Subgroups — C₁₉×#62041 #18068000

Order 4864.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1204 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, complemented
2	C₁₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3333	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3314	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3273	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3268	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3262	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3224	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3124	C₂	1	2	yes	maximal, complemented
20	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₉×#3045	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
27	C₁₉×#560	—	2	2	no	—
28	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#554	C₂²	1	2	yes	complemented
31	C₁₉×#553	—	2	1	no	—
32	C₁₉×#552	—	2	1	no	—
33	C₁₉×#551	—	2	2	no	—
34	C₁₉×#550	C₂²	1	2	yes	—
35	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#548	—	2	1	no	—
38	C₁₉×#547	C₂²	1	1	yes	characteristic
39	C₁₉×#547	C₂²	1	1	yes	characteristic
40	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#546	—	2	1	no	—
42	C₁₉×#546	C₂²	1	2	yes	—
43	C₁₉×#546	C₂²	1	2	yes	complemented
44	D₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#542	C₂²	1	2	yes	complemented
46	C₁₉×#542	C₂²	1	2	yes	complemented
47	C₁₉×#539	—	2	2	no	—
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	complemented
52	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#532	C₂²	1	1	yes	characteristic
54	C₁₉×#532	C₂²	1	1	yes	characteristic
55	C₁₉×#529	C₂²	1	1	yes	characteristic
56	C₁₉×#525	—	2	1	no	—
57	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
58	C₁₉×#520	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#496	C₂²	1	2	yes	complemented
61	C₁₉×#495	C₂²	1	2	yes	—
62	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#489	C₂²	1	2	yes	complemented
65	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#486	C₂²	1	2	yes	complemented
68	C₁₉×#484	C₂²	1	2	yes	complemented
69	C₁₉×#480	C₂²	1	1	yes	characteristic
70	C₁₉×#480	C₂²	1	2	yes	complemented
71	C₁₉×#480	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#477	C₂²	1	2	yes	complemented
73	C₁₉×#477	C₂²	1	2	yes	complemented
74	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
75	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#474	C₂²	1	2	yes	complemented
78	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#468	C₂²	1	2	yes	—
80	C₁₉×#468	C₂²	1	2	yes	complemented
81	C₁₉×#468	C₂²	1	2	yes	complemented
82	C₁₉×#468	C₂²	1	2	yes	complemented
83	C₁₉×#467	C₂²	1	2	yes	complemented
84	C₁₉×#466	C₂²	1	2	yes	—
85	C₁₉×#464	C₂²	1	2	yes	complemented
86	C₁₉×#464	C₂²	1	2	yes	complemented
87	C₁₉×#464	C₂²	1	2	yes	complemented
88	C₁₉×#464	C₂²	1	2	yes	complemented
89	C₁₉×#463	C₂²	1	2	yes	—
90	C₁₉×#463	C₂²	1	2	yes	complemented
91	C₁₉×#463	C₂²	1	2	yes	complemented
92	C₁₉×#463	C₂²	1	2	yes	complemented
93	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
94	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
95	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
96	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
97	C₁₉×#460	C₂²	1	2	yes	complemented
98	C₁₉×#460	C₂²	1	2	yes	complemented
99	C₁₉×#459	C₂²	1	1	yes	characteristic
100	C₁₉×#459	C₂²	1	1	yes	characteristic
101	C₁₉×#459	C₂²	1	1	yes	characteristic
102	C₁₉×#459	C₂²	1	1	yes	characteristic
103	C₁₉×#459	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×#450	C₂²	1	2	yes	complemented
109	C₁₉×#449	C₂²	1	2	yes	—
110	C₁₉×#449	C₂²	1	2	yes	complemented
111	C₁₉×#447	C₂²	1	2	yes	—
112	C₁₉×#447	C₂²	1	1	yes	characteristic
113	C₁₉×#447	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×#440	C₂²	1	2	yes	complemented
117	C₁₉×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
119	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
121	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
122	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
124	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
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, complemented
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×#417	C₂²	1	2	yes	complemented
133	C₁₉×#417	C₂²	1	2	yes	complemented
134	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	1	no	—
137	C₂×#41×C₁₉	—	2	1	no	—
138	C₂×#41×C₁₉	C₂³	1	2	yes	—
139	C₂×#41×C₁₉	C₂³	1	2	yes	—
140	C₂×#41×C₁₉	C₂³	1	2	yes	—
141	C₂²×Q₈×C₁₉	—	2	1	no	—
142	C₂²×D₄×C₁₉	—	2	1	no	—
143	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₉	—	2	1	no	—
146	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
147	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
148	C₁₉×#135	—	4	4	no	—
149	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
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	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
157	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₁₉	C₂³	1	2	yes	—
160	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₁₉	C₂³	1	2	yes	—
163	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
164	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
165	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
166	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
180	C₁₉×#125	—	2	2	no	—
181	C₁₉×#125	—	2	1	no	—
182	C₁₉×#125	D₄	1	1	yes	characteristic
183	C₁₉×#124	—	2	2	no	—
184	C₁₉×#124	—	2	2	no	—
185	C₁₉×#124	—	2	1	no	—
186	C₁₉×#124	D₄	1	1	yes	characteristic
187	C₁₉×#124	C₂³	1	2	yes	—
188	C₁₉×#124	C₂³	1	2	yes	—
189	C₁₉×#124	C₂³	1	2	yes	—
190	C₁₉×#123	—	2	2	no	—
191	C₁₉×#123	—	2	2	no	—
192	C₁₉×#123	—	2	2	no	—
193	C₁₉×#123	—	2	2	no	—
194	C₁₉×#123	—	2	2	no	—
195	C₁₉×#123	—	2	2	no	—
196	C₁₉×#123	—	2	2	no	—
197	C₁₉×#123	D₄	1	2	yes	—
198	C₁₉×C₂²⋊Q₈	—	2	1	no	—
199	C₁₉×C₂²⋊Q₈	—	2	1	no	—
200	C₁₉×C₂²⋊Q₈	—	2	1	no	—
201	C₁₉×C₂²⋊Q₈	—	2	2	no	—
202	C₁₉×C₂²⋊Q₈	—	2	1	no	—
203	C₁₉×C₂²⋊Q₈	—	2	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×#121	—	2	1	no	—
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	—	2	2	no	—
226	C₁₉×#121	D₄	1	1	yes	characteristic
227	C₁₉×#121	C₂³	1	2	yes	—
228	C₁₉×#121	C₂³	1	1	yes	characteristic
229	C₁₉×#121	C₂³	1	1	yes	characteristic
230	C₁₉×#121	C₂³	1	2	yes	—
231	C₁₉×#120	—	2	2	no	—
232	C₁₉×#120	—	2	2	no	—
233	C₁₉×#120	—	2	2	no	—
234	C₁₉×#120	—	2	2	no	—
235	C₁₉×#120	—	2	2	no	—
236	C₄×Q₈×C₁₉	—	2	1	no	—
237	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₉	—	2	2	no	—
242	C₄×D₄×C₁₉	—	2	2	no	—
243	C₄×D₄×C₁₉	—	2	2	no	—
244	C₄×D₄×C₁₉	—	2	2	no	—
245	C₄×D₄×C₁₉	—	2	1	no	—
246	C₄×D₄×C₁₉	—	2	1	no	—
247	C₄×D₄×C₁₉	—	2	1	no	—
248	C₄×D₄×C₁₉	—	2	1	no	—
249	C₄×D₄×C₁₉	—	2	1	no	—
250	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₉	C₂³	1	2	yes	—
255	C₄×D₄×C₁₉	C₂³	1	2	yes	—
256	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₉	C₂³	1	2	yes	—
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	—	2	2	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	—	2	1	no	—
264	C₁₉×#117	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
266	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
267	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
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	1	yes	characteristic
276	C₁₉×#107	C₂³	1	1	yes	characteristic
277	C₁₉×#107	C₂³	1	1	yes	characteristic
278	C₁₉×#107	C₂³	1	2	yes	—
279	C₁₉×#107	C₂³	1	2	yes	—
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	2	yes	—
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#102	C₂³	1	1	yes	characteristic
294	C₁₉×#102	C₂³	1	2	yes	—
295	C₁₉×#102	C₂³	1	2	yes	—
296	C₁₉×#102	C₂³	1	2	yes	—
297	C₁₉×#102	C₂³	1	1	yes	characteristic
298	C₁₉×#102	C₂³	1	2	yes	—
299	C₁₉×#102	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	1	yes	characteristic
301	C₁₉×#102	C₂³	1	1	yes	characteristic
302	C₁₉×#102	C₂³	1	1	yes	characteristic
303	C₁₉×#102	C₂³	1	1	yes	characteristic
304	C₁₉×#102	C₂³	1	2	yes	—
305	C₁₉×#102	C₂³	1	1	yes	characteristic
306	C₁₉×#102	C₂³	1	1	yes	characteristic
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	1	no	—
316	C₂⁴×C₁₉	—	2	2	no	—
317	#41×C₁₉	—	2	4	no	—
318	#41×C₁₉	—	4	2	no	—
319	#41×C₁₉	—	4	2	no	—
320	#41×C₁₉	—	4	2	no	—
321	#41×C₁₉	—	4	2	no	—
322	#41×C₁₉	—	4	2	no	—
323	#41×C₁₉	—	8	2	no	—
324	#41×C₁₉	—	8	2	no	—
325	#41×C₁₉	—	8	2	no	—
326	C₂×Q₈×C₁₉	—	2	1	no	—
327	C₂×Q₈×C₁₉	—	2	2	no	—
328	C₂×Q₈×C₁₉	—	2	1	no	—
329	C₂×Q₈×C₁₉	—	8	2	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	2	yes	—
333	C₂×D₄×C₁₉	—	2	2	no	—
334	C₂×D₄×C₁₉	—	2	2	no	—
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	2	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	1	no	—
344	C₂×D₄×C₁₉	—	2	1	no	—
345	C₂×D₄×C₁₉	—	2	2	no	—
346	C₂×D₄×C₁₉	—	2	1	no	—
347	C₂×D₄×C₁₉	—	2	2	no	—
348	C₂×D₄×C₁₉	—	2	2	no	—
349	C₂×D₄×C₁₉	—	4	1	no	—
350	C₂×D₄×C₁₉	—	4	2	no	—
351	C₂×D₄×C₁₉	—	4	2	no	—
352	C₂×D₄×C₁₉	—	8	2	no	—
353	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
358	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₁₉	—	2	1	no	—
361	C₂²×C₄×C₁₉	—	2	2	no	—
362	C₂²×C₄×C₁₉	—	2	2	no	—
363	C₂²×C₄×C₁₉	—	2	1	no	—
364	C₂²×C₄×C₁₉	—	2	1	no	—
365	C₂²×C₄×C₁₉	—	2	1	no	—
366	C₂²×C₄×C₁₉	—	2	1	no	—
367	C₂²×C₄×C₁₉	—	2	2	no	—
368	C₂²×C₄×C₁₉	—	2	2	no	—
369	C₂²×C₄×C₁₉	—	2	2	no	—
370	C₂²×C₄×C₁₉	—	2	1	no	—
371	C₂²×C₄×C₁₉	—	2	2	no	—
372	C₂²×C₄×C₁₉	—	2	1	no	—
373	C₂²×C₄×C₁₉	—	8	2	no	—
374	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
378	Q₁₆×C₁₉	—	4	2	no	—
379	Q₁₆×C₁₉	—	4	2	no	—
380	SD₁₆×C₁₉	—	2	4	no	—
381	SD₁₆×C₁₉	—	4	2	no	—
382	SD₁₆×C₁₉	—	4	2	no	—
383	SD₁₆×C₁₉	—	4	2	no	—
384	SD₁₆×C₁₉	—	4	2	no	—
385	SD₁₆×C₁₉	—	4	2	no	—
386	D₈×C₁₉	—	2	2	no	—
387	D₈×C₁₉	—	2	4	no	—
388	D₈×C₁₉	—	2	2	no	—
389	D₈×C₁₉	—	4	1	no	—
390	D₈×C₁₉	—	4	1	no	—
391	D₈×C₁₉	—	4	2	no	—
392	M₁₆×C₁₉	—	4	2	no	—
393	M₁₆×C₁₉	—	4	2	no	—
394	C₂×C₈×C₁₉	—	4	2	no	—
395	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
397	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
398	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₁₉	—	2	2	no	—
402	C₄⋊C₄×C₁₉	—	2	1	no	—
403	C₄⋊C₄×C₁₉	—	2	1	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	2	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	1	no	—
413	C₄⋊C₄×C₁₉	—	2	2	no	—
414	C₄⋊C₄×C₁₉	—	2	2	no	—
415	C₄⋊C₄×C₁₉	—	2	2	no	—
416	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₁₉	—	2	2	no	—
428	C₂²⋊C₄×C₁₉	—	2	2	no	—
429	C₂²⋊C₄×C₁₉	—	2	2	no	—
430	C₂²⋊C₄×C₁₉	—	2	1	no	—
431	C₂²⋊C₄×C₁₉	—	2	1	no	—
432	C₂²⋊C₄×C₁₉	—	2	1	no	—
433	C₂²⋊C₄×C₁₉	—	2	1	no	—
434	C₂²⋊C₄×C₁₉	—	2	1	no	—
435	C₂²⋊C₄×C₁₉	—	2	2	no	—
436	C₂²⋊C₄×C₁₉	—	2	2	no	—
437	C₂²⋊C₄×C₁₉	—	2	2	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	—	2	2	no	—
444	C₂²⋊C₄×C₁₉	—	2	2	no	—
445	C₂²⋊C₄×C₁₉	—	2	1	no	—
446	C₂²⋊C₄×C₁₉	—	2	2	no	—
447	C₂²⋊C₄×C₁₉	—	2	1	no	—
448	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
453	C₄²×C₁₉	—	2	2	no	—
454	C₄²×C₁₉	—	2	2	no	—
455	C₄²×C₁₉	—	2	2	no	—
456	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
460	C₄²×C₁₉	C₂⁴	1	2	yes	—
461	#62041	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
462	C₂³×C₁₉	—	2	1	no	—
463	C₂³×C₁₉	—	2	1	no	—
464	C₂³×C₁₉	—	2	1	no	—
465	C₂³×C₁₉	—	2	2	no	—
466	C₂³×C₁₉	—	2	1	no	—
467	C₂³×C₁₉	—	4	2	no	—
468	C₂³×C₁₉	—	4	2	no	—
469	C₂³×C₁₉	—	8	1	no	—
470	C₂³×C₁₉	—	8	2	no	—
471	C₂³×C₁₉	—	8	2	no	—
472	C₂³×C₁₉	—	8	2	no	—
473	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
474	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
475	Q₈×C₁₉	—	2	2	no	—
476	Q₈×C₁₉	—	2	2	no	—
477	Q₈×C₁₉	—	2	2	no	—
478	Q₈×C₁₉	—	2	2	no	—
479	Q₈×C₁₉	—	2	2	no	—
480	Q₈×C₁₉	—	4	2	no	—
481	Q₈×C₁₉	—	8	2	no	—
482	Q₈×C₁₉	—	8	1	no	—
483	D₄×C₁₉	—	2	2	no	—
484	D₄×C₁₉	—	2	2	no	—
485	D₄×C₁₉	—	2	1	no	—
486	D₄×C₁₉	—	2	1	no	—
487	D₄×C₁₉	—	2	1	no	—
488	D₄×C₁₉	—	2	1	no	—
489	D₄×C₁₉	—	2	1	no	—
490	D₄×C₁₉	—	2	1	no	—
491	D₄×C₁₉	—	2	1	no	—
492	D₄×C₁₉	—	2	2	no	—
493	D₄×C₁₉	—	4	2	no	—
494	D₄×C₁₉	—	4	2	no	—
495	D₄×C₁₉	—	4	4	no	—
496	D₄×C₁₉	—	4	2	no	—
497	D₄×C₁₉	—	8	1	no	—
498	D₄×C₁₉	—	8	1	no	—
499	D₄×C₁₉	—	8	2	no	—
500	D₄×C₁₉	—	8	2	no	—
501	D₄×C₁₉	—	8	1	no	—
502	D₄×C₁₉	—	8	2	no	—
503	D₄×C₁₉	—	8	2	no	—
504	D₄×C₁₉	—	8	2	no	—
505	D₄×C₁₉	—	8	2	no	—
506	D₄×C₁₉	—	8	1	no	—
507	D₄×C₁₉	—	8	1	no	—
508	D₄×C₁₉	—	8	2	no	—
509	D₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
510	C₂×C₄×C₁₉	—	2	2	no	—
511	C₂×C₄×C₁₉	—	2	2	no	—
512	C₂×C₄×C₁₉	—	2	1	no	—
513	C₂×C₄×C₁₉	—	2	2	no	—
514	C₂×C₄×C₁₉	—	2	1	no	—
515	C₂×C₄×C₁₉	—	2	2	no	—
516	C₂×C₄×C₁₉	—	2	1	no	—
517	C₂×C₄×C₁₉	—	2	1	no	—
518	C₂×C₄×C₁₉	—	2	2	no	—
519	C₂×C₄×C₁₉	—	2	2	no	—
520	C₂×C₄×C₁₉	—	2	1	no	—
521	C₂×C₄×C₁₉	—	2	1	no	—
522	C₂×C₄×C₁₉	—	4	1	no	—
523	C₂×C₄×C₁₉	—	4	4	no	—
524	C₂×C₄×C₁₉	—	4	2	no	—
525	C₂×C₄×C₁₉	—	4	2	no	—
526	C₂×C₄×C₁₉	—	4	2	no	—
527	C₂×C₄×C₁₉	—	4	2	no	—
528	C₂×C₄×C₁₉	—	8	1	no	—
529	C₂×C₄×C₁₉	—	8	1	no	—
530	C₂×C₄×C₁₉	—	8	2	no	—
531	C₂×C₄×C₁₉	—	8	2	no	—
532	C₂×C₄×C₁₉	—	8	2	no	—
533	C₂×C₄×C₁₉	—	8	2	no	—
534	C₂×C₄×C₁₉	—	8	1	no	—
535	C₂×C₄×C₁₉	—	8	2	no	—
536	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
545	C₈×C₁₉	—	2	1	no	—
546	C₈×C₁₉	—	2	2	no	—
547	C₈×C₁₉	—	2	2	no	—
548	C₈×C₁₉	—	2	1	no	—
549	C₈×C₁₉	—	2	1	no	—
550	C₈×C₁₉	—	2	1	no	—
551	#3546	C₂×C₁₉	1	1	yes	characteristic, complemented
552	#3520	C₂×C₁₉	1	1	yes	characteristic, complemented
553	#3397	C₂×C₁₉	1	1	yes	characteristic, complemented
554	#3393	C₂×C₁₉	1	1	yes	characteristic, complemented
555	#3367	C₂×C₁₉	1	1	yes	characteristic, complemented
556	#3358	C₂×C₁₉	1	1	yes	characteristic, complemented
557	#3333	C₂×C₁₉	1	2	yes	complemented
558	#3330	C₂×C₁₉	1	1	yes	characteristic, complemented
559	#3314	C₂×C₁₉	1	2	yes	complemented
560	#3294	C₂×C₁₉	1	1	yes	characteristic, complemented
561	#3283	C₂×C₁₉	1	1	yes	characteristic, complemented
562	#3273	C₂×C₁₉	1	2	yes	complemented
563	#3272	C₂×C₁₉	1	1	yes	characteristic, complemented
564	#3268	C₂×C₁₉	1	2	yes	complemented
565	#3262	C₂×C₁₉	1	2	yes	complemented
566	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
567	#3224	C₂×C₁₉	1	2	yes	complemented
568	#3210	C₂×C₁₉	1	1	yes	characteristic, complemented
569	#3124	C₂×C₁₉	1	2	yes	complemented
570	#3100	C₂×C₁₉	1	1	yes	characteristic, complemented
571	#3045	C₂×C₁₉	1	2	yes	complemented
572	#3036	C₂×C₁₉	1	1	yes	characteristic, complemented
573	#2993	C₂×C₁₉	1	1	yes	characteristic, complemented
574	C₂²×C₁₉	—	2	1	no	—
575	C₂²×C₁₉	—	2	2	no	—
576	C₂²×C₁₉	—	2	2	no	—
577	C₂²×C₁₉	—	2	1	no	—
578	C₂²×C₁₉	—	2	2	no	—
579	C₂²×C₁₉	—	2	1	no	—
580	C₂²×C₁₉	—	2	2	no	—
581	C₂²×C₁₉	—	4	1	no	—
582	C₂²×C₁₉	—	4	1	no	—
583	C₂²×C₁₉	—	4	1	no	—
584	C₂²×C₁₉	—	4	2	no	—
585	C₂²×C₁₉	—	4	1	no	—
586	C₂²×C₁₉	—	4	1	no	—
587	C₂²×C₁₉	—	4	1	no	—
588	C₂²×C₁₉	—	4	2	no	—
589	C₂²×C₁₉	—	4	1	no	—
590	C₂²×C₁₉	—	4	1	no	—
591	C₂²×C₁₉	—	4	1	no	—
592	C₂²×C₁₉	—	4	1	no	—
593	C₂²×C₁₉	—	4	1	no	—
594	C₂²×C₁₉	—	4	2	no	—
595	C₂²×C₁₉	—	8	4	no	—
596	C₂²×C₁₉	—	16	4	no	—
597	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₁₉	—	2	1	no	—
599	C₄×C₁₉	—	2	1	no	—
600	C₄×C₁₉	—	2	2	no	—
601	C₄×C₁₉	—	2	2	no	—
602	C₄×C₁₉	—	2	1	no	—
603	C₄×C₁₉	—	2	1	no	—
604	C₄×C₁₉	—	2	2	no	—
605	C₄×C₁₉	—	4	2	no	—
606	C₄×C₁₉	—	4	2	no	—
607	C₄×C₁₉	—	4	1	no	—
608	C₄×C₁₉	—	4	1	no	—
609	C₄×C₁₉	—	4	1	no	—
610	C₄×C₁₉	—	4	1	no	—
611	C₄×C₁₉	—	4	2	no	—
612	C₄×C₁₉	#576	1	2	yes	—
613	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
614	C₄×C₁₉	#585	1	1	yes	characteristic
615	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
616	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
617	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
618	#560	—	2	2	no	—
619	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
620	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
621	#554	C₂²×C₁₉	1	2	yes	complemented
622	#553	—	2	1	no	—
623	#552	—	2	1	no	—
624	#551	—	2	2	no	—
625	#550	C₂²×C₁₉	1	2	yes	—
626	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
627	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
628	#548	—	2	1	no	—
629	#547	C₂²×C₁₉	1	1	yes	characteristic
630	#547	C₂²×C₁₉	1	1	yes	characteristic
631	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
632	#546	—	2	1	no	—
633	#546	C₂²×C₁₉	1	2	yes	—
634	#546	C₂²×C₁₉	1	2	yes	complemented
635	D₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
636	#542	C₂²×C₁₉	1	2	yes	complemented
637	#542	C₂²×C₁₉	1	2	yes	complemented
638	#539	—	2	2	no	—
639	#538	—	2	2	no	—
640	#537	—	2	1	no	—
641	#535	—	2	1	no	—
642	#535	C₂²×C₁₉	1	2	yes	complemented
643	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
644	#532	C₂²×C₁₉	1	1	yes	characteristic
645	#532	C₂²×C₁₉	1	1	yes	characteristic
646	#529	C₂²×C₁₉	1	1	yes	characteristic
647	#525	—	2	1	no	—
648	C₂×C₂²⋊Q₈	—	2	1	no	—
649	#520	C₂²×C₁₉	1	2	yes	complemented
650	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
651	#496	C₂²×C₁₉	1	2	yes	complemented
652	#495	C₂²×C₁₉	1	2	yes	—
653	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
654	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
655	#489	C₂²×C₁₉	1	2	yes	complemented
656	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#486	C₂²×C₁₉	1	2	yes	complemented
658	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
659	#484	C₂²×C₁₉	1	2	yes	complemented
660	#480	C₂²×C₁₉	1	1	yes	characteristic
661	#480	C₂²×C₁₉	1	1	yes	characteristic, complemented
662	#480	C₂²×C₁₉	1	2	yes	complemented
663	#477	C₂²×C₁₉	1	2	yes	complemented
664	#477	C₂²×C₁₉	1	2	yes	complemented
665	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	#474	C₂²×C₁₉	1	2	yes	complemented
669	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	#468	C₂²×C₁₉	1	2	yes	—
671	#468	C₂²×C₁₉	1	2	yes	complemented
672	#468	C₂²×C₁₉	1	2	yes	complemented
673	#468	C₂²×C₁₉	1	2	yes	complemented
674	#467	C₂²×C₁₉	1	2	yes	complemented
675	#466	C₂²×C₁₉	1	2	yes	—
676	#464	C₂²×C₁₉	1	2	yes	complemented
677	#464	C₂²×C₁₉	1	2	yes	complemented
678	#464	C₂²×C₁₉	1	2	yes	complemented
679	#464	C₂²×C₁₉	1	2	yes	complemented
680	#463	C₂²×C₁₉	1	2	yes	—
681	#463	C₂²×C₁₉	1	2	yes	complemented
682	#463	C₂²×C₁₉	1	2	yes	complemented
683	#463	C₂²×C₁₉	1	2	yes	complemented
684	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
685	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
686	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
687	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
688	#460	C₂²×C₁₉	1	2	yes	complemented
689	#460	C₂²×C₁₉	1	2	yes	complemented
690	#459	C₂²×C₁₉	1	1	yes	characteristic
691	#459	C₂²×C₁₉	1	1	yes	characteristic
692	#459	C₂²×C₁₉	1	1	yes	characteristic
693	#459	C₂²×C₁₉	1	1	yes	characteristic
694	#459	C₂²×C₁₉	1	2	yes	complemented
695	#452	C₂²×C₁₉	1	2	yes	complemented
696	#452	C₂²×C₁₉	1	2	yes	complemented
697	#452	C₂²×C₁₉	1	2	yes	complemented
698	#452	C₂²×C₁₉	1	2	yes	complemented
699	#450	C₂²×C₁₉	1	2	yes	complemented
700	#449	C₂²×C₁₉	1	2	yes	—
701	#449	C₂²×C₁₉	1	2	yes	complemented
702	#447	C₂²×C₁₉	1	1	yes	characteristic
703	#447	C₂²×C₁₉	1	2	yes	—
704	#447	C₂²×C₁₉	1	1	yes	characteristic, complemented
705	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
706	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
707	#440	C₂²×C₁₉	1	2	yes	complemented
708	#440	C₂²×C₁₉	1	2	yes	complemented
709	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
710	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
711	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
712	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
713	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
714	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
715	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
716	#436	C₂²×C₁₉	1	2	yes	complemented
717	#435	C₂²×C₁₉	1	2	yes	complemented
718	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
719	#433	C₂²×C₁₉	1	2	yes	complemented
720	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
721	#424	C₂²×C₁₉	1	2	yes	complemented
722	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
723	#417	C₂²×C₁₉	1	2	yes	complemented
724	#417	C₂²×C₁₉	1	2	yes	complemented
725	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
726	C₂×C₁₉	—	4	1	no	—
727	C₂×C₁₉	—	4	2	no	—
728	C₂×C₁₉	—	4	2	no	—
729	C₂×C₁₉	—	8	1	no	—
730	C₂×C₁₉	—	8	1	no	—
731	C₂×C₁₉	—	8	2	no	—
732	C₂×C₁₉	—	8	1	no	—
733	C₂×C₁₉	#3488	1	1	yes	characteristic
734	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
735	C₂×C₁₉	#3586	1	1	yes	characteristic
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	C₂³×C₁₉	1	2	yes	—
740	C₂×#41	C₂³×C₁₉	1	2	yes	—
741	C₂×#41	C₂³×C₁₉	1	2	yes	—
742	C₂²×Q₈	—	2	1	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
746	C₂³×C₄	—	2	1	no	—
747	AGL(1,ℤ/8)	—	4	4	no	—
748	AGL(1,ℤ/8)	—	4	4	no	—
749	#135	—	4	4	no	—
750	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
751	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
758	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
759	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₁₉	1	2	yes	—
761	C₂×D₈	C₂³×C₁₉	1	2	yes	—
762	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
763	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
764	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
765	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
766	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
767	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
768	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
772	#127	—	2	2	no	—
773	#127	C₂³×C₁₉	1	1	yes	characteristic
774	#127	C₂³×C₁₉	1	1	yes	characteristic
775	#127	C₂³×C₁₉	1	2	yes	—
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#126	D₄×C₁₉	1	2	yes	—
781	#125	—	2	2	no	—
782	#125	—	2	1	no	—
783	#125	D₄×C₁₉	1	1	yes	characteristic
784	#124	—	2	2	no	—
785	#124	—	2	2	no	—
786	#124	—	2	1	no	—
787	#124	D₄×C₁₉	1	1	yes	characteristic
788	#124	C₂³×C₁₉	1	2	yes	—
789	#124	C₂³×C₁₉	1	2	yes	—
790	#124	C₂³×C₁₉	1	2	yes	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	D₄×C₁₉	1	2	yes	—
799	C₂²⋊Q₈	—	2	1	no	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	1	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
810	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
811	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
812	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	1	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	D₄×C₁₉	1	1	yes	characteristic
828	#121	C₂³×C₁₉	1	1	yes	characteristic
829	#121	C₂³×C₁₉	1	1	yes	characteristic
830	#121	C₂³×C₁₉	1	2	yes	—
831	#121	C₂³×C₁₉	1	2	yes	—
832	#120	—	2	2	no	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
839	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
840	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
841	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₁₉	1	2	yes	—
856	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₁₉	1	2	yes	—
859	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
860	C₄×D₄	C₂³×C₁₉	1	2	yes	—
861	#117	—	2	1	no	—
862	#117	—	2	2	no	—
863	#117	—	2	1	no	—
864	#117	—	2	1	no	—
865	#117	C₂³×C₁₉	1	2	yes	—
866	C₂×C₄⋊C₄	—	2	2	no	—
867	C₂×C₄⋊C₄	—	2	1	no	—
868	C₂×C₄⋊C₄	—	2	1	no	—
869	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
871	C₂×C₂²⋊C₄	—	2	1	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
875	#107	C₂³×C₁₉	1	1	yes	characteristic
876	#107	C₂³×C₁₉	1	1	yes	characteristic
877	#107	C₂³×C₁₉	1	1	yes	characteristic
878	#107	C₂³×C₁₉	1	1	yes	characteristic
879	#107	C₂³×C₁₉	1	2	yes	—
880	#107	C₂³×C₁₉	1	2	yes	—
881	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
882	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
886	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
887	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
888	#103	C₂³×C₁₉	1	2	yes	—
889	#103	C₂³×C₁₉	1	2	yes	—
890	#103	C₂³×C₁₉	1	2	yes	—
891	#103	C₂³×C₁₉	1	2	yes	—
892	#103	C₂³×C₁₉	1	2	yes	—
893	#103	C₂³×C₁₉	1	2	yes	—
894	#102	C₂³×C₁₉	1	1	yes	characteristic
895	#102	C₂³×C₁₉	1	2	yes	—
896	#102	C₂³×C₁₉	1	2	yes	—
897	#102	C₂³×C₁₉	1	2	yes	—
898	#102	C₂³×C₁₉	1	1	yes	characteristic
899	#102	C₂³×C₁₉	1	2	yes	—
900	#102	C₂³×C₁₉	1	2	yes	—
901	#102	C₂³×C₁₉	1	1	yes	characteristic
902	#102	C₂³×C₁₉	1	1	yes	characteristic
903	#102	C₂³×C₁₉	1	1	yes	characteristic
904	#102	C₂³×C₁₉	1	1	yes	characteristic
905	#102	C₂³×C₁₉	1	2	yes	—
906	#102	C₂³×C₁₉	1	1	yes	characteristic
907	#102	C₂³×C₁₉	1	1	yes	characteristic
908	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
912	#97	C₂³×C₁₉	1	2	yes	—
913	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₁₉	1	2	yes	—
916	C₁₉	#62041	1	1	yes	characteristic, direct product factor, Sylow
917	C₂⁴	—	2	1	no	—
918	C₂⁴	—	2	2	no	—
919	#41	—	2	4	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	8	2	no	—
926	#41	—	8	2	no	—
927	#41	—	8	2	no	—
928	C₂×Q₈	—	2	1	no	—
929	C₂×Q₈	—	2	2	no	—
930	C₂×Q₈	—	2	1	no	—
931	C₂×Q₈	—	8	2	no	—
932	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
933	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
934	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	4	1	no	—
952	C₂×D₄	—	4	2	no	—
953	C₂×D₄	—	4	2	no	—
954	C₂×D₄	—	8	2	no	—
955	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
956	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
957	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
959	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
961	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	8	2	no	—
976	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
977	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
980	Q₁₆	—	4	2	no	—
981	Q₁₆	—	4	2	no	—
982	SD₁₆	—	2	4	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	—	4	2	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	D₈	—	2	2	no	—
989	D₈	—	2	4	no	—
990	D₈	—	2	2	no	—
991	D₈	—	4	1	no	—
992	D₈	—	4	1	no	—
993	D₈	—	4	2	no	—
994	M₁₆	—	4	2	no	—
995	M₁₆	—	4	2	no	—
996	C₂×C₈	—	4	2	no	—
997	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1002	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1020	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
1021	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1022	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1026	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
1027	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1052	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1053	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1054	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1059	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₁₉	1	2	yes	—
1062	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	4	2	no	—
1069	C₂³	—	4	2	no	—
1070	C₂³	—	8	1	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	—	8	2	no	—
1073	C₂³	—	8	2	no	—
1074	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
1075	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1076	Q₈	—	2	2	no	—
1077	Q₈	—	2	2	no	—
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	8	2	no	—
1083	Q₈	—	8	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	2	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	—	8	2	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	1	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	2	no	—
1110	D₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1143	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1145	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1146	C₈	—	2	1	no	—
1147	C₈	—	2	2	no	—
1148	C₈	—	2	1	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	8	4	no	—
1174	C₂²	—	16	4	no	—
1175	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1176	C₄	—	2	2	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	1	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	2	no	—
1190	C₄	C₁₉×#576	1	2	yes	—
1191	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₄	C₁₉×#585	1	1	yes	characteristic
1193	C₂	—	4	1	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	4	2	no	—
1196	C₂	—	8	1	no	—
1197	C₂	—	8	1	no	—
1198	C₂	—	8	2	no	—
1199	C₂	—	8	1	no	—
1200	C₂	C₁₉×#3488	1	1	yes	characteristic
1201	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
1202	C₂	C₁₉×#3586	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3546	C₂	semidirect
2. C₁₉×#3520	C₂	semidirect
3. C₁₉×#3397	C₂	semidirect
4. C₁₉×#3393	C₂	semidirect
5. C₁₉×#3367	C₂	semidirect
6. C₁₉×#3358	C₂	semidirect
7. C₁₉×#3333	C₂	semidirect
8. C₁₉×#3330	C₂	semidirect
9. C₁₉×#3314	C₂	semidirect
10. C₁₉×#3294	C₂	semidirect
11. C₁₉×#3283	C₂	semidirect
12. C₁₉×#3273	C₂	semidirect
13. C₁₉×#3272	C₂	semidirect
14. C₁₉×#3268	C₂	semidirect
15. C₁₉×#3262	C₂	semidirect
16. C₁₉×#3254	C₂	semidirect
17. C₁₉×#3224	C₂	semidirect
18. C₁₉×#3210	C₂	semidirect
19. C₁₉×#3124	C₂	semidirect
20. C₁₉×#3100	C₂	semidirect
21. C₁₉×#3045	C₂	semidirect
22. C₁₉×#3036	C₂	semidirect
23. C₁₉×#2993	C₂	semidirect
25. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₁₉×#135	C₂²	semidirect
28. C₁₉×#556	C₂²	semidirect
29. C₁₉×#556	C₂²	semidirect
30. C₁₉×#554	C₂²	semidirect
35. C₁₉×#550	C₂²	semidirect
36. D₄×Q₈×C₁₉	C₂²	semidirect
40. C₁₉×#547	C₂²	semidirect
43. C₁₉×#546	C₂²	semidirect
44. D₄²×C₁₉	C₂²	semidirect
45. C₁₉×#542	C₂²	semidirect
46. C₁₉×#542	C₂²	semidirect
51. C₁₉×#535	C₂²	semidirect
52. C₁₉×#533	C₂²	semidirect
58. C₁₉×#520	C₂²	semidirect
59. C₂×C₄×D₄×C₁₉	C₂²	semidirect
60. C₁₉×#496	C₂²	semidirect
62. C₁₉×#494	C₂²	semidirect
63. C₁₉×#492	C₂²	semidirect
64. C₁₉×#489	C₂²	semidirect
65. C₁₉×#487	C₂²	semidirect
66. C₁₉×#486	C₂²	semidirect
67. C₁₉×#486	C₂²	semidirect
68. C₁₉×#484	C₂²	semidirect
70. C₁₉×#480	C₂²	semidirect
71. C₁₉×#480	C₂²	semidirect
72. C₁₉×#477	C₂²	semidirect
73. C₁₉×#477	C₂²	semidirect
74. C₁₉×#474	C₂²	semidirect
75. C₁₉×#474	C₂²	semidirect
76. C₁₉×#474	C₂²	semidirect
77. C₁₉×#474	C₂²	semidirect
78. C₁₉×#474	C₂²	semidirect
80. C₁₉×#468	C₂²	semidirect
81. C₁₉×#468	C₂²	semidirect
82. C₁₉×#468	C₂²	semidirect
83. C₁₉×#467	C₂²	semidirect
85. C₁₉×#464	C₂²	semidirect
86. C₁₉×#464	C₂²	semidirect
87. C₁₉×#464	C₂²	semidirect
88. C₁₉×#464	C₂²	semidirect
90. C₁₉×#463	C₂²	semidirect
91. C₁₉×#463	C₂²	semidirect
92. C₁₉×#463	C₂²	semidirect
93. C₁₉×#461	C₂²	semidirect
94. C₁₉×#461	C₂²	semidirect
95. C₁₉×#461	C₂²	semidirect
96. C₁₉×#461	C₂²	semidirect
97. C₁₉×#460	C₂²	semidirect
98. C₁₉×#460	C₂²	semidirect
103. C₁₉×#459	C₂²	semidirect
104. C₁₉×#452	C₂²	semidirect
105. C₁₉×#452	C₂²	semidirect
106. C₁₉×#452	C₂²	semidirect
107. C₁₉×#452	C₂²	semidirect
108. C₁₉×#450	C₂²	semidirect
110. C₁₉×#449	C₂²	semidirect
113. C₁₉×#447	C₂²	semidirect
114. C₁₉×#446	C₂²	semidirect
115. C₈×Q₈×C₁₉	C₂²	semidirect
116. C₁₉×#440	C₂²	semidirect
117. C₁₉×#440	C₂²	semidirect
118. C₄×Q₁₆×C₁₉	C₂²	semidirect
121. C₄×D₈×C₁₉	C₂²	semidirect
122. C₄×D₈×C₁₉	C₂²	semidirect
123. C₄×D₈×C₁₉	C₂²	semidirect
124. C₁₉×#436	C₂²	semidirect
125. C₁₉×#436	C₂²	semidirect
126. C₁₉×#435	C₂²	semidirect
127. C₈×D₄×C₁₉	C₂²	semidirect
128. C₁₉×#433	C₂²	semidirect
129. C₁₉×#431	C₂²	semidirect
130. C₁₉×#424	C₂²	semidirect
131. C₁₉×#423	C₂²	semidirect
132. C₁₉×#417	C₂²	semidirect
133. C₁₉×#417	C₂²	semidirect
134. C₂×C₁₉×#102	C₂²	semidirect
461. #62041	C₁₉	direct (N × H)
551. #3546	C₂×C₁₉	semidirect
552. #3520	C₂×C₁₉	semidirect
553. #3397	C₂×C₁₉	semidirect
554. #3393	C₂×C₁₉	semidirect
555. #3367	C₂×C₁₉	semidirect
556. #3358	C₂×C₁₉	semidirect
557. #3333	C₂×C₁₉	semidirect
558. #3330	C₂×C₁₉	semidirect
559. #3314	C₂×C₁₉	semidirect
560. #3294	C₂×C₁₉	semidirect
561. #3283	C₂×C₁₉	semidirect
562. #3273	C₂×C₁₉	semidirect
563. #3272	C₂×C₁₉	semidirect
564. #3268	C₂×C₁₉	semidirect
565. #3262	C₂×C₁₉	semidirect
566. #3254	C₂×C₁₉	semidirect
567. #3224	C₂×C₁₉	semidirect
568. #3210	C₂×C₁₉	semidirect
569. #3124	C₂×C₁₉	semidirect
570. #3100	C₂×C₁₉	semidirect
571. #3045	C₂×C₁₉	semidirect
572. #3036	C₂×C₁₉	semidirect
573. #2993	C₂×C₁₉	semidirect
616. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
617. C₂×#135	C₂²×C₁₉	semidirect
619. #556	C₂²×C₁₉	semidirect
620. #556	C₂²×C₁₉	semidirect
621. #554	C₂²×C₁₉	semidirect
626. #550	C₂²×C₁₉	semidirect
627. D₄×Q₈	C₂²×C₁₉	semidirect
631. #547	C₂²×C₁₉	semidirect
634. #546	C₂²×C₁₉	semidirect
635. D₄²	C₂²×C₁₉	semidirect
636. #542	C₂²×C₁₉	semidirect
637. #542	C₂²×C₁₉	semidirect
642. #535	C₂²×C₁₉	semidirect
643. #533	C₂²×C₁₉	semidirect
649. #520	C₂²×C₁₉	semidirect
650. C₂×C₄×D₄	C₂²×C₁₉	semidirect
651. #496	C₂²×C₁₉	semidirect
653. #494	C₂²×C₁₉	semidirect
654. #492	C₂²×C₁₉	semidirect
655. #489	C₂²×C₁₉	semidirect
656. #487	C₂²×C₁₉	semidirect
657. #486	C₂²×C₁₉	semidirect
658. #486	C₂²×C₁₉	semidirect
659. #484	C₂²×C₁₉	semidirect
661. #480	C₂²×C₁₉	semidirect
662. #480	C₂²×C₁₉	semidirect
663. #477	C₂²×C₁₉	semidirect
664. #477	C₂²×C₁₉	semidirect
665. #474	C₂²×C₁₉	semidirect
666. #474	C₂²×C₁₉	semidirect
667. #474	C₂²×C₁₉	semidirect
668. #474	C₂²×C₁₉	semidirect
669. #474	C₂²×C₁₉	semidirect
671. #468	C₂²×C₁₉	semidirect
672. #468	C₂²×C₁₉	semidirect
673. #468	C₂²×C₁₉	semidirect
674. #467	C₂²×C₁₉	semidirect
676. #464	C₂²×C₁₉	semidirect
677. #464	C₂²×C₁₉	semidirect
678. #464	C₂²×C₁₉	semidirect
679. #464	C₂²×C₁₉	semidirect
681. #463	C₂²×C₁₉	semidirect
682. #463	C₂²×C₁₉	semidirect
683. #463	C₂²×C₁₉	semidirect
684. #461	C₂²×C₁₉	semidirect
685. #461	C₂²×C₁₉	semidirect
686. #461	C₂²×C₁₉	semidirect
687. #461	C₂²×C₁₉	semidirect
688. #460	C₂²×C₁₉	semidirect
689. #460	C₂²×C₁₉	semidirect
694. #459	C₂²×C₁₉	semidirect
695. #452	C₂²×C₁₉	semidirect
696. #452	C₂²×C₁₉	semidirect
697. #452	C₂²×C₁₉	semidirect
698. #452	C₂²×C₁₉	semidirect
699. #450	C₂²×C₁₉	semidirect
701. #449	C₂²×C₁₉	semidirect
704. #447	C₂²×C₁₉	semidirect
705. #446	C₂²×C₁₉	semidirect
706. C₈×Q₈	C₂²×C₁₉	semidirect
707. #440	C₂²×C₁₉	semidirect
708. #440	C₂²×C₁₉	semidirect
709. C₄×Q₁₆	C₂²×C₁₉	semidirect
712. C₄×D₈	C₂²×C₁₉	semidirect
713. C₄×D₈	C₂²×C₁₉	semidirect
714. C₄×D₈	C₂²×C₁₉	semidirect
715. #436	C₂²×C₁₉	semidirect
716. #436	C₂²×C₁₉	semidirect
717. #435	C₂²×C₁₉	semidirect
718. C₈×D₄	C₂²×C₁₉	semidirect
719. #433	C₂²×C₁₉	semidirect
720. #431	C₂²×C₁₉	semidirect
721. #424	C₂²×C₁₉	semidirect
722. #423	C₂²×C₁₉	semidirect
723. #417	C₂²×C₁₉	semidirect
724. #417	C₂²×C₁₉	semidirect
725. C₂×#102	C₂²×C₁₉	semidirect
916. C₁₉	#62041	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×#3520	2
C₁₉×#3397	2
C₁₉×#3393	2
C₁₉×#3367	2
C₁₉×#3358	2
C₁₉×#3333	2
C₁₉×#3330	2
C₁₉×#3314	2
C₁₉×#3294	2
C₁₉×#3283	2
C₁₉×#3273	2
C₁₉×#3272	2
C₁₉×#3268	2
C₁₉×#3262	2
C₁₉×#3254	2
C₁₉×#3224	2
C₁₉×#3210	2
C₁₉×#3124	2
C₁₉×#3100	2
C₁₉×#3045	2
C₁₉×#3036	2
C₁₉×#2993	2
#62041	19

Subgroups — C19×#62041 #18068000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62041 #18068000