Subgroups — C₁₉×#61159 #18067118

Order 4864.

2120 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3331	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3330	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3315	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3307	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3303	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3302	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3095	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3056	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3005	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₉	C₂²	1	2	yes	—
19	C₂×C₁₉×#137	C₂²	1	2	yes	—
20	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#556	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#555	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#553	C₂²	1	2	yes	complemented
26	C₁₉×#552	—	2	1	no	—
27	C₁₉×#552	C₂²	1	2	yes	complemented
28	C₁₉×#551	—	2	2	no	—
29	C₁₉×#547	—	2	1	no	—
30	C₁₉×#547	—	2	1	no	—
31	C₁₉×#547	—	2	2	no	—
32	C₁₉×#547	C₂²	1	2	yes	—
33	C₁₉×#547	C₂²	1	4	yes	—
34	C₁₉×#547	C₂²	1	2	yes	—
35	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#546	—	2	1	no	—
37	C₁₉×#533	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₁₉×#529	—	2	2	no	—
40	C₁₉×#529	—	2	1	no	—
41	C₁₉×#525	C₂²	1	2	yes	—
42	C₂×C₁₉×#123	—	2	2	no	—
43	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₁₉×#121	—	2	1	no	—
45	C₄×#41×C₁₉	—	2	1	no	—
46	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#117	C₂²	1	2	yes	—
50	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₁₉×#491	C₂²	1	4	yes	complemented
52	C₁₉×#487	C₂²	1	2	yes	complemented
53	C₁₉×#487	C₂²	1	2	yes	complemented
54	C₁₉×#485	C₂²	1	4	yes	complemented
55	C₁₉×#485	C₂²	1	4	yes	complemented
56	C₁₉×#484	C₂²	1	4	yes	complemented
57	C₁₉×#483	C₂²	1	4	yes	complemented
58	C₁₉×#478	C₂²	1	4	yes	complemented
59	C₁₉×#476	C₂²	1	2	yes	complemented
60	C₁₉×#474	C₂²	1	2	yes	complemented
61	C₁₉×#470	C₂²	1	4	yes	complemented
62	C₁₉×#468	C₂²	1	4	yes	complemented
63	C₁₉×#467	C₂²	1	4	yes	complemented
64	C₁₉×#465	C₂²	1	4	yes	complemented
65	C₁₉×#462	C₂²	1	2	yes	complemented
66	C₁₉×#462	C₂²	1	2	yes	complemented
67	C₁₉×#461	C₂²	1	2	yes	complemented
68	C₁₉×#461	C₂²	1	2	yes	complemented
69	C₁₉×#452	C₂²	1	4	yes	complemented
70	C₁₉×#452	C₂²	1	4	yes	complemented
71	C₁₉×#449	C₂²	1	4	yes	complemented
72	C₁₉×#449	C₂²	1	4	yes	complemented
73	C₁₉×#442	C₂²	1	2	yes	complemented
74	C₁₉×#440	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
76	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
77	C₁₉×#436	C₂²	1	2	yes	complemented
78	C₁₉×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
80	C₁₉×#428	C₂²	1	1	yes	characteristic
81	C₁₉×#428	C₂²	1	2	yes	—
82	C₁₉×#423	C₂²	1	1	yes	characteristic
83	C₁₉×#419	C₂²	1	2	yes	—
84	C₁₉×#419	C₂²	1	2	yes	—
85	C₁₉×#419	C₂²	1	2	yes	—
86	C₁₉×#418	C₂²	1	1	yes	characteristic
87	C₁₉×#418	C₂²	1	2	yes	—
88	C₁₉×#417	C₂²	1	1	yes	characteristic
89	C₁₉×#417	C₂²	1	4	yes	complemented
90	C₁₉×#417	C₂²	1	4	yes	complemented
91	C₁₉×#416	C₂²	1	4	yes	complemented
92	C₁₉×#416	C₂²	1	4	yes	complemented
93	C₁₉×#407	C₂²	1	2	yes	—
94	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
95	C₂×#41×C₁₉	—	2	1	no	—
96	C₂×#41×C₁₉	—	2	2	no	—
97	C₂×#41×C₁₉	—	2	2	no	—
98	C₂×#41×C₁₉	—	2	8	no	—
99	C₂×#41×C₁₉	—	4	4	no	—
100	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×#41×C₁₉	C₂³	1	4	yes	—
102	C₂×#41×C₁₉	C₂³	1	4	yes	—
103	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₉	—	2	2	no	—
105	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₉	—	2	1	no	—
108	C₂³×C₄×C₁₉	—	2	2	no	—
109	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
110	C₁₉×#137	—	4	4	no	—
111	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
112	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
115	C₂×D₈×C₁₉	C₂³	1	2	yes	—
116	C₂×M₁₆×C₁₉	—	4	4	no	—
117	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
120	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
121	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
122	C₁₉×C₄⋊Q₈	—	2	1	no	—
123	C₁₉×C₄⋊Q₈	—	2	1	no	—
124	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₉×#126	—	2	2	no	—
129	C₁₉×#126	—	2	2	no	—
130	C₁₉×#126	—	2	2	no	—
131	C₁₉×#125	—	2	2	no	—
132	C₁₉×#125	—	2	1	no	—
133	C₁₉×#125	C₂³	1	2	yes	—
134	C₁₉×#124	—	2	1	no	—
135	C₁₉×#124	—	2	2	no	—
136	C₁₉×#123	—	2	2	no	—
137	C₁₉×#123	—	2	2	no	—
138	C₁₉×#123	—	2	4	no	—
139	C₁₉×#123	—	2	4	no	—
140	C₁₉×#123	—	2	4	no	—
141	C₁₉×#123	—	2	4	no	—
142	C₁₉×#123	—	2	2	no	—
143	C₁₉×#123	—	2	2	no	—
144	C₁₉×C₂²⋊Q₈	—	2	2	no	—
145	C₁₉×C₂²⋊Q₈	—	2	2	no	—
146	C₁₉×C₂²⋊Q₈	—	2	1	no	—
147	C₁₉×C₂²⋊Q₈	—	2	1	no	—
148	C₁₉×C₂²⋊Q₈	—	2	1	no	—
149	C₁₉×C₂²⋊Q₈	—	2	2	no	—
150	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₉×#121	—	2	2	no	—
155	C₁₉×#121	—	2	2	no	—
156	C₁₉×#121	—	2	4	no	—
157	C₁₉×#121	—	2	2	no	—
158	C₁₉×#121	—	2	1	no	—
159	C₁₉×#121	C₂³	1	2	yes	—
160	C₁₉×#121	C₂³	1	2	yes	—
161	C₁₉×#120	—	2	2	no	—
162	C₄×Q₈×C₁₉	—	2	1	no	—
163	C₄×Q₈×C₁₉	—	2	1	no	—
164	C₄×Q₈×C₁₉	—	2	1	no	—
165	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₁₉	—	2	1	no	—
168	C₄×D₄×C₁₉	—	2	2	no	—
169	C₄×D₄×C₁₉	—	2	1	no	—
170	C₄×D₄×C₁₉	—	2	1	no	—
171	C₄×D₄×C₁₉	—	2	2	no	—
172	C₄×D₄×C₁₉	—	2	2	no	—
173	C₄×D₄×C₁₉	—	2	1	no	—
174	C₄×D₄×C₁₉	—	2	1	no	—
175	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
176	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
177	C₄×D₄×C₁₉	D₄	1	2	yes	—
178	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₉	C₂³	1	2	yes	—
180	C₄×D₄×C₁₉	C₂³	1	2	yes	—
181	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₉	C₂³	1	2	yes	—
184	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
185	C₁₉×#117	—	2	2	no	—
186	C₁₉×#117	—	2	2	no	—
187	C₁₉×#117	—	2	1	no	—
188	C₁₉×#117	—	2	2	no	—
189	C₁₉×#117	—	2	1	no	—
190	C₁₉×#117	C₂³	1	2	yes	—
191	C₁₉×#117	C₂³	1	2	yes	—
192	C₁₉×#117	C₂³	1	1	yes	characteristic
193	C₁₉×#117	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
200	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
208	C₂×C₄²×C₁₉	—	2	2	no	—
209	C₂×C₄²×C₁₉	—	2	1	no	—
210	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
211	C₁₉×#107	C₂³	1	2	yes	—
212	C₁₉×#107	C₂³	1	4	yes	—
213	C₁₉×#106	C₂³	1	2	yes	—
214	C₁₉×#106	C₂³	1	4	yes	—
215	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₉×#103	C₂³	1	4	yes	—
218	C₁₉×#103	C₂³	1	4	yes	—
219	C₁₉×#103	C₂³	1	4	yes	—
220	C₁₉×#103	C₂³	1	4	yes	—
221	C₁₉×#103	C₂³	1	2	yes	—
222	C₁₉×#103	C₂³	1	4	yes	—
223	C₁₉×#103	C₂³	1	4	yes	—
224	C₁₉×#102	C₂³	1	2	yes	—
225	C₁₉×#102	C₂³	1	2	yes	—
226	C₁₉×#102	C₂³	1	4	yes	—
227	C₁₉×#102	C₂³	1	4	yes	—
228	C₁₉×#102	C₂³	1	2	yes	—
229	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₉×#97	C₂³	1	2	yes	—
232	C₄×C₈×C₁₉	C₂³	1	2	yes	—
233	C₂⁴×C₁₉	—	2	1	no	—
234	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
235	#41×C₁₉	—	2	8	no	—
236	#41×C₁₉	—	2	8	no	—
237	#41×C₁₉	—	2	2	no	—
238	#41×C₁₉	—	2	2	no	—
239	#41×C₁₉	—	4	4	no	—
240	#41×C₁₉	—	4	4	no	—
241	#41×C₁₉	—	4	8	no	—
242	#41×C₁₉	—	4	8	no	—
243	#41×C₁₉	—	4	4	no	—
244	C₂×Q₈×C₁₉	—	2	1	no	—
245	C₂×Q₈×C₁₉	—	2	2	no	—
246	C₂×Q₈×C₁₉	—	2	1	no	—
247	C₂×Q₈×C₁₉	—	2	4	no	—
248	C₂×Q₈×C₁₉	—	2	4	no	—
249	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
251	C₂×D₄×C₁₉	—	2	1	no	—
252	C₂×D₄×C₁₉	—	2	2	no	—
253	C₂×D₄×C₁₉	—	2	4	no	—
254	C₂×D₄×C₁₉	—	2	4	no	—
255	C₂×D₄×C₁₉	—	2	2	no	—
256	C₂×D₄×C₁₉	—	2	1	no	—
257	C₂×D₄×C₁₉	—	2	2	no	—
258	C₂×D₄×C₁₉	—	4	2	no	—
259	C₂×D₄×C₁₉	—	4	8	no	—
260	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₁₉	#41	1	4	yes	complemented
264	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
265	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₉	—	2	4	no	—
267	C₂²×C₄×C₁₉	—	2	4	no	—
268	C₂²×C₄×C₁₉	—	2	2	no	—
269	C₂²×C₄×C₁₉	—	2	1	no	—
270	C₂²×C₄×C₁₉	—	2	2	no	—
271	C₂²×C₄×C₁₉	—	2	2	no	—
272	C₂²×C₄×C₁₉	—	2	1	no	—
273	C₂²×C₄×C₁₉	—	2	1	no	—
274	C₂²×C₄×C₁₉	—	2	2	no	—
275	C₂²×C₄×C₁₉	—	2	2	no	—
276	C₂²×C₄×C₁₉	—	2	4	no	—
277	C₂²×C₄×C₁₉	—	2	4	no	—
278	C₂²×C₄×C₁₉	—	2	1	no	—
279	C₂²×C₄×C₁₉	—	4	8	no	—
280	C₂²×C₄×C₁₉	—	4	4	no	—
281	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
289	Q₁₆×C₁₉	—	4	4	no	—
290	SD₁₆×C₁₉	—	2	4	no	—
291	SD₁₆×C₁₉	—	4	4	no	—
292	D₈×C₁₉	—	2	4	no	—
293	M₁₆×C₁₉	—	2	2	no	—
294	M₁₆×C₁₉	—	2	2	no	—
295	M₁₆×C₁₉	—	2	4	no	—
296	M₁₆×C₁₉	—	4	4	no	—
297	C₂×C₈×C₁₉	—	4	4	no	—
298	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
300	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₁₉	—	2	2	no	—
302	C₄⋊C₄×C₁₉	—	2	2	no	—
303	C₄⋊C₄×C₁₉	—	2	4	no	—
304	C₄⋊C₄×C₁₉	—	2	4	no	—
305	C₄⋊C₄×C₁₉	—	2	2	no	—
306	C₄⋊C₄×C₁₉	—	2	2	no	—
307	C₄⋊C₄×C₁₉	—	2	2	no	—
308	C₄⋊C₄×C₁₉	—	2	2	no	—
309	C₄⋊C₄×C₁₉	—	2	1	no	—
310	C₄⋊C₄×C₁₉	—	2	1	no	—
311	C₄⋊C₄×C₁₉	—	2	2	no	—
312	C₄⋊C₄×C₁₉	—	2	2	no	—
313	C₄⋊C₄×C₁₉	—	2	1	no	—
314	C₄⋊C₄×C₁₉	—	2	1	no	—
315	C₄⋊C₄×C₁₉	—	2	2	no	—
316	C₄⋊C₄×C₁₉	—	2	2	no	—
317	C₄⋊C₄×C₁₉	—	2	1	no	—
318	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
321	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
326	C₂²⋊C₄×C₁₉	—	2	1	no	—
327	C₂²⋊C₄×C₁₉	—	2	2	no	—
328	C₂²⋊C₄×C₁₉	—	2	2	no	—
329	C₂²⋊C₄×C₁₉	—	2	2	no	—
330	C₂²⋊C₄×C₁₉	—	2	4	no	—
331	C₂²⋊C₄×C₁₉	—	2	4	no	—
332	C₂²⋊C₄×C₁₉	—	2	2	no	—
333	C₂²⋊C₄×C₁₉	—	2	2	no	—
334	C₂²⋊C₄×C₁₉	—	2	2	no	—
335	C₂²⋊C₄×C₁₉	—	2	2	no	—
336	C₂²⋊C₄×C₁₉	—	2	2	no	—
337	C₂²⋊C₄×C₁₉	—	2	1	no	—
338	C₂²⋊C₄×C₁₉	—	2	1	no	—
339	C₂²⋊C₄×C₁₉	—	2	2	no	—
340	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
344	C₄²×C₁₉	—	2	1	no	—
345	C₄²×C₁₉	—	2	2	no	—
346	C₄²×C₁₉	—	2	1	no	—
347	C₄²×C₁₉	—	2	2	no	—
348	C₄²×C₁₉	—	2	2	no	—
349	C₄²×C₁₉	—	2	1	no	—
350	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
353	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
354	#61159	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂³×C₁₉	—	2	4	no	—
356	C₂³×C₁₉	—	2	2	no	—
357	C₂³×C₁₉	—	2	4	no	—
358	C₂³×C₁₉	—	2	1	no	—
359	C₂³×C₁₉	—	4	2	no	—
360	C₂³×C₁₉	—	4	2	no	—
361	C₂³×C₁₉	—	4	2	no	—
362	C₂³×C₁₉	—	4	2	no	—
363	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
364	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
365	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₁₉	—	2	1	no	—
367	Q₈×C₁₉	—	2	4	no	—
368	Q₈×C₁₉	—	2	4	no	—
369	Q₈×C₁₉	—	2	1	no	—
370	Q₈×C₁₉	—	4	4	no	—
371	Q₈×C₁₉	—	4	2	no	—
372	Q₈×C₁₉	—	8	1	no	—
373	D₄×C₁₉	—	2	4	no	—
374	D₄×C₁₉	—	2	2	no	—
375	D₄×C₁₉	—	2	2	no	—
376	D₄×C₁₉	—	2	1	no	—
377	D₄×C₁₉	—	2	2	no	—
378	D₄×C₁₉	—	2	1	no	—
379	D₄×C₁₉	—	4	2	no	—
380	D₄×C₁₉	—	4	8	no	—
381	D₄×C₁₉	—	4	8	no	—
382	D₄×C₁₉	—	4	4	no	—
383	D₄×C₁₉	—	4	2	no	—
384	D₄×C₁₉	—	8	2	no	—
385	D₄×C₁₉	C₂×#41	1	4	yes	—
386	C₂×C₄×C₁₉	—	2	4	no	—
387	C₂×C₄×C₁₉	—	2	4	no	—
388	C₂×C₄×C₁₉	—	2	4	no	—
389	C₂×C₄×C₁₉	—	2	2	no	—
390	C₂×C₄×C₁₉	—	2	2	no	—
391	C₂×C₄×C₁₉	—	2	2	no	—
392	C₂×C₄×C₁₉	—	2	2	no	—
393	C₂×C₄×C₁₉	—	2	2	no	—
394	C₂×C₄×C₁₉	—	2	1	no	—
395	C₂×C₄×C₁₉	—	2	1	no	—
396	C₂×C₄×C₁₉	—	2	1	no	—
397	C₂×C₄×C₁₉	—	2	2	no	—
398	C₂×C₄×C₁₉	—	2	2	no	—
399	C₂×C₄×C₁₉	—	2	2	no	—
400	C₂×C₄×C₁₉	—	2	4	no	—
401	C₂×C₄×C₁₉	—	4	1	no	—
402	C₂×C₄×C₁₉	—	4	8	no	—
403	C₂×C₄×C₁₉	—	4	8	no	—
404	C₂×C₄×C₁₉	—	4	4	no	—
405	C₂×C₄×C₁₉	—	4	2	no	—
406	C₂×C₄×C₁₉	—	4	4	no	—
407	C₂×C₄×C₁₉	—	4	4	no	—
408	C₂×C₄×C₁₉	—	4	2	no	—
409	C₂×C₄×C₁₉	—	4	4	no	—
410	C₂×C₄×C₁₉	—	4	2	no	—
411	C₂×C₄×C₁₉	—	8	1	no	—
412	C₂×C₄×C₁₉	—	8	2	no	—
413	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
421	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
423	C₈×C₁₉	—	2	2	no	—
424	C₈×C₁₉	—	2	2	no	—
425	C₈×C₁₉	—	2	4	no	—
426	#3475	C₂×C₁₉	1	1	yes	characteristic, complemented
427	C₂×#547	C₂×C₁₉	1	1	yes	characteristic, complemented
428	#3331	C₂×C₁₉	1	2	yes	complemented
429	#3330	C₂×C₁₉	1	2	yes	complemented
430	#3315	C₂×C₁₉	1	4	yes	complemented
431	#3307	C₂×C₁₉	1	4	yes	complemented
432	#3303	C₂×C₁₉	1	2	yes	complemented
433	#3302	C₂×C₁₉	1	2	yes	complemented
434	#3139	C₂×C₁₉	1	1	yes	characteristic, complemented
435	#3095	C₂×C₁₉	1	2	yes	complemented
436	#3077	C₂×C₁₉	1	1	yes	characteristic, complemented
437	#3056	C₂×C₁₉	1	2	yes	complemented
438	#3039	C₂×C₁₉	1	1	yes	characteristic, complemented
439	#3005	C₂×C₁₉	1	2	yes	complemented
440	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic, complemented
441	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
442	#2896	C₂×C₁₉	1	2	yes	complemented
443	C₂²×C₁₉	—	2	1	no	—
444	C₂²×C₁₉	—	2	1	no	—
445	C₂²×C₁₉	—	2	2	no	—
446	C₂²×C₁₉	—	2	2	no	—
447	C₂²×C₁₉	—	2	2	no	—
448	C₂²×C₁₉	—	2	2	no	—
449	C₂²×C₁₉	—	2	4	no	—
450	C₂²×C₁₉	—	2	2	no	—
451	C₂²×C₁₉	—	2	2	no	—
452	C₂²×C₁₉	—	4	8	no	—
453	C₂²×C₁₉	—	4	2	no	—
454	C₂²×C₁₉	—	4	2	no	—
455	C₂²×C₁₉	—	4	1	no	—
456	C₂²×C₁₉	—	4	1	no	—
457	C₂²×C₁₉	—	4	1	no	—
458	C₂²×C₁₉	—	8	4	no	—
459	C₂²×C₁₉	#546	1	2	yes	—
460	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₁₉	—	2	1	no	—
462	C₄×C₁₉	—	2	1	no	—
463	C₄×C₁₉	—	2	2	no	—
464	C₄×C₁₉	—	2	2	no	—
465	C₄×C₁₉	—	2	1	no	—
466	C₄×C₁₉	—	4	1	no	—
467	C₄×C₁₉	—	4	2	no	—
468	C₄×C₁₉	—	4	4	no	—
469	C₄×C₁₉	—	4	1	no	—
470	C₄×C₁₉	—	4	1	no	—
471	C₄×C₁₉	—	4	2	no	—
472	C₄×C₁₉	—	4	2	no	—
473	C₄×C₁₉	#546	1	2	yes	—
474	C₄×C₁₉	#575	1	2	yes	—
475	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
476	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂²×#41	C₂²×C₁₉	1	2	yes	—
478	C₂×#137	C₂²×C₁₉	1	2	yes	—
479	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
480	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
481	#556	C₂²×C₁₉	1	1	yes	characteristic, complemented
482	#555	C₂²×C₁₉	1	1	yes	characteristic, complemented
483	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
484	#553	C₂²×C₁₉	1	2	yes	complemented
485	#552	—	2	1	no	—
486	#552	C₂²×C₁₉	1	2	yes	complemented
487	#551	—	2	2	no	—
488	#547	—	2	1	no	—
489	#547	—	2	1	no	—
490	#547	—	2	2	no	—
491	#547	C₂²×C₁₉	1	2	yes	—
492	#547	C₂²×C₁₉	1	2	yes	—
493	#547	C₂²×C₁₉	1	4	yes	—
494	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
495	#546	—	2	1	no	—
496	#533	C₂²×C₁₉	1	1	yes	characteristic
497	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
498	#529	—	2	2	no	—
499	#529	—	2	1	no	—
500	#525	C₂²×C₁₉	1	2	yes	—
501	C₂×#123	—	2	2	no	—
502	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
503	C₂×#121	—	2	1	no	—
504	C₄×#41	—	2	1	no	—
505	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
508	C₂×#117	C₂²×C₁₉	1	2	yes	—
509	C₂²×C₄⋊C₄	—	2	1	no	—
510	#491	C₂²×C₁₉	1	4	yes	complemented
511	#487	C₂²×C₁₉	1	2	yes	complemented
512	#487	C₂²×C₁₉	1	2	yes	complemented
513	#485	C₂²×C₁₉	1	4	yes	complemented
514	#485	C₂²×C₁₉	1	4	yes	complemented
515	#484	C₂²×C₁₉	1	4	yes	complemented
516	#483	C₂²×C₁₉	1	4	yes	complemented
517	#478	C₂²×C₁₉	1	4	yes	complemented
518	#476	C₂²×C₁₉	1	2	yes	complemented
519	#474	C₂²×C₁₉	1	2	yes	complemented
520	#470	C₂²×C₁₉	1	4	yes	complemented
521	#468	C₂²×C₁₉	1	4	yes	complemented
522	#467	C₂²×C₁₉	1	4	yes	complemented
523	#465	C₂²×C₁₉	1	4	yes	complemented
524	#462	C₂²×C₁₉	1	2	yes	complemented
525	#462	C₂²×C₁₉	1	2	yes	complemented
526	#461	C₂²×C₁₉	1	2	yes	complemented
527	#461	C₂²×C₁₉	1	2	yes	complemented
528	#452	C₂²×C₁₉	1	4	yes	complemented
529	#452	C₂²×C₁₉	1	4	yes	complemented
530	#449	C₂²×C₁₉	1	4	yes	complemented
531	#449	C₂²×C₁₉	1	4	yes	complemented
532	#442	C₂²×C₁₉	1	2	yes	complemented
533	#440	C₂²×C₁₉	1	2	yes	complemented
534	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
535	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
536	#436	C₂²×C₁₉	1	2	yes	complemented
537	#435	C₂²×C₁₉	1	4	yes	complemented
538	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
539	#428	C₂²×C₁₉	1	2	yes	—
540	#428	C₂²×C₁₉	1	1	yes	characteristic
541	#423	C₂²×C₁₉	1	1	yes	characteristic
542	#419	C₂²×C₁₉	1	2	yes	—
543	#419	C₂²×C₁₉	1	2	yes	—
544	#419	C₂²×C₁₉	1	2	yes	—
545	#418	C₂²×C₁₉	1	2	yes	—
546	#418	C₂²×C₁₉	1	1	yes	characteristic
547	#417	C₂²×C₁₉	1	1	yes	characteristic
548	#417	C₂²×C₁₉	1	4	yes	complemented
549	#417	C₂²×C₁₉	1	4	yes	complemented
550	#416	C₂²×C₁₉	1	4	yes	complemented
551	#416	C₂²×C₁₉	1	4	yes	complemented
552	#407	C₂²×C₁₉	1	2	yes	—
553	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
554	C₂×C₁₉	—	2	2	no	—
555	C₂×C₁₉	—	4	2	no	—
556	C₂×C₁₉	—	4	2	no	—
557	C₂×C₁₉	—	4	4	no	—
558	C₂×C₁₉	—	8	1	no	—
559	C₂×C₁₉	C₂×#546	1	1	yes	characteristic
560	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
561	C₂×C₁₉	#3586	1	1	yes	characteristic
562	C₂×#41	—	2	1	no	—
563	C₂×#41	—	2	2	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	8	no	—
566	C₂×#41	—	4	4	no	—
567	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
568	C₂×#41	C₂³×C₁₉	1	4	yes	—
569	C₂×#41	C₂³×C₁₉	1	4	yes	—
570	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
571	C₂²×D₄	—	2	2	no	—
572	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	—	2	2	no	—
576	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
577	#137	—	4	4	no	—
578	AGL(1,ℤ/8)	—	2	4	no	—
579	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
582	C₂×D₈	C₂³×C₁₉	1	2	yes	—
583	C₂×M₁₆	—	4	4	no	—
584	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
586	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
587	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
588	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
589	C₄⋊Q₈	—	2	1	no	—
590	C₄⋊Q₈	—	2	1	no	—
591	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
593	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
594	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#125	—	2	2	no	—
599	#125	—	2	1	no	—
600	#125	C₂³×C₁₉	1	2	yes	—
601	#124	—	2	1	no	—
602	#124	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	4	no	—
606	#123	—	2	4	no	—
607	#123	—	2	4	no	—
608	#123	—	2	4	no	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	1	no	—
614	C₂²⋊Q₈	—	2	1	no	—
615	C₂²⋊Q₈	—	2	1	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
618	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
619	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
620	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
621	#121	—	2	2	no	—
622	#121	—	2	2	no	—
623	#121	—	2	4	no	—
624	#121	—	2	2	no	—
625	#121	—	2	1	no	—
626	#121	C₂³×C₁₉	1	2	yes	—
627	#121	C₂³×C₁₉	1	2	yes	—
628	#120	—	2	2	no	—
629	C₄×Q₈	—	2	1	no	—
630	C₄×Q₈	—	2	1	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
633	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
643	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
644	C₄×D₄	D₄×C₁₉	1	2	yes	—
645	C₄×D₄	C₂³×C₁₉	1	2	yes	—
646	C₄×D₄	C₂³×C₁₉	1	2	yes	—
647	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
648	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
649	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₁₉	1	2	yes	—
651	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
652	#117	—	2	2	no	—
653	#117	—	2	2	no	—
654	#117	—	2	1	no	—
655	#117	—	2	2	no	—
656	#117	—	2	1	no	—
657	#117	C₂³×C₁₉	1	1	yes	characteristic
658	#117	C₂³×C₁₉	1	2	yes	—
659	#117	C₂³×C₁₉	1	2	yes	—
660	#117	C₂³×C₁₉	1	2	yes	—
661	C₂×C₄⋊C₄	—	2	1	no	—
662	C₂×C₄⋊C₄	—	2	2	no	—
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	—	2	4	no	—
667	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	—	2	2	no	—
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₂²⋊C₄	—	2	1	no	—
674	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
675	C₂×C₄²	—	2	2	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
678	#107	C₂³×C₁₉	1	2	yes	—
679	#107	C₂³×C₁₉	1	4	yes	—
680	#106	C₂³×C₁₉	1	2	yes	—
681	#106	C₂³×C₁₉	1	4	yes	—
682	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
683	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
684	#103	C₂³×C₁₉	1	4	yes	—
685	#103	C₂³×C₁₉	1	4	yes	—
686	#103	C₂³×C₁₉	1	4	yes	—
687	#103	C₂³×C₁₉	1	4	yes	—
688	#103	C₂³×C₁₉	1	2	yes	—
689	#103	C₂³×C₁₉	1	4	yes	—
690	#103	C₂³×C₁₉	1	4	yes	—
691	#102	C₂³×C₁₉	1	2	yes	—
692	#102	C₂³×C₁₉	1	2	yes	—
693	#102	C₂³×C₁₉	1	4	yes	—
694	#102	C₂³×C₁₉	1	4	yes	—
695	#102	C₂³×C₁₉	1	2	yes	—
696	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
697	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
698	#97	C₂³×C₁₉	1	2	yes	—
699	C₄×C₈	C₂³×C₁₉	1	2	yes	—
700	C₁₉	#61159	1	1	yes	characteristic, direct product factor, Sylow
701	C₂⁴	—	2	1	no	—
702	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
703	#41	—	2	8	no	—
704	#41	—	2	8	no	—
705	#41	—	2	2	no	—
706	#41	—	2	2	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	8	no	—
710	#41	—	4	8	no	—
711	#41	—	4	4	no	—
712	C₂×Q₈	—	2	1	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	4	no	—
716	C₂×Q₈	—	2	4	no	—
717	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
718	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	8	no	—
728	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
729	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
730	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
731	C₂×D₄	#41×C₁₉	1	4	yes	complemented
732	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
733	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	4	8	no	—
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
750	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
751	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
752	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
753	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
757	Q₁₆	—	4	4	no	—
758	SD₁₆	—	2	4	no	—
759	SD₁₆	—	4	4	no	—
760	D₈	—	2	4	no	—
761	M₁₆	—	2	2	no	—
762	M₁₆	—	2	2	no	—
763	M₁₆	—	2	4	no	—
764	M₁₆	—	4	4	no	—
765	C₂×C₈	—	4	4	no	—
766	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
767	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
768	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
787	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
788	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
789	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
791	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	1	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
809	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
810	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
811	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	1	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	1	no	—
818	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
819	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
820	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
821	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	4	2	no	—
830	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
831	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
832	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
833	Q₈	—	2	1	no	—
834	Q₈	—	2	4	no	—
835	Q₈	—	2	4	no	—
836	Q₈	—	2	1	no	—
837	Q₈	—	4	4	no	—
838	Q₈	—	4	2	no	—
839	Q₈	—	8	1	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	1	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	1	no	—
846	D₄	—	4	2	no	—
847	D₄	—	4	8	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	2	no	—
852	D₄	C₂×#41×C₁₉	1	4	yes	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	8	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	8	1	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
887	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
888	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
889	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
890	C₈	—	2	2	no	—
891	C₈	—	2	2	no	—
892	C₈	—	2	4	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	4	8	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	8	4	no	—
909	C₂²	C₁₉×#546	1	2	yes	—
910	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	4	4	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	C₁₉×#546	1	2	yes	—
924	C₄	C₁₉×#575	1	2	yes	—
925	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
926	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
927	C₂	—	2	2	no	—
928	C₂	—	4	2	no	—
929	C₂	—	4	2	no	—
930	C₂	—	4	4	no	—
931	C₂	—	8	1	no	—
932	C₂	C₂×C₁₉×#546	1	1	yes	characteristic
933	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
934	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 ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3475	C₂	semidirect
2. C₂×C₁₉×#547	C₂	semidirect
3. C₁₉×#3331	C₂	semidirect
4. C₁₉×#3330	C₂	semidirect
5. C₁₉×#3315	C₂	semidirect
6. C₁₉×#3307	C₂	semidirect
7. C₁₉×#3303	C₂	semidirect
8. C₁₉×#3302	C₂	semidirect
9. C₁₉×#3139	C₂	semidirect
10. C₁₉×#3095	C₂	semidirect
11. C₁₉×#3077	C₂	semidirect
12. C₁₉×#3056	C₂	semidirect
13. C₁₉×#3039	C₂	semidirect
14. C₁₉×#3005	C₂	semidirect
15. C₄×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
16. D₄×M₁₆×C₁₉	C₂	semidirect
17. C₁₉×#2896	C₂	semidirect
22. C₁₉×#556	C₂²	semidirect
23. C₁₉×#555	C₂²	semidirect
24. C₁₉×#554	C₂²	semidirect
25. C₁₉×#553	C₂²	semidirect
27. C₁₉×#552	C₂²	semidirect
35. C₁₉×#547	C₂²	semidirect
51. C₁₉×#491	C₂²	semidirect
52. C₁₉×#487	C₂²	semidirect
53. C₁₉×#487	C₂²	semidirect
54. C₁₉×#485	C₂²	semidirect
55. C₁₉×#485	C₂²	semidirect
56. C₁₉×#484	C₂²	semidirect
57. C₁₉×#483	C₂²	semidirect
58. C₁₉×#478	C₂²	semidirect
59. C₁₉×#476	C₂²	semidirect
60. C₁₉×#474	C₂²	semidirect
61. C₁₉×#470	C₂²	semidirect
62. C₁₉×#468	C₂²	semidirect
63. C₁₉×#467	C₂²	semidirect
64. C₁₉×#465	C₂²	semidirect
65. C₁₉×#462	C₂²	semidirect
66. C₁₉×#462	C₂²	semidirect
67. C₁₉×#461	C₂²	semidirect
68. C₁₉×#461	C₂²	semidirect
69. C₁₉×#452	C₂²	semidirect
70. C₁₉×#452	C₂²	semidirect
71. C₁₉×#449	C₂²	semidirect
72. C₁₉×#449	C₂²	semidirect
73. C₁₉×#442	C₂²	semidirect
74. C₁₉×#440	C₂²	semidirect
75. C₄×SD₁₆×C₁₉	C₂²	semidirect
76. C₄×D₈×C₁₉	C₂²	semidirect
77. C₁₉×#436	C₂²	semidirect
78. C₁₉×#435	C₂²	semidirect
79. C₈×D₄×C₁₉	C₂²	semidirect
89. C₁₉×#417	C₂²	semidirect
90. C₁₉×#417	C₂²	semidirect
91. C₁₉×#416	C₂²	semidirect
92. C₁₉×#416	C₂²	semidirect
263. C₂×D₄×C₁₉	#41	semidirect
354. #61159	C₁₉	direct (N × H)
426. #3475	C₂×C₁₉	semidirect
427. C₂×#547	C₂×C₁₉	semidirect
428. #3331	C₂×C₁₉	semidirect
429. #3330	C₂×C₁₉	semidirect
430. #3315	C₂×C₁₉	semidirect
431. #3307	C₂×C₁₉	semidirect
432. #3303	C₂×C₁₉	semidirect
433. #3302	C₂×C₁₉	semidirect
434. #3139	C₂×C₁₉	semidirect
435. #3095	C₂×C₁₉	semidirect
436. #3077	C₂×C₁₉	semidirect
437. #3056	C₂×C₁₉	semidirect
438. #3039	C₂×C₁₉	semidirect
439. #3005	C₂×C₁₉	semidirect
440. C₄×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
441. D₄×M₁₆	C₂×C₁₉	semidirect
442. #2896	C₂×C₁₉	semidirect
481. #556	C₂²×C₁₉	semidirect
482. #555	C₂²×C₁₉	semidirect
483. #554	C₂²×C₁₉	semidirect
484. #553	C₂²×C₁₉	semidirect
486. #552	C₂²×C₁₉	semidirect
494. #547	C₂²×C₁₉	semidirect
510. #491	C₂²×C₁₉	semidirect
511. #487	C₂²×C₁₉	semidirect
512. #487	C₂²×C₁₉	semidirect
513. #485	C₂²×C₁₉	semidirect
514. #485	C₂²×C₁₉	semidirect
515. #484	C₂²×C₁₉	semidirect
516. #483	C₂²×C₁₉	semidirect
517. #478	C₂²×C₁₉	semidirect
518. #476	C₂²×C₁₉	semidirect
519. #474	C₂²×C₁₉	semidirect
520. #470	C₂²×C₁₉	semidirect
521. #468	C₂²×C₁₉	semidirect
522. #467	C₂²×C₁₉	semidirect
523. #465	C₂²×C₁₉	semidirect
524. #462	C₂²×C₁₉	semidirect
525. #462	C₂²×C₁₉	semidirect
526. #461	C₂²×C₁₉	semidirect
527. #461	C₂²×C₁₉	semidirect
528. #452	C₂²×C₁₉	semidirect
529. #452	C₂²×C₁₉	semidirect
530. #449	C₂²×C₁₉	semidirect
531. #449	C₂²×C₁₉	semidirect
532. #442	C₂²×C₁₉	semidirect
533. #440	C₂²×C₁₉	semidirect
534. C₄×SD₁₆	C₂²×C₁₉	semidirect
535. C₄×D₈	C₂²×C₁₉	semidirect
536. #436	C₂²×C₁₉	semidirect
537. #435	C₂²×C₁₉	semidirect
538. C₈×D₄	C₂²×C₁₉	semidirect
548. #417	C₂²×C₁₉	semidirect
549. #417	C₂²×C₁₉	semidirect
550. #416	C₂²×C₁₉	semidirect
551. #416	C₂²×C₁₉	semidirect
700. C₁₉	#61159	direct (N × H)
731. C₂×D₄	#41×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3475	2
C₂×C₁₉×#547	2
C₁₉×#3331	2
C₁₉×#3330	2
C₁₉×#3315	2
C₁₉×#3307	2
C₁₉×#3303	2
C₁₉×#3302	2
C₁₉×#3139	2
C₁₉×#3095	2
C₁₉×#3077	2
C₁₉×#3056	2
C₁₉×#3039	2
C₁₉×#3005	2
C₄×C₁₉×AGL(1,ℤ/8)	2
D₄×M₁₆×C₁₉	2
C₁₉×#2896	2
#61159	19

Subgroups — C19×#61159 #18067118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61159 #18067118