Subgroups — C₁₉×#62292 #18068251

Order 4864.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3355	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3351	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3318	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3310	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3309	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3307	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3274	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3272	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3260	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3259	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3198	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3194	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3176	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3174	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3062	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3055	C₂	1	2	yes	maximal, complemented
19	C₁₉×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#560	—	2	2	no	—
25	C₁₉×#560	—	2	2	no	—
26	C₁₉×#553	—	2	2	no	—
27	C₁₉×#553	C₂²	1	2	yes	—
28	C₁₉×#553	C₂²	1	2	yes	—
29	C₁₉×#553	C₂²	1	2	yes	complemented
30	C₁₉×#552	C₂²	1	2	yes	complemented
31	C₁₉×#550	C₂²	1	2	yes	complemented
32	C₁₉×#547	C₂²	1	2	yes	complemented
33	D₄²×C₁₉	—	2	2	no	—
34	D₄²×C₁₉	C₂²	1	2	yes	—
35	D₄²×C₁₉	C₂²	1	2	yes	—
36	C₁₉×#541	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#540	—	2	2	no	—
38	C₁₉×#540	C₂²	1	1	yes	characteristic
39	C₁₉×#540	C₂²	1	1	yes	characteristic
40	C₁₉×#540	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#539	—	2	2	no	—
42	C₁₉×#538	—	2	2	no	—
43	C₁₉×#537	C₂²	1	2	yes	complemented
44	C₁₉×#535	C₂²	1	2	yes	—
45	C₁₉×#534	—	2	2	no	—
46	C₁₉×#525	C₂²	1	1	yes	characteristic
47	C₁₉×#525	C₂²	1	2	yes	complemented
48	C₂×C₁₉×#121	C₂²	1	2	yes	—
49	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#485	C₂²	1	2	yes	complemented
58	C₁₉×#483	C₂²	1	2	yes	complemented
59	C₁₉×#482	C₂²	1	2	yes	complemented
60	C₁₉×#482	C₂²	1	2	yes	complemented
61	C₁₉×#482	C₂²	1	2	yes	complemented
62	C₁₉×#481	C₂²	1	2	yes	complemented
63	C₁₉×#480	C₂²	1	2	yes	complemented
64	C₁₉×#480	C₂²	1	2	yes	complemented
65	C₁₉×#479	C₂²	1	2	yes	complemented
66	C₁₉×#478	C₂²	1	2	yes	complemented
67	C₁₉×#478	C₂²	1	2	yes	complemented
68	C₁₉×#478	C₂²	1	2	yes	complemented
69	C₁₉×#469	C₂²	1	2	yes	complemented
70	C₁₉×#469	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×#468	C₂²	1	2	yes	complemented
78	C₁₉×#468	C₂²	1	2	yes	complemented
79	C₁₉×#466	C₂²	1	2	yes	complemented
80	C₁₉×#466	C₂²	1	2	yes	complemented
81	C₁₉×#466	C₂²	1	2	yes	complemented
82	C₁₉×#465	C₂²	1	2	yes	complemented
83	C₁₉×#465	C₂²	1	2	yes	complemented
84	C₁₉×#465	C₂²	1	2	yes	complemented
85	C₁₉×#461	C₂²	1	2	yes	complemented
86	C₁₉×#460	C₂²	1	2	yes	complemented
87	C₁₉×#459	C₂²	1	2	yes	complemented
88	C₁₉×#459	C₂²	1	2	yes	complemented
89	C₁₉×#450	C₂²	1	2	yes	complemented
90	C₁₉×#450	C₂²	1	2	yes	complemented
91	C₁₉×#449	C₂²	1	2	yes	complemented
92	C₁₉×#449	C₂²	1	2	yes	complemented
93	C₁₉×#449	C₂²	1	2	yes	complemented
94	C₁₉×#449	C₂²	1	2	yes	complemented
95	C₁₉×#447	C₂²	1	2	yes	complemented
96	C₁₉×#447	C₂²	1	2	yes	complemented
97	C₁₉×#442	C₂²	1	2	yes	complemented
98	C₁₉×#440	C₂²	1	2	yes	complemented
99	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
100	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
101	C₁₉×#436	C₂²	1	2	yes	complemented
102	C₁₉×#436	C₂²	1	2	yes	complemented
103	C₁₉×#435	C₂²	1	2	yes	complemented
104	C₁₉×#435	C₂²	1	2	yes	complemented
105	C₁₉×#428	C₂²	1	2	yes	complemented
106	C₁₉×#428	C₂²	1	2	yes	complemented
107	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
108	C₁₉×#418	C₂²	1	2	yes	complemented
109	C₁₉×#417	C₂²	1	2	yes	complemented
110	C₁₉×#416	C₂²	1	2	yes	complemented
111	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
112	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
113	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
114	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₁₉	C₂³	1	2	yes	—
116	C₂×#41×C₁₉	C₂³	1	2	yes	—
117	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₁₉	—	2	2	no	—
119	C₂²×D₄×C₁₉	—	2	2	no	—
120	C₂²×D₄×C₁₉	—	2	2	no	—
121	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
125	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
126	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
130	C₂×D₈×C₁₉	C₂³	1	2	yes	—
131	C₂×D₈×C₁₉	C₂³	1	2	yes	—
132	C₂×D₈×C₁₉	C₂³	1	2	yes	—
133	C₂×D₈×C₁₉	C₂³	1	2	yes	—
134	C₁₉×#131	—	4	2	no	—
135	C₂×M₁₆×C₁₉	—	4	2	no	—
136	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
137	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
138	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
141	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
144	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₁₉×#127	—	2	2	no	—
146	C₁₉×#127	—	2	2	no	—
147	C₁₉×#127	C₂³	1	1	yes	characteristic
148	C₁₉×#127	C₂³	1	1	yes	characteristic
149	C₁₉×#127	C₂³	1	1	yes	characteristic
150	C₁₉×#126	—	2	2	no	—
151	C₁₉×#126	—	2	2	no	—
152	C₁₉×#126	—	2	2	no	—
153	C₁₉×#126	—	2	2	no	—
154	C₁₉×#126	—	2	2	no	—
155	C₁₉×#125	—	2	2	no	—
156	C₁₉×#125	—	2	2	no	—
157	C₁₉×#125	C₂³	1	1	yes	characteristic
158	C₁₉×#125	C₂³	1	1	yes	characteristic
159	C₁₉×#125	C₂³	1	1	yes	characteristic
160	C₁₉×#125	C₂³	1	1	yes	characteristic
161	C₁₉×#124	—	2	2	no	—
162	C₁₉×#123	—	2	2	no	—
163	C₁₉×#123	—	2	2	no	—
164	C₁₉×#123	—	2	2	no	—
165	C₁₉×#123	—	2	2	no	—
166	C₁₉×#123	—	2	2	no	—
167	C₁₉×#123	—	2	2	no	—
168	C₁₉×#123	—	2	2	no	—
169	C₁₉×#123	—	2	2	no	—
170	C₁₉×#123	—	2	2	no	—
171	C₁₉×#123	—	2	2	no	—
172	C₁₉×#123	D₄	1	2	yes	—
173	C₁₉×C₂²⋊Q₈	—	2	2	no	—
174	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
175	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₉×#121	—	2	2	no	—
179	C₁₉×#121	—	2	2	no	—
180	C₁₉×#121	—	2	2	no	—
181	C₁₉×#121	—	2	2	no	—
182	C₁₉×#121	—	2	2	no	—
183	C₁₉×#121	—	2	2	no	—
184	C₁₉×#121	—	2	2	no	—
185	C₁₉×#121	—	2	2	no	—
186	C₁₉×#121	—	2	2	no	—
187	C₁₉×#121	—	2	2	no	—
188	C₁₉×#121	—	2	2	no	—
189	C₁₉×#121	—	2	2	no	—
190	C₁₉×#121	—	2	2	no	—
191	C₁₉×#121	—	2	2	no	—
192	C₁₉×#121	—	2	2	no	—
193	C₁₉×#121	—	2	2	no	—
194	C₁₉×#121	D₄	1	2	yes	—
195	C₁₉×#121	C₂³	1	2	yes	—
196	C₁₉×#121	C₂³	1	2	yes	—
197	C₁₉×#121	C₂³	1	2	yes	—
198	C₁₉×#121	C₂³	1	2	yes	—
199	C₁₉×#121	C₂³	1	2	yes	—
200	C₁₉×#121	C₂³	1	2	yes	—
201	C₁₉×#121	C₂³	1	2	yes	—
202	C₁₉×#121	C₂³	1	2	yes	—
203	C₁₉×#121	C₂³	1	2	yes	—
204	C₁₉×#120	—	2	2	no	—
205	C₁₉×#120	—	2	2	no	—
206	C₁₉×#120	—	2	2	no	—
207	C₁₉×#120	—	2	2	no	—
208	C₁₉×#120	—	2	2	no	—
209	C₁₉×#120	—	2	2	no	—
210	C₁₉×#120	—	2	2	no	—
211	C₁₉×#120	D₄	1	2	yes	—
212	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
213	C₄×D₄×C₁₉	—	2	2	no	—
214	C₄×D₄×C₁₉	—	2	2	no	—
215	C₄×D₄×C₁₉	—	2	2	no	—
216	C₄×D₄×C₁₉	—	2	2	no	—
217	C₄×D₄×C₁₉	—	2	2	no	—
218	C₄×D₄×C₁₉	—	2	2	no	—
219	C₄×D₄×C₁₉	C₂³	1	2	yes	—
220	C₄×D₄×C₁₉	C₂³	1	2	yes	—
221	C₄×D₄×C₁₉	C₂³	1	2	yes	—
222	C₄×D₄×C₁₉	C₂³	1	2	yes	—
223	C₄×D₄×C₁₉	C₂³	1	2	yes	—
224	C₁₉×#117	—	2	2	no	—
225	C₁₉×#117	C₂³	1	2	yes	—
226	C₁₉×#117	C₂³	1	2	yes	—
227	C₁₉×#117	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
229	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
232	C₁₉×#107	C₂³	1	2	yes	—
233	C₁₉×#107	C₂³	1	2	yes	—
234	C₁₉×#107	C₂³	1	2	yes	—
235	C₁₉×#107	C₂³	1	2	yes	—
236	C₁₉×#106	C₂³	1	2	yes	—
237	C₁₉×#106	C₂³	1	2	yes	—
238	C₁₉×#106	C₂³	1	2	yes	—
239	C₁₉×#106	C₂³	1	2	yes	—
240	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
241	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
242	C₁₉×#103	C₂³	1	2	yes	—
243	C₁₉×#103	C₂³	1	2	yes	—
244	C₁₉×#103	C₂³	1	2	yes	—
245	C₁₉×#103	C₂³	1	2	yes	—
246	C₁₉×#102	C₂³	1	2	yes	—
247	C₁₉×#102	C₂³	1	2	yes	—
248	C₁₉×#102	C₂³	1	2	yes	—
249	C₁₉×#102	C₂³	1	2	yes	—
250	C₁₉×#102	C₂³	1	2	yes	—
251	C₁₉×#102	C₂³	1	2	yes	—
252	C₁₉×#102	C₂³	1	2	yes	—
253	C₁₉×#102	C₂³	1	2	yes	—
254	C₁₉×#102	C₂³	1	2	yes	—
255	C₁₉×#102	C₂³	1	2	yes	—
256	C₁₉×#102	C₂³	1	2	yes	—
257	C₁₉×#102	C₂³	1	2	yes	—
258	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₁₉×#97	C₂³	1	1	yes	characteristic
263	C₁₉×#97	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
266	C₂⁴×C₁₉	—	2	2	no	—
267	C₂⁴×C₁₉	—	2	2	no	—
268	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
269	#41×C₁₉	—	4	1	no	—
270	#41×C₁₉	—	4	1	no	—
271	#41×C₁₉	—	4	2	no	—
272	#41×C₁₉	—	4	2	no	—
273	#41×C₁₉	—	4	2	no	—
274	#41×C₁₉	—	4	2	no	—
275	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
276	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
277	C₂×D₄×C₁₉	—	2	2	no	—
278	C₂×D₄×C₁₉	—	2	2	no	—
279	C₂×D₄×C₁₉	—	2	2	no	—
280	C₂×D₄×C₁₉	—	2	2	no	—
281	C₂×D₄×C₁₉	—	2	2	no	—
282	C₂×D₄×C₁₉	—	2	2	no	—
283	C₂×D₄×C₁₉	—	2	2	no	—
284	C₂×D₄×C₁₉	—	2	2	no	—
285	C₂×D₄×C₁₉	—	2	2	no	—
286	C₂×D₄×C₁₉	—	2	2	no	—
287	C₂×D₄×C₁₉	—	2	2	no	—
288	C₂×D₄×C₁₉	—	2	2	no	—
289	C₂×D₄×C₁₉	—	2	2	no	—
290	C₂×D₄×C₁₉	—	2	2	no	—
291	C₂×D₄×C₁₉	—	2	2	no	—
292	C₂×D₄×C₁₉	—	2	2	no	—
293	C₂×D₄×C₁₉	—	4	2	no	—
294	C₂×D₄×C₁₉	—	4	2	no	—
295	C₂×D₄×C₁₉	—	4	2	no	—
296	C₂×D₄×C₁₉	—	4	2	no	—
297	C₂×D₄×C₁₉	—	8	4	no	—
298	C₂×D₄×C₁₉	—	8	4	no	—
299	C₂×D₄×C₁₉	—	8	4	no	—
300	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
302	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
303	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
305	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
306	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₉	—	2	2	no	—
308	C₂²×C₄×C₁₉	—	2	2	no	—
309	C₂²×C₄×C₁₉	—	2	2	no	—
310	C₂²×C₄×C₁₉	—	2	2	no	—
311	C₂²×C₄×C₁₉	—	2	2	no	—
312	C₂²×C₄×C₁₉	—	2	2	no	—
313	C₂²×C₄×C₁₉	—	2	2	no	—
314	C₂²×C₄×C₁₉	—	4	1	no	—
315	C₂²×C₄×C₁₉	—	4	1	no	—
316	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
317	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
321	SD₁₆×C₁₉	—	2	4	no	—
322	SD₁₆×C₁₉	—	4	2	no	—
323	SD₁₆×C₁₉	—	4	2	no	—
324	SD₁₆×C₁₉	—	4	2	no	—
325	D₈×C₁₉	—	2	4	no	—
326	D₈×C₁₉	—	4	2	no	—
327	D₈×C₁₉	—	4	2	no	—
328	D₈×C₁₉	—	4	2	no	—
329	M₁₆×C₁₉	—	2	4	no	—
330	M₁₆×C₁₉	—	2	4	no	—
331	M₁₆×C₁₉	—	4	2	no	—
332	M₁₆×C₁₉	—	4	1	no	—
333	M₁₆×C₁₉	—	4	1	no	—
334	C₂×C₈×C₁₉	—	2	2	no	—
335	C₂×C₈×C₁₉	—	4	1	no	—
336	C₂×C₈×C₁₉	—	4	2	no	—
337	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
339	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
340	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
343	C₄⋊C₄×C₁₉	—	2	2	no	—
344	C₄⋊C₄×C₁₉	—	2	2	no	—
345	C₄⋊C₄×C₁₉	—	2	2	no	—
346	C₄⋊C₄×C₁₉	—	2	2	no	—
347	C₄⋊C₄×C₁₉	—	2	2	no	—
348	C₄⋊C₄×C₁₉	—	2	2	no	—
349	C₄⋊C₄×C₁₉	—	2	2	no	—
350	C₄⋊C₄×C₁₉	—	2	2	no	—
351	C₄⋊C₄×C₁₉	—	2	2	no	—
352	C₄⋊C₄×C₁₉	—	2	2	no	—
353	C₄⋊C₄×C₁₉	—	2	2	no	—
354	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
361	C₂²⋊C₄×C₁₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₉	—	2	2	no	—
364	C₂²⋊C₄×C₁₉	—	2	2	no	—
365	C₂²⋊C₄×C₁₉	—	2	2	no	—
366	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
371	C₂²⋊C₄×C₁₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₉	—	2	2	no	—
373	C₂²⋊C₄×C₁₉	—	2	2	no	—
374	C₂²⋊C₄×C₁₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₉	—	2	2	no	—
378	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
383	C₄²×C₁₉	—	2	2	no	—
384	C₄²×C₁₉	—	2	2	no	—
385	C₄²×C₁₉	—	2	2	no	—
386	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
387	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
388	#62292	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂³×C₁₉	—	2	2	no	—
390	C₂³×C₁₉	—	2	2	no	—
391	C₂³×C₁₉	—	2	2	no	—
392	C₂³×C₁₉	—	4	1	no	—
393	C₂³×C₁₉	—	4	2	no	—
394	C₂³×C₁₉	—	4	4	no	—
395	C₂³×C₁₉	—	8	2	no	—
396	C₂³×C₁₉	—	8	2	no	—
397	C₂³×C₁₉	—	8	2	no	—
398	C₂³×C₁₉	—	8	2	no	—
399	C₂³×C₁₉	—	8	2	no	—
400	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
401	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
402	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
403	Q₈×C₁₉	—	2	2	no	—
404	Q₈×C₁₉	—	2	2	no	—
405	Q₈×C₁₉	—	4	1	no	—
406	D₄×C₁₉	—	2	2	no	—
407	D₄×C₁₉	—	2	2	no	—
408	D₄×C₁₉	—	2	2	no	—
409	D₄×C₁₉	—	2	2	no	—
410	D₄×C₁₉	—	2	2	no	—
411	D₄×C₁₉	—	2	2	no	—
412	D₄×C₁₉	—	4	2	no	—
413	D₄×C₁₉	—	4	2	no	—
414	D₄×C₁₉	—	4	1	no	—
415	D₄×C₁₉	—	4	2	no	—
416	D₄×C₁₉	—	4	4	no	—
417	D₄×C₁₉	—	4	4	no	—
418	D₄×C₁₉	—	8	2	no	—
419	D₄×C₁₉	—	8	2	no	—
420	D₄×C₁₉	—	8	2	no	—
421	D₄×C₁₉	—	8	2	no	—
422	D₄×C₁₉	—	8	2	no	—
423	D₄×C₁₉	—	8	2	no	—
424	D₄×C₁₉	—	8	2	no	—
425	D₄×C₁₉	—	8	2	no	—
426	D₄×C₁₉	—	8	2	no	—
427	D₄×C₁₉	—	8	2	no	—
428	D₄×C₁₉	—	8	2	no	—
429	D₄×C₁₉	—	8	2	no	—
430	D₄×C₁₉	—	8	2	no	—
431	D₄×C₁₉	—	8	2	no	—
432	C₂×C₄×C₁₉	—	2	1	no	—
433	C₂×C₄×C₁₉	—	2	2	no	—
434	C₂×C₄×C₁₉	—	2	2	no	—
435	C₂×C₄×C₁₉	—	2	1	no	—
436	C₂×C₄×C₁₉	—	2	2	no	—
437	C₂×C₄×C₁₉	—	2	2	no	—
438	C₂×C₄×C₁₉	—	2	2	no	—
439	C₂×C₄×C₁₉	—	2	2	no	—
440	C₂×C₄×C₁₉	—	2	2	no	—
441	C₂×C₄×C₁₉	—	2	2	no	—
442	C₂×C₄×C₁₉	—	2	2	no	—
443	C₂×C₄×C₁₉	—	4	1	no	—
444	C₂×C₄×C₁₉	—	4	2	no	—
445	C₂×C₄×C₁₉	—	8	2	no	—
446	C₂×C₄×C₁₉	—	8	2	no	—
447	C₂×C₄×C₁₉	—	8	2	no	—
448	C₂×C₄×C₁₉	—	8	2	no	—
449	C₂×C₄×C₁₉	—	8	2	no	—
450	C₂×C₄×C₁₉	—	8	2	no	—
451	C₂×C₄×C₁₉	—	8	2	no	—
452	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
458	C₈×C₁₉	—	2	1	no	—
459	C₈×C₁₉	—	2	2	no	—
460	C₈×C₁₉	—	2	2	no	—
461	C₈×C₁₉	—	2	1	no	—
462	C₈×C₁₉	—	2	1	no	—
463	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
464	#3539	C₂×C₁₉	1	1	yes	characteristic, complemented
465	#3537	C₂×C₁₉	1	1	yes	characteristic, complemented
466	#3355	C₂×C₁₉	1	2	yes	complemented
467	#3351	C₂×C₁₉	1	2	yes	complemented
468	#3318	C₂×C₁₉	1	2	yes	complemented
469	#3310	C₂×C₁₉	1	2	yes	complemented
470	#3309	C₂×C₁₉	1	2	yes	complemented
471	#3307	C₂×C₁₉	1	2	yes	complemented
472	#3274	C₂×C₁₉	1	2	yes	complemented
473	#3272	C₂×C₁₉	1	2	yes	complemented
474	#3260	C₂×C₁₉	1	1	yes	characteristic, complemented
475	#3259	C₂×C₁₉	1	1	yes	characteristic, complemented
476	#3198	C₂×C₁₉	1	2	yes	complemented
477	#3194	C₂×C₁₉	1	2	yes	complemented
478	#3176	C₂×C₁₉	1	1	yes	characteristic, complemented
479	#3174	C₂×C₁₉	1	1	yes	characteristic, complemented
480	#3062	C₂×C₁₉	1	2	yes	complemented
481	#3055	C₂×C₁₉	1	2	yes	complemented
482	#2930	C₂×C₁₉	1	1	yes	characteristic, complemented
483	C₂²×C₁₉	—	2	2	no	—
484	C₂²×C₁₉	—	2	2	no	—
485	C₂²×C₁₉	—	2	2	no	—
486	C₂²×C₁₉	—	2	2	no	—
487	C₂²×C₁₉	—	2	2	no	—
488	C₂²×C₁₉	—	2	1	no	—
489	C₂²×C₁₉	—	2	2	no	—
490	C₂²×C₁₉	—	2	2	no	—
491	C₂²×C₁₉	—	4	2	no	—
492	C₂²×C₁₉	—	4	2	no	—
493	C₂²×C₁₉	—	4	2	no	—
494	C₂²×C₁₉	—	4	2	no	—
495	C₂²×C₁₉	—	4	2	no	—
496	C₂²×C₁₉	—	4	2	no	—
497	C₂²×C₁₉	—	4	2	no	—
498	C₂²×C₁₉	—	4	2	no	—
499	C₂²×C₁₉	—	4	2	no	—
500	C₂²×C₁₉	—	8	2	no	—
501	C₂²×C₁₉	—	16	4	no	—
502	C₂²×C₁₉	—	16	4	no	—
503	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₁₉	—	2	2	no	—
505	C₄×C₁₉	—	2	2	no	—
506	C₄×C₁₉	—	2	2	no	—
507	C₄×C₁₉	—	2	1	no	—
508	C₄×C₁₉	—	2	2	no	—
509	C₄×C₁₉	—	4	2	no	—
510	C₄×C₁₉	—	4	2	no	—
511	C₄×C₁₉	—	4	2	no	—
512	C₄×C₁₉	—	4	2	no	—
513	C₄×C₁₉	—	4	2	no	—
514	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₄×C₁₉	#585	1	1	yes	characteristic
516	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
517	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	complemented
518	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
519	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
520	#560	—	2	2	no	—
521	#560	—	2	2	no	—
522	#553	—	2	2	no	—
523	#553	C₂²×C₁₉	1	2	yes	—
524	#553	C₂²×C₁₉	1	2	yes	—
525	#553	C₂²×C₁₉	1	2	yes	complemented
526	#552	C₂²×C₁₉	1	2	yes	complemented
527	#550	C₂²×C₁₉	1	2	yes	complemented
528	#547	C₂²×C₁₉	1	2	yes	complemented
529	D₄²	—	2	2	no	—
530	D₄²	C₂²×C₁₉	1	2	yes	—
531	D₄²	C₂²×C₁₉	1	2	yes	—
532	#541	C₂²×C₁₉	1	1	yes	characteristic, complemented
533	#540	—	2	2	no	—
534	#540	C₂²×C₁₉	1	1	yes	characteristic
535	#540	C₂²×C₁₉	1	1	yes	characteristic
536	#540	C₂²×C₁₉	1	1	yes	characteristic, complemented
537	#539	—	2	2	no	—
538	#538	—	2	2	no	—
539	#537	C₂²×C₁₉	1	2	yes	complemented
540	#535	C₂²×C₁₉	1	2	yes	—
541	#534	—	2	2	no	—
542	#525	C₂²×C₁₉	1	1	yes	characteristic
543	#525	C₂²×C₁₉	1	2	yes	complemented
544	C₂×#121	C₂²×C₁₉	1	2	yes	—
545	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
546	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
547	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
548	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
549	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
550	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
551	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
552	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
553	#485	C₂²×C₁₉	1	2	yes	complemented
554	#483	C₂²×C₁₉	1	2	yes	complemented
555	#482	C₂²×C₁₉	1	2	yes	complemented
556	#482	C₂²×C₁₉	1	2	yes	complemented
557	#482	C₂²×C₁₉	1	2	yes	complemented
558	#481	C₂²×C₁₉	1	2	yes	complemented
559	#480	C₂²×C₁₉	1	2	yes	complemented
560	#480	C₂²×C₁₉	1	2	yes	complemented
561	#479	C₂²×C₁₉	1	2	yes	complemented
562	#478	C₂²×C₁₉	1	2	yes	complemented
563	#478	C₂²×C₁₉	1	2	yes	complemented
564	#478	C₂²×C₁₉	1	2	yes	complemented
565	#469	C₂²×C₁₉	1	2	yes	complemented
566	#469	C₂²×C₁₉	1	2	yes	complemented
567	#469	C₂²×C₁₉	1	2	yes	complemented
568	#469	C₂²×C₁₉	1	2	yes	complemented
569	#469	C₂²×C₁₉	1	2	yes	complemented
570	#468	C₂²×C₁₉	1	2	yes	complemented
571	#468	C₂²×C₁₉	1	2	yes	complemented
572	#468	C₂²×C₁₉	1	2	yes	complemented
573	#468	C₂²×C₁₉	1	2	yes	complemented
574	#468	C₂²×C₁₉	1	2	yes	complemented
575	#466	C₂²×C₁₉	1	2	yes	complemented
576	#466	C₂²×C₁₉	1	2	yes	complemented
577	#466	C₂²×C₁₉	1	2	yes	complemented
578	#465	C₂²×C₁₉	1	2	yes	complemented
579	#465	C₂²×C₁₉	1	2	yes	complemented
580	#465	C₂²×C₁₉	1	2	yes	complemented
581	#461	C₂²×C₁₉	1	2	yes	complemented
582	#460	C₂²×C₁₉	1	2	yes	complemented
583	#459	C₂²×C₁₉	1	2	yes	complemented
584	#459	C₂²×C₁₉	1	2	yes	complemented
585	#450	C₂²×C₁₉	1	2	yes	complemented
586	#450	C₂²×C₁₉	1	2	yes	complemented
587	#449	C₂²×C₁₉	1	2	yes	complemented
588	#449	C₂²×C₁₉	1	2	yes	complemented
589	#449	C₂²×C₁₉	1	2	yes	complemented
590	#449	C₂²×C₁₉	1	2	yes	complemented
591	#447	C₂²×C₁₉	1	2	yes	complemented
592	#447	C₂²×C₁₉	1	2	yes	complemented
593	#442	C₂²×C₁₉	1	2	yes	complemented
594	#440	C₂²×C₁₉	1	2	yes	complemented
595	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
596	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
597	#436	C₂²×C₁₉	1	2	yes	complemented
598	#436	C₂²×C₁₉	1	2	yes	complemented
599	#435	C₂²×C₁₉	1	2	yes	complemented
600	#435	C₂²×C₁₉	1	2	yes	complemented
601	#428	C₂²×C₁₉	1	2	yes	complemented
602	#428	C₂²×C₁₉	1	2	yes	complemented
603	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
604	#418	C₂²×C₁₉	1	2	yes	complemented
605	#417	C₂²×C₁₉	1	2	yes	complemented
606	#416	C₂²×C₁₉	1	2	yes	complemented
607	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
608	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
609	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
610	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
611	C₂×C₁₉	—	4	1	no	—
612	C₂×C₁₉	—	4	2	no	—
613	C₂×C₁₉	—	4	2	no	—
614	C₂×C₁₉	—	8	2	no	—
615	C₂×C₁₉	—	8	2	no	—
616	C₂×C₁₉	—	8	2	no	—
617	C₂×C₁₉	#3496	1	1	yes	characteristic
618	C₂×C₁₉	#3585	1	2	yes	—
619	C₂×#41	C₂³×C₁₉	1	2	yes	—
620	C₂×#41	C₂³×C₁₉	1	2	yes	—
621	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
622	C₂²×D₄	—	2	2	no	—
623	C₂²×D₄	—	2	2	no	—
624	C₂²×D₄	—	2	2	no	—
625	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
626	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
627	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
628	AGL(1,ℤ/8)	—	4	4	no	—
629	AGL(1,ℤ/8)	—	4	4	no	—
630	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
634	C₂×D₈	C₂³×C₁₉	1	2	yes	—
635	C₂×D₈	C₂³×C₁₉	1	2	yes	—
636	C₂×D₈	C₂³×C₁₉	1	2	yes	—
637	C₂×D₈	C₂³×C₁₉	1	2	yes	—
638	#131	—	4	2	no	—
639	C₂×M₁₆	—	4	2	no	—
640	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
641	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
642	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
643	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
644	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
645	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
646	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
647	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
648	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
649	#127	—	2	2	no	—
650	#127	—	2	2	no	—
651	#127	C₂³×C₁₉	1	1	yes	characteristic
652	#127	C₂³×C₁₉	1	1	yes	characteristic
653	#127	C₂³×C₁₉	1	1	yes	characteristic
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#125	—	2	2	no	—
660	#125	—	2	2	no	—
661	#125	C₂³×C₁₉	1	1	yes	characteristic
662	#125	C₂³×C₁₉	1	1	yes	characteristic
663	#125	C₂³×C₁₉	1	1	yes	characteristic
664	#125	C₂³×C₁₉	1	1	yes	characteristic
665	#124	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	D₄×C₁₉	1	2	yes	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
679	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
680	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
681	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
682	#121	—	2	2	no	—
683	#121	—	2	2	no	—
684	#121	—	2	2	no	—
685	#121	—	2	2	no	—
686	#121	—	2	2	no	—
687	#121	—	2	2	no	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	—	2	2	no	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	D₄×C₁₉	1	2	yes	—
699	#121	C₂³×C₁₉	1	2	yes	—
700	#121	C₂³×C₁₉	1	2	yes	—
701	#121	C₂³×C₁₉	1	2	yes	—
702	#121	C₂³×C₁₉	1	2	yes	—
703	#121	C₂³×C₁₉	1	2	yes	—
704	#121	C₂³×C₁₉	1	2	yes	—
705	#121	C₂³×C₁₉	1	2	yes	—
706	#121	C₂³×C₁₉	1	2	yes	—
707	#121	C₂³×C₁₉	1	2	yes	—
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	#120	—	2	2	no	—
711	#120	—	2	2	no	—
712	#120	—	2	2	no	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	#120	D₄×C₁₉	1	2	yes	—
716	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	C₂³×C₁₉	1	2	yes	—
724	C₄×D₄	C₂³×C₁₉	1	2	yes	—
725	C₄×D₄	C₂³×C₁₉	1	2	yes	—
726	C₄×D₄	C₂³×C₁₉	1	2	yes	—
727	C₄×D₄	C₂³×C₁₉	1	2	yes	—
728	#117	—	2	2	no	—
729	#117	C₂³×C₁₉	1	2	yes	—
730	#117	C₂³×C₁₉	1	2	yes	—
731	#117	C₂³×C₁₉	1	1	yes	characteristic
732	C₂×C₄⋊C₄	—	2	2	no	—
733	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
735	C₂×C₂²⋊C₄	—	2	2	no	—
736	#107	C₂³×C₁₉	1	2	yes	—
737	#107	C₂³×C₁₉	1	2	yes	—
738	#107	C₂³×C₁₉	1	2	yes	—
739	#107	C₂³×C₁₉	1	2	yes	—
740	#106	C₂³×C₁₉	1	2	yes	—
741	#106	C₂³×C₁₉	1	2	yes	—
742	#106	C₂³×C₁₉	1	2	yes	—
743	#106	C₂³×C₁₉	1	2	yes	—
744	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
745	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
746	#103	C₂³×C₁₉	1	2	yes	—
747	#103	C₂³×C₁₉	1	2	yes	—
748	#103	C₂³×C₁₉	1	2	yes	—
749	#103	C₂³×C₁₉	1	2	yes	—
750	#102	C₂³×C₁₉	1	2	yes	—
751	#102	C₂³×C₁₉	1	2	yes	—
752	#102	C₂³×C₁₉	1	2	yes	—
753	#102	C₂³×C₁₉	1	2	yes	—
754	#102	C₂³×C₁₉	1	2	yes	—
755	#102	C₂³×C₁₉	1	2	yes	—
756	#102	C₂³×C₁₉	1	2	yes	—
757	#102	C₂³×C₁₉	1	2	yes	—
758	#102	C₂³×C₁₉	1	2	yes	—
759	#102	C₂³×C₁₉	1	2	yes	—
760	#102	C₂³×C₁₉	1	2	yes	—
761	#102	C₂³×C₁₉	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
766	#97	C₂³×C₁₉	1	1	yes	characteristic
767	#97	C₂³×C₁₉	1	1	yes	characteristic
768	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
769	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
770	C₁₉	#62292	1	1	yes	characteristic, direct product factor, Sylow
771	C₂⁴	—	2	2	no	—
772	C₂⁴	—	2	2	no	—
773	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
774	#41	—	4	1	no	—
775	#41	—	4	1	no	—
776	#41	—	4	2	no	—
777	#41	—	4	2	no	—
778	#41	—	4	2	no	—
779	#41	—	4	2	no	—
780	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
781	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	8	4	no	—
803	C₂×D₄	—	8	4	no	—
804	C₂×D₄	—	8	4	no	—
805	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
806	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
807	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
808	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
809	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
810	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
811	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
822	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
826	SD₁₆	—	2	4	no	—
827	SD₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	D₈	—	2	4	no	—
831	D₈	—	4	2	no	—
832	D₈	—	4	2	no	—
833	D₈	—	4	2	no	—
834	M₁₆	—	2	4	no	—
835	M₁₆	—	2	4	no	—
836	M₁₆	—	4	2	no	—
837	M₁₆	—	4	1	no	—
838	M₁₆	—	4	1	no	—
839	C₂×C₈	—	2	2	no	—
840	C₂×C₈	—	4	1	no	—
841	C₂×C₈	—	4	2	no	—
842	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
843	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
844	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
845	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
846	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
847	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
860	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
861	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
862	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
884	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
885	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
886	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
887	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	2	no	—
891	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
892	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	4	1	no	—
897	C₂³	—	4	2	no	—
898	C₂³	—	4	4	no	—
899	C₂³	—	8	2	no	—
900	C₂³	—	8	2	no	—
901	C₂³	—	8	2	no	—
902	C₂³	—	8	2	no	—
903	C₂³	—	8	2	no	—
904	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
905	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
906	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
907	Q₈	—	2	2	no	—
908	Q₈	—	2	2	no	—
909	Q₈	—	4	1	no	—
910	D₄	—	2	2	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	4	2	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	1	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	4	no	—
922	D₄	—	8	2	no	—
923	D₄	—	8	2	no	—
924	D₄	—	8	2	no	—
925	D₄	—	8	2	no	—
926	D₄	—	8	2	no	—
927	D₄	—	8	2	no	—
928	D₄	—	8	2	no	—
929	D₄	—	8	2	no	—
930	D₄	—	8	2	no	—
931	D₄	—	8	2	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	2	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	2	no	—
949	C₂×C₄	—	8	2	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	—	8	2	no	—
956	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
959	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
960	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
962	C₈	—	2	1	no	—
963	C₈	—	2	2	no	—
964	C₈	—	2	2	no	—
965	C₈	—	2	1	no	—
966	C₈	—	2	1	no	—
967	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	8	2	no	—
986	C₂²	—	16	4	no	—
987	C₂²	—	16	4	no	—
988	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
989	C₄	—	2	2	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	2	no	—
992	C₄	—	2	2	no	—
993	C₄	—	2	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	2	no	—
999	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1000	C₄	C₁₉×#585	1	1	yes	characteristic
1001	C₂	—	4	2	no	—
1002	C₂	—	4	1	no	—
1003	C₂	—	4	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	2	no	—
1006	C₂	—	8	2	no	—
1007	C₂	C₁₉×#3496	1	1	yes	characteristic
1008	C₂	C₁₉×#3585	1	2	yes	—

	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×#3539	C₂	semidirect
2. C₁₉×#3537	C₂	semidirect
3. C₁₉×#3355	C₂	semidirect
4. C₁₉×#3351	C₂	semidirect
5. C₁₉×#3318	C₂	semidirect
6. C₁₉×#3310	C₂	semidirect
7. C₁₉×#3309	C₂	semidirect
8. C₁₉×#3307	C₂	semidirect
9. C₁₉×#3274	C₂	semidirect
10. C₁₉×#3272	C₂	semidirect
11. C₁₉×#3260	C₂	semidirect
12. C₁₉×#3259	C₂	semidirect
13. C₁₉×#3198	C₂	semidirect
14. C₁₉×#3194	C₂	semidirect
15. C₁₉×#3176	C₂	semidirect
16. C₁₉×#3174	C₂	semidirect
17. C₁₉×#3062	C₂	semidirect
18. C₁₉×#3055	C₂	semidirect
19. C₁₉×#2930	C₂	semidirect
20. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₉×#131	C₂²	semidirect
23. C₂²×M₁₆×C₁₉	C₂²	semidirect
29. C₁₉×#553	C₂²	semidirect
30. C₁₉×#552	C₂²	semidirect
31. C₁₉×#550	C₂²	semidirect
32. C₁₉×#547	C₂²	semidirect
36. C₁₉×#541	C₂²	semidirect
40. C₁₉×#540	C₂²	semidirect
43. C₁₉×#537	C₂²	semidirect
47. C₁₉×#525	C₂²	semidirect
49. C₁₉×#499	C₂²	semidirect
50. C₁₉×#499	C₂²	semidirect
51. C₁₉×#493	C₂²	semidirect
52. C₁₉×#492	C₂²	semidirect
53. C₁₉×#491	C₂²	semidirect
54. C₁₉×#490	C₂²	semidirect
55. C₁₉×#490	C₂²	semidirect
56. C₁₉×#490	C₂²	semidirect
57. C₁₉×#485	C₂²	semidirect
58. C₁₉×#483	C₂²	semidirect
59. C₁₉×#482	C₂²	semidirect
60. C₁₉×#482	C₂²	semidirect
61. C₁₉×#482	C₂²	semidirect
62. C₁₉×#481	C₂²	semidirect
63. C₁₉×#480	C₂²	semidirect
64. C₁₉×#480	C₂²	semidirect
65. C₁₉×#479	C₂²	semidirect
66. C₁₉×#478	C₂²	semidirect
67. C₁₉×#478	C₂²	semidirect
68. C₁₉×#478	C₂²	semidirect
69. C₁₉×#469	C₂²	semidirect
70. C₁₉×#469	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×#468	C₂²	semidirect
78. C₁₉×#468	C₂²	semidirect
79. C₁₉×#466	C₂²	semidirect
80. C₁₉×#466	C₂²	semidirect
81. C₁₉×#466	C₂²	semidirect
82. C₁₉×#465	C₂²	semidirect
83. C₁₉×#465	C₂²	semidirect
84. C₁₉×#465	C₂²	semidirect
85. C₁₉×#461	C₂²	semidirect
86. C₁₉×#460	C₂²	semidirect
87. C₁₉×#459	C₂²	semidirect
88. C₁₉×#459	C₂²	semidirect
89. C₁₉×#450	C₂²	semidirect
90. C₁₉×#450	C₂²	semidirect
91. C₁₉×#449	C₂²	semidirect
92. C₁₉×#449	C₂²	semidirect
93. C₁₉×#449	C₂²	semidirect
94. C₁₉×#449	C₂²	semidirect
95. C₁₉×#447	C₂²	semidirect
96. C₁₉×#447	C₂²	semidirect
97. C₁₉×#442	C₂²	semidirect
98. C₁₉×#440	C₂²	semidirect
99. C₄×SD₁₆×C₁₉	C₂²	semidirect
100. C₄×D₈×C₁₉	C₂²	semidirect
101. C₁₉×#436	C₂²	semidirect
102. C₁₉×#436	C₂²	semidirect
103. C₁₉×#435	C₂²	semidirect
104. C₁₉×#435	C₂²	semidirect
105. C₁₉×#428	C₂²	semidirect
106. C₁₉×#428	C₂²	semidirect
107. C₁₉×#424	C₂²	semidirect
108. C₁₉×#418	C₂²	semidirect
109. C₁₉×#417	C₂²	semidirect
110. C₁₉×#416	C₂²	semidirect
111. C₂×C₁₉×#102	C₂²	semidirect
112. C₁₉×#408	C₂²	semidirect
113. C₁₉×#407	C₂²	semidirect
114. C₁₉×#405	C₂²	semidirect
388. #62292	C₁₉	direct (N × H)
464. #3539	C₂×C₁₉	semidirect
465. #3537	C₂×C₁₉	semidirect
466. #3355	C₂×C₁₉	semidirect
467. #3351	C₂×C₁₉	semidirect
468. #3318	C₂×C₁₉	semidirect
469. #3310	C₂×C₁₉	semidirect
470. #3309	C₂×C₁₉	semidirect
471. #3307	C₂×C₁₉	semidirect
472. #3274	C₂×C₁₉	semidirect
473. #3272	C₂×C₁₉	semidirect
474. #3260	C₂×C₁₉	semidirect
475. #3259	C₂×C₁₉	semidirect
476. #3198	C₂×C₁₉	semidirect
477. #3194	C₂×C₁₉	semidirect
478. #3176	C₂×C₁₉	semidirect
479. #3174	C₂×C₁₉	semidirect
480. #3062	C₂×C₁₉	semidirect
481. #3055	C₂×C₁₉	semidirect
482. #2930	C₂×C₁₉	semidirect
516. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
517. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
518. C₂×#131	C₂²×C₁₉	semidirect
519. C₂²×M₁₆	C₂²×C₁₉	semidirect
525. #553	C₂²×C₁₉	semidirect
526. #552	C₂²×C₁₉	semidirect
527. #550	C₂²×C₁₉	semidirect
528. #547	C₂²×C₁₉	semidirect
532. #541	C₂²×C₁₉	semidirect
536. #540	C₂²×C₁₉	semidirect
539. #537	C₂²×C₁₉	semidirect
543. #525	C₂²×C₁₉	semidirect
545. #499	C₂²×C₁₉	semidirect
546. #499	C₂²×C₁₉	semidirect
547. #493	C₂²×C₁₉	semidirect
548. #492	C₂²×C₁₉	semidirect
549. #491	C₂²×C₁₉	semidirect
550. #490	C₂²×C₁₉	semidirect
551. #490	C₂²×C₁₉	semidirect
552. #490	C₂²×C₁₉	semidirect
553. #485	C₂²×C₁₉	semidirect
554. #483	C₂²×C₁₉	semidirect
555. #482	C₂²×C₁₉	semidirect
556. #482	C₂²×C₁₉	semidirect
557. #482	C₂²×C₁₉	semidirect
558. #481	C₂²×C₁₉	semidirect
559. #480	C₂²×C₁₉	semidirect
560. #480	C₂²×C₁₉	semidirect
561. #479	C₂²×C₁₉	semidirect
562. #478	C₂²×C₁₉	semidirect
563. #478	C₂²×C₁₉	semidirect
564. #478	C₂²×C₁₉	semidirect
565. #469	C₂²×C₁₉	semidirect
566. #469	C₂²×C₁₉	semidirect
567. #469	C₂²×C₁₉	semidirect
568. #469	C₂²×C₁₉	semidirect
569. #469	C₂²×C₁₉	semidirect
570. #468	C₂²×C₁₉	semidirect
571. #468	C₂²×C₁₉	semidirect
572. #468	C₂²×C₁₉	semidirect
573. #468	C₂²×C₁₉	semidirect
574. #468	C₂²×C₁₉	semidirect
575. #466	C₂²×C₁₉	semidirect
576. #466	C₂²×C₁₉	semidirect
577. #466	C₂²×C₁₉	semidirect
578. #465	C₂²×C₁₉	semidirect
579. #465	C₂²×C₁₉	semidirect
580. #465	C₂²×C₁₉	semidirect
581. #461	C₂²×C₁₉	semidirect
582. #460	C₂²×C₁₉	semidirect
583. #459	C₂²×C₁₉	semidirect
584. #459	C₂²×C₁₉	semidirect
585. #450	C₂²×C₁₉	semidirect
586. #450	C₂²×C₁₉	semidirect
587. #449	C₂²×C₁₉	semidirect
588. #449	C₂²×C₁₉	semidirect
589. #449	C₂²×C₁₉	semidirect
590. #449	C₂²×C₁₉	semidirect
591. #447	C₂²×C₁₉	semidirect
592. #447	C₂²×C₁₉	semidirect
593. #442	C₂²×C₁₉	semidirect
594. #440	C₂²×C₁₉	semidirect
595. C₄×SD₁₆	C₂²×C₁₉	semidirect
596. C₄×D₈	C₂²×C₁₉	semidirect
597. #436	C₂²×C₁₉	semidirect
598. #436	C₂²×C₁₉	semidirect
599. #435	C₂²×C₁₉	semidirect
600. #435	C₂²×C₁₉	semidirect
601. #428	C₂²×C₁₉	semidirect
602. #428	C₂²×C₁₉	semidirect
603. #424	C₂²×C₁₉	semidirect
604. #418	C₂²×C₁₉	semidirect
605. #417	C₂²×C₁₉	semidirect
606. #416	C₂²×C₁₉	semidirect
607. C₂×#102	C₂²×C₁₉	semidirect
608. #408	C₂²×C₁₉	semidirect
609. #407	C₂²×C₁₉	semidirect
610. #405	C₂²×C₁₉	semidirect
770. C₁₉	#62292	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×#3539	2
C₁₉×#3537	2
C₁₉×#3355	2
C₁₉×#3351	2
C₁₉×#3318	2
C₁₉×#3310	2
C₁₉×#3309	2
C₁₉×#3307	2
C₁₉×#3274	2
C₁₉×#3272	2
C₁₉×#3260	2
C₁₉×#3259	2
C₁₉×#3198	2
C₁₉×#3194	2
C₁₉×#3176	2
C₁₉×#3174	2
C₁₉×#3062	2
C₁₉×#3055	2
C₁₉×#2930	2
#62292	19

Subgroups — C19×#62292 #18068251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62292 #18068251