁₉	C₂²	semidirect
118. C₈×D₄×C₁₉	C₂²	semidirect
119. C₁₉×#427	C₂²	semidirect
120. C₁₉×#427	C₂²	semidirect
121. C₂×C₁₉×#107	C₂²	semidirect
122. C₂×C₁₉×#107	C₂²	semidirect
123. C₁₉×#424	C₂²	semidirect
124. C₁₉×#418	C₂²	semidirect
125. C₁₉×#417	C₂²	semidirect
126. C₁₉×#416	C₂²	semidirect
127. C₂×C₁₉×#102	C₂²	semidirect
128. C₁₉×#408	C₂²	semidirect
129. C₁₉×#407	C₂²	semidirect
130. C₁₉×#405	C₂²	semidirect
444. #62266	C₁₉	direct (N × H)
537. #3542	C₂×C₁₉	semidirect
538. #3341	C₂×C₁₉	semidirect
539. #3339	C₂×C₁₉	semidirect
540. #3336	C₂×C₁₉	semidirect
541. #3334	C₂×C₁₉	semidirect
542. #3319	C₂×C₁₉	semidirect
543. #3310	C₂×C₁₉	semidirect
544. #3309	C₂×C₁₉	semidirect
545. #3306	C₂×C₁₉	semidirect
546. #3287	C₂×C₁₉	semidirect
547. #3280	C₂×C₁₉	semidirect
548. #3280	C₂×C₁₉	semidirect
549. D₄×D₈	C₂×C₁₉	semidirect
550. #3257	C₂×C₁₉	semidirect
551. #3198	C₂×C₁₉	semidirect
552. #3194	C₂×C₁₉	semidirect
553. #3176	C₂×C₁₉	semidirect
554. #3175	C₂×C₁₉	semidirect
555. #3061	C₂×C₁₉	semidirect
556. #3058	C₂×C₁₉	semidirect
557. #3050	C₂×C₁₉	semidirect
558. C₂×#466	C₂×C₁₉	semidirect
559. #2929	C₂×C₁₉	semidirect
604. C₂×#135	C₂²×C₁₉	semidirect
605. C₂×#135	C₂²×C₁₉	semidirect
607. C₂²×D₈	C₂²×C₁₉	semidirect
608. C₂×#131	C₂²×C₁₉	semidirect
609. C₂³×C₈	C₂²×C₁₉	semidirect
612. #555	C₂²×C₁₉	semidirect
613. #553	C₂²×C₁₉	semidirect
616. #550	C₂²×C₁₉	semidirect
617. #547	C₂²×C₁₉	semidirect
619. #546	C₂²×C₁₉	semidirect
620. #546	C₂²×C₁₉	semidirect
622. #542	C₂²×C₁₉	semidirect
624. #540	C₂²×C₁₉	semidirect
626. #537	C₂²×C₁₉	semidirect
628. #535	C₂²×C₁₉	semidirect
631. #525	C₂²×C₁₉	semidirect
632. C₂×#121	C₂²×C₁₉	semidirect
633. #500	C₂²×C₁₉	semidirect
634. #499	C₂²×C₁₉	semidirect
635. #495	C₂²×C₁₉	semidirect
636. #493	C₂²×C₁₉	semidirect
637. #490	C₂²×C₁₉	semidirect
638. #489	C₂²×C₁₉	semidirect
639. #485	C₂²×C₁₉	semidirect
640. #483	C₂²×C₁₉	semidirect
641. #482	C₂²×C₁₉	semidirect
642. #482	C₂²×C₁₉	semidirect
643. #482	C₂²×C₁₉	semidirect
644. #481	C₂²×C₁₉	semidirect
645. #480	C₂²×C₁₉	semidirect
646. #480	C₂²×C₁₉	semidirect
647. #479	C₂²×C₁₉	semidirect
648. #478	C₂²×C₁₉	semidirect
649. #476	C₂²×C₁₉	semidirect
650. #474	C₂²×C₁₉	semidirect
651. #469	C₂²×C₁₉	semidirect
652. #469	C₂²×C₁₉	semidirect
653. #469	C₂²×C₁₉	semidirect
654. #468	C₂²×C₁₉	semidirect
655. #468	C₂²×C₁₉	semidirect
656. #468	C₂²×C₁₉	semidirect
657. #467	C₂²×C₁₉	semidirect
658. #467	C₂²×C₁₉	semidirect
659. #467	C₂²×C₁₉	semidirect
663. #466	C₂²×C₁₉	semidirect
664. #466	C₂²×C₁₉	semidirect
665. #466	C₂²×C₁₉	semidirect
666. #466	C₂²×C₁₉	semidirect
667. #466	C₂²×C₁₉	semidirect
668. #466	C₂²×C₁₉	semidirect
669. #466	C₂²×C₁₉	semidirect
670. #466	C₂²×C₁₉	semidirect
671. #465	C₂²×C₁₉	semidirect
672. #465	C₂²×C₁₉	semidirect
673. #463	C₂²×C₁₉	semidirect
674. #463	C₂²×C₁₉	semidirect
675. #460	C₂²×C₁₉	semidirect
676. #459	C₂²×C₁₉	semidirect
677. #450	C₂²×C₁₉	semidirect
678. #450	C₂²×C₁₉	semidirect
679. #449	C₂²×C₁₉	semidirect
680. #449	C₂²×C₁₉	semidirect
681. #449	C₂²×C₁₉	semidirect
682. #449	C₂²×C₁₉	semidirect
684. #447	C₂²×C₁₉	semidirect
685. #442	C₂²×C₁₉	semidirect
686. #440	C₂²×C₁₉	semidirect
687. C₄×Q₁₆	C₂²×C₁₉	semidirect
688. C₄×D₈	C₂²×C₁₉	semidirect
689. C₄×D₈	C₂²×C₁₉	semidirect
690. C₄×D₈	C₂²×C₁₉	semidirect
692. #435	C₂²×C₁₉	semidirect
693. #435	C₂²×C₁₉	semidirect
694. #435	C₂²×C₁₉	semidirect
696. C₈×D₄	C₂²×C₁₉	semidirect
697. C₈×D₄	C₂²×C₁₉	semidirect
698. C₈×D₄	C₂²×C₁₉	semidirect
699. #427	C₂²×C₁₉	semidirect
700. #427	C₂²×C₁₉	semidirect
701. C₂×#107	C₂²×C₁₉	semidirect
702. C₂×#107	C₂²×C₁₉	semidirect
703. #424	C₂²×C₁₉	semidirect
704. #418	C₂²×C₁₉	semidirect
705. #417	C₂²×C₁₉	semidirect
706. #416	C₂²×C₁₉	semidirect
707. C₂×#102	C₂²×C₁₉	semidirect
708. #408	C₂²×C₁₉	semidirect
709. #407	C₂²×C₁₉	semidirect
710. #405	C₂²×C₁₉	semidirect
891. C₁₉	#62266	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×#3542	2
C₁₉×#3341	2
C₁₉×#3339	2
C₁₉×#3336	2
C₁₉×#3334	2
C₁₉×#3319	2
C₁₉×#3310	2
C₁₉×#3309	2
C₁₉×#3306	2
C₁₉×#3287	2
C₁₉×#3280	2
D₄×D₈×C₁₉	2
C₁₉×#3257	2
C₁₉×#3198	2
C₁₉×#3194	2
C₁₉×#3176	2
C₁₉×#3175	2
C₁₉×#3061	2
C₁₉×#3058	2
C₁₉×#3050	2
C₂×C₁₉×#466	2
C₁₉×#2929	2
#62266	19

Subgroups — C19×#62266 #18068225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62266 #18068225