Subgroups — C₁₉×#62258 #18068217

Order 4864.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3520	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3349	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3343	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3315	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3313	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3312	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3308	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3270	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3269	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3250	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3191	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3190	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3181	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3056	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic, complemented
22	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#556	C₂²	1	2	yes	—
26	C₁₉×#554	—	2	2	no	—
27	C₁₉×#552	C₂²	1	2	yes	—
28	C₁₉×#552	C₂²	1	2	yes	—
29	C₁₉×#551	—	2	2	no	—
30	C₁₉×#551	—	2	2	no	—
31	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
32	C₁₉×#548	C₂²	1	2	yes	—
33	C₁₉×#548	C₂²	1	2	yes	—
34	C₁₉×#547	C₂²	1	2	yes	—
35	C₁₉×#547	C₂²	1	2	yes	—
36	C₁₉×#546	—	2	2	no	—
37	C₁₉×#542	—	2	2	no	—
38	C₁₉×#539	—	2	2	no	—
39	C₁₉×#539	—	2	2	no	—
40	C₁₉×#533	C₂²	1	2	yes	—
41	C₁₉×#529	C₂²	1	2	yes	—
42	C₁₉×#525	C₂²	1	2	yes	—
43	C₁₉×#525	C₂²	1	2	yes	—
44	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₁₉×#520	—	2	2	no	—
47	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#501	C₂²	1	2	yes	complemented
49	C₁₉×#497	C₂²	1	2	yes	complemented
50	C₁₉×#491	C₂²	1	2	yes	complemented
51	C₁₉×#489	C₂²	1	2	yes	complemented
52	C₁₉×#485	C₂²	1	2	yes	complemented
53	C₁₉×#485	C₂²	1	2	yes	complemented
54	C₁₉×#485	C₂²	1	2	yes	complemented
55	C₁₉×#484	C₂²	1	2	yes	complemented
56	C₁₉×#484	C₂²	1	2	yes	complemented
57	C₁₉×#483	C₂²	1	2	yes	complemented
58	C₁₉×#482	C₂²	1	2	yes	complemented
59	C₁₉×#480	C₂²	1	2	yes	complemented
60	C₁₉×#479	C₂²	1	2	yes	complemented
61	C₁₉×#478	C₂²	1	2	yes	complemented
62	C₁₉×#477	C₂²	1	2	yes	complemented
63	C₁₉×#477	C₂²	1	2	yes	complemented
64	C₁₉×#470	C₂²	1	2	yes	complemented
65	C₁₉×#470	C₂²	1	2	yes	complemented
66	C₁₉×#468	C₂²	1	2	yes	complemented
67	C₁₉×#468	C₂²	1	2	yes	complemented
68	C₁₉×#467	C₂²	1	2	yes	—
69	C₁₉×#467	C₂²	1	2	yes	—
70	C₁₉×#467	C₂²	1	1	yes	characteristic
71	C₁₉×#467	C₂²	1	1	yes	characteristic
72	C₁₉×#467	C₂²	1	2	yes	—
73	C₁₉×#467	C₂²	1	1	yes	characteristic
74	C₁₉×#467	C₂²	1	2	yes	complemented
75	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
77	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
78	C₁₉×#466	C₂²	1	1	yes	characteristic
79	C₁₉×#466	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#465	C₂²	1	2	yes	—
81	C₁₉×#465	C₂²	1	2	yes	—
82	C₁₉×#465	C₂²	1	2	yes	—
83	C₁₉×#465	C₂²	1	2	yes	complemented
84	C₁₉×#464	C₂²	1	2	yes	complemented
85	C₁₉×#463	C₂²	1	2	yes	complemented
86	C₁₉×#462	C₂²	1	2	yes	complemented
87	C₁₉×#462	C₂²	1	2	yes	complemented
88	C₁₉×#452	C₂²	1	2	yes	complemented
89	C₁₉×#452	C₂²	1	2	yes	complemented
90	C₁₉×#452	C₂²	1	2	yes	complemented
91	C₁₉×#451	C₂²	1	2	yes	complemented
92	C₁₉×#451	C₂²	1	2	yes	complemented
93	C₁₉×#451	C₂²	1	2	yes	complemented
94	C₁₉×#449	C₂²	1	2	yes	complemented
95	C₁₉×#448	C₂²	1	2	yes	complemented
96	C₁₉×#441	C₂²	1	2	yes	complemented
97	C₁₉×#441	C₂²	1	2	yes	complemented
98	C₁₉×#440	C₂²	1	2	yes	complemented
99	C₁₉×#440	C₂²	1	2	yes	complemented
100	C₁₉×#435	C₂²	1	2	yes	—
101	C₁₉×#435	C₂²	1	2	yes	—
102	C₁₉×#435	C₂²	1	2	yes	—
103	C₁₉×#435	C₂²	1	2	yes	—
104	C₁₉×#428	C₂²	1	2	yes	complemented
105	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
108	C₁₉×#419	C₂²	1	2	yes	complemented
109	C₁₉×#417	C₂²	1	2	yes	complemented
110	C₁₉×#416	C₂²	1	2	yes	complemented
111	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
112	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
114	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
115	C₂×#41×C₁₉	—	2	2	no	—
116	C₂×#41×C₁₉	C₂³	1	2	yes	—
117	C₂×#41×C₁₉	C₂³	1	2	yes	—
118	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
119	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
120	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
121	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₁₉×#137	—	4	4	no	—
124	C₁₉×#135	—	4	2	no	—
125	C₂×Q₁₆×C₁₉	—	4	2	no	—
126	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
128	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
135	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₁₉	—	4	2	no	—
137	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
138	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
139	C₂²×C₈×C₁₉	—	4	2	no	—
140	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
148	C₁₉×C₄⋊Q₈	—	2	2	no	—
149	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
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×#126	—	2	2	no	—
156	C₁₉×#125	—	2	2	no	—
157	C₁₉×#125	—	2	2	no	—
158	C₁₉×#125	—	2	2	no	—
159	C₁₉×#125	C₂³	1	2	yes	—
160	C₁₉×#124	—	2	2	no	—
161	C₁₉×#124	—	2	2	no	—
162	C₁₉×#124	—	2	2	no	—
163	C₁₉×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
173	C₁₉×C₂²⋊Q₈	—	2	2	no	—
174	C₁₉×C₂²⋊Q₈	—	2	2	no	—
175	C₁₉×C₂²⋊Q₈	—	2	2	no	—
176	C₁₉×C₂²⋊Q₈	—	2	2	no	—
177	C₁₉×C₂²⋊Q₈	—	2	2	no	—
178	C₁₉×C₂²⋊Q₈	—	2	2	no	—
179	C₁₉×C₂²⋊Q₈	—	2	2	no	—
180	C₁₉×C₂²⋊Q₈	—	2	2	no	—
181	C₁₉×C₂²⋊Q₈	—	2	2	no	—
182	C₁₉×C₂²⋊Q₈	—	2	2	no	—
183	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
184	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
185	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
186	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₁₉×#121	—	2	2	no	—
193	C₁₉×#121	—	2	2	no	—
194	C₁₉×#121	—	2	2	no	—
195	C₁₉×#121	C₂³	1	2	yes	—
196	C₁₉×#121	C₂³	1	2	yes	—
197	C₁₉×#121	C₂³	1	2	yes	—
198	C₁₉×#120	—	2	2	no	—
199	C₁₉×#120	—	2	2	no	—
200	C₄×Q₈×C₁₉	—	2	2	no	—
201	C₄×Q₈×C₁₉	—	2	2	no	—
202	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
204	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
205	C₄×D₄×C₁₉	—	2	2	no	—
206	C₄×D₄×C₁₉	—	2	2	no	—
207	C₄×D₄×C₁₉	—	2	2	no	—
208	C₄×D₄×C₁₉	—	2	2	no	—
209	C₄×D₄×C₁₉	—	2	2	no	—
210	C₄×D₄×C₁₉	—	2	2	no	—
211	C₄×D₄×C₁₉	—	2	2	no	—
212	C₄×D₄×C₁₉	—	2	2	no	—
213	C₄×D₄×C₁₉	D₄	1	2	yes	—
214	C₄×D₄×C₁₉	D₄	1	2	yes	—
215	C₄×D₄×C₁₉	C₂³	1	2	yes	—
216	C₄×D₄×C₁₉	C₂³	1	2	yes	—
217	C₄×D₄×C₁₉	C₂³	1	2	yes	—
218	C₁₉×#117	—	2	2	no	—
219	C₁₉×#117	—	2	2	no	—
220	C₁₉×#117	—	2	2	no	—
221	C₁₉×#117	—	2	2	no	—
222	C₁₉×#117	C₂³	1	2	yes	—
223	C₁₉×#117	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
225	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
226	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
227	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
232	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
233	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
234	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
235	C₁₉×#107	C₂³	1	2	yes	—
236	C₁₉×#107	C₂³	1	1	yes	characteristic
237	C₁₉×#107	C₂³	1	1	yes	characteristic
238	C₁₉×#107	C₂³	1	1	yes	characteristic
239	C₁₉×#107	C₂³	1	1	yes	characteristic
240	C₁₉×#107	C₂³	1	2	yes	—
241	C₁₉×#107	C₂³	1	2	yes	—
242	C₁₉×#106	C₂³	1	2	yes	—
243	C₁₉×#106	C₂³	1	2	yes	—
244	C₁₉×#106	C₂³	1	2	yes	—
245	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
247	C₁₉×#103	C₂³	1	2	yes	—
248	C₁₉×#103	C₂³	1	2	yes	—
249	C₁₉×#103	C₂³	1	2	yes	—
250	C₁₉×#103	C₂³	1	2	yes	—
251	C₁₉×#103	C₂³	1	2	yes	—
252	C₁₉×#103	C₂³	1	2	yes	—
253	C₁₉×#103	C₂³	1	2	yes	—
254	C₁₉×#103	C₂³	1	2	yes	—
255	C₁₉×#103	C₂³	1	2	yes	—
256	C₁₉×#103	C₂³	1	2	yes	—
257	C₁₉×#103	C₂³	1	2	yes	—
258	C₁₉×#103	C₂³	1	2	yes	—
259	C₁₉×#102	C₂³	1	2	yes	—
260	C₁₉×#102	C₂³	1	2	yes	—
261	C₁₉×#102	C₂³	1	2	yes	—
262	C₁₉×#102	C₂³	1	2	yes	—
263	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₁₉×#97	C₂³	1	2	yes	—
268	C₁₉×#97	C₂³	1	2	yes	—
269	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
270	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	#41×C₁₉	—	4	8	no	—
276	C₂×Q₈×C₁₉	—	2	2	no	—
277	C₂×Q₈×C₁₉	—	2	2	no	—
278	C₂×Q₈×C₁₉	—	2	2	no	—
279	C₂×Q₈×C₁₉	—	4	2	no	—
280	C₂×Q₈×C₁₉	—	4	2	no	—
281	C₂×Q₈×C₁₉	—	4	2	no	—
282	C₂×Q₈×C₁₉	—	4	2	no	—
283	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
284	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
285	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
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	—	4	2	no	—
292	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
293	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
294	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₉	—	2	2	no	—
296	C₂²×C₄×C₁₉	—	2	2	no	—
297	C₂²×C₄×C₁₉	—	2	2	no	—
298	C₂²×C₄×C₁₉	—	2	2	no	—
299	C₂²×C₄×C₁₉	—	2	2	no	—
300	C₂²×C₄×C₁₉	—	2	2	no	—
301	C₂²×C₄×C₁₉	—	2	2	no	—
302	C₂²×C₄×C₁₉	—	4	1	no	—
303	C₂²×C₄×C₁₉	—	4	1	no	—
304	C₂²×C₄×C₁₉	—	4	1	no	—
305	C₂²×C₄×C₁₉	—	4	1	no	—
306	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
317	Q₁₆×C₁₉	—	2	4	no	—
318	Q₁₆×C₁₉	—	4	1	no	—
319	Q₁₆×C₁₉	—	4	1	no	—
320	Q₁₆×C₁₉	—	4	2	no	—
321	Q₁₆×C₁₉	—	4	1	no	—
322	Q₁₆×C₁₉	—	4	2	no	—
323	SD₁₆×C₁₉	—	2	4	no	—
324	SD₁₆×C₁₉	—	4	2	no	—
325	SD₁₆×C₁₉	—	4	2	no	—
326	D₈×C₁₉	—	4	1	no	—
327	M₁₆×C₁₉	—	2	4	no	—
328	M₁₆×C₁₉	—	4	2	no	—
329	C₂×C₈×C₁₉	—	2	2	no	—
330	C₂×C₈×C₁₉	—	2	2	no	—
331	C₂×C₈×C₁₉	—	2	2	no	—
332	C₂×C₈×C₁₉	—	4	1	no	—
333	C₂×C₈×C₁₉	—	4	1	no	—
334	C₂×C₈×C₁₉	—	4	1	no	—
335	C₂×C₈×C₁₉	—	4	1	no	—
336	C₂×C₈×C₁₉	—	4	1	no	—
337	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
339	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
341	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
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	—	2	2	no	—
355	C₄⋊C₄×C₁₉	—	2	2	no	—
356	C₄⋊C₄×C₁₉	—	2	2	no	—
357	C₄⋊C₄×C₁₉	—	2	2	no	—
358	C₄⋊C₄×C₁₉	—	2	2	no	—
359	C₄⋊C₄×C₁₉	—	2	2	no	—
360	C₄⋊C₄×C₁₉	—	2	2	no	—
361	C₄⋊C₄×C₁₉	—	2	2	no	—
362	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
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	—	2	2	no	—
379	C₂²⋊C₄×C₁₉	—	2	2	no	—
380	C₂²⋊C₄×C₁₉	—	2	2	no	—
381	C₂²⋊C₄×C₁₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₉	—	2	2	no	—
383	C₂²⋊C₄×C₁₉	—	2	2	no	—
384	C₂²⋊C₄×C₁₉	—	2	2	no	—
385	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
389	C₄²×C₁₉	—	2	2	no	—
390	C₄²×C₁₉	—	2	2	no	—
391	C₄²×C₁₉	—	2	2	no	—
392	C₄²×C₁₉	—	2	2	no	—
393	C₄²×C₁₉	—	2	2	no	—
394	C₄²×C₁₉	C₂×D₄	1	2	yes	—
395	C₄²×C₁₉	C₂⁴	1	2	yes	—
396	#62258	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂³×C₁₉	—	2	2	no	—
398	C₂³×C₁₉	—	2	2	no	—
399	C₂³×C₁₉	—	2	2	no	—
400	C₂³×C₁₉	—	2	2	no	—
401	C₂³×C₁₉	—	4	1	no	—
402	C₂³×C₁₉	—	4	1	no	—
403	C₂³×C₁₉	—	4	1	no	—
404	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
405	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
406	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
407	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
408	Q₈×C₁₉	—	2	2	no	—
409	Q₈×C₁₉	—	2	2	no	—
410	Q₈×C₁₉	—	2	2	no	—
411	Q₈×C₁₉	—	2	2	no	—
412	Q₈×C₁₉	—	2	2	no	—
413	Q₈×C₁₉	—	2	2	no	—
414	Q₈×C₁₉	—	4	4	no	—
415	Q₈×C₁₉	—	8	2	no	—
416	Q₈×C₁₉	—	8	2	no	—
417	D₄×C₁₉	—	2	4	no	—
418	D₄×C₁₉	—	2	2	no	—
419	D₄×C₁₉	—	2	2	no	—
420	D₄×C₁₉	—	4	2	no	—
421	D₄×C₁₉	—	4	4	no	—
422	D₄×C₁₉	—	4	4	no	—
423	D₄×C₁₉	—	4	4	no	—
424	D₄×C₁₉	—	8	2	no	—
425	D₄×C₁₉	—	8	2	no	—
426	C₂×C₄×C₁₉	—	2	2	no	—
427	C₂×C₄×C₁₉	—	2	1	no	—
428	C₂×C₄×C₁₉	—	2	1	no	—
429	C₂×C₄×C₁₉	—	2	1	no	—
430	C₂×C₄×C₁₉	—	2	2	no	—
431	C₂×C₄×C₁₉	—	2	1	no	—
432	C₂×C₄×C₁₉	—	2	1	no	—
433	C₂×C₄×C₁₉	—	2	2	no	—
434	C₂×C₄×C₁₉	—	2	1	no	—
435	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
443	C₂×C₄×C₁₉	—	4	2	no	—
444	C₂×C₄×C₁₉	—	4	1	no	—
445	C₂×C₄×C₁₉	—	4	1	no	—
446	C₂×C₄×C₁₉	—	4	1	no	—
447	C₂×C₄×C₁₉	—	4	1	no	—
448	C₂×C₄×C₁₉	—	4	4	no	—
449	C₂×C₄×C₁₉	—	4	4	no	—
450	C₂×C₄×C₁₉	—	4	4	no	—
451	C₂×C₄×C₁₉	—	8	2	no	—
452	C₂×C₄×C₁₉	—	8	2	no	—
453	C₂×C₄×C₁₉	—	8	2	no	—
454	C₂×C₄×C₁₉	—	8	2	no	—
455	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
462	C₈×C₁₉	—	2	1	no	—
463	C₈×C₁₉	—	2	1	no	—
464	C₈×C₁₉	—	2	1	no	—
465	C₈×C₁₉	—	2	2	no	—
466	C₈×C₁₉	—	2	2	no	—
467	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
468	#3520	C₂×C₁₉	1	2	yes	complemented
469	#3349	C₂×C₁₉	1	2	yes	complemented
470	#3343	C₂×C₁₉	1	2	yes	complemented
471	#3315	C₂×C₁₉	1	2	yes	complemented
472	#3313	C₂×C₁₉	1	2	yes	complemented
473	#3312	C₂×C₁₉	1	2	yes	complemented
474	#3308	C₂×C₁₉	1	2	yes	complemented
475	#3270	C₂×C₁₉	1	2	yes	complemented
476	#3269	C₂×C₁₉	1	2	yes	complemented
477	#3250	C₂×C₁₉	1	1	yes	characteristic, complemented
478	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
479	#3191	C₂×C₁₉	1	1	yes	characteristic, complemented
480	#3190	C₂×C₁₉	1	2	yes	complemented
481	#3189	C₂×C₁₉	1	1	yes	characteristic, complemented
482	#3181	C₂×C₁₉	1	2	yes	complemented
483	#3056	C₂×C₁₉	1	2	yes	complemented
484	#3050	C₂×C₁₉	1	1	yes	characteristic, complemented
485	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
486	C₂×#435	C₂×C₁₉	1	1	yes	characteristic, complemented
487	C₂²×C₁₉	—	2	1	no	—
488	C₂²×C₁₉	—	2	1	no	—
489	C₂²×C₁₉	—	2	1	no	—
490	C₂²×C₁₉	—	2	1	no	—
491	C₂²×C₁₉	—	2	2	no	—
492	C₂²×C₁₉	—	2	1	no	—
493	C₂²×C₁₉	—	2	2	no	—
494	C₂²×C₁₉	—	2	1	no	—
495	C₂²×C₁₉	—	2	1	no	—
496	C₂²×C₁₉	—	2	2	no	—
497	C₂²×C₁₉	—	4	4	no	—
498	C₂²×C₁₉	—	4	2	no	—
499	C₂²×C₁₉	—	4	2	no	—
500	C₂²×C₁₉	—	4	2	no	—
501	C₂²×C₁₉	—	8	2	no	—
502	C₂²×C₁₉	#575	1	2	yes	—
503	C₂²×C₁₉	#578	1	2	yes	—
504	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₁₉	—	2	1	no	—
506	C₄×C₁₉	—	2	1	no	—
507	C₄×C₁₉	—	2	2	no	—
508	C₄×C₁₉	—	2	1	no	—
509	C₄×C₁₉	—	2	2	no	—
510	C₄×C₁₉	—	2	2	no	—
511	C₄×C₁₉	—	4	2	no	—
512	C₄×C₁₉	—	4	2	no	—
513	C₄×C₁₉	—	4	2	no	—
514	C₄×C₁₉	—	4	2	no	—
515	C₄×C₁₉	—	4	2	no	—
516	C₄×C₁₉	—	4	2	no	—
517	C₄×C₁₉	—	4	2	no	—
518	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
519	C₄×C₁₉	#585	1	1	yes	characteristic
520	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
521	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic, complemented
522	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
523	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
524	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
525	#556	C₂²×C₁₉	1	2	yes	—
526	#554	—	2	2	no	—
527	#552	C₂²×C₁₉	1	2	yes	—
528	#552	C₂²×C₁₉	1	2	yes	—
529	#551	—	2	2	no	—
530	#551	—	2	2	no	—
531	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
532	#548	C₂²×C₁₉	1	2	yes	—
533	#548	C₂²×C₁₉	1	2	yes	—
534	#547	C₂²×C₁₉	1	2	yes	—
535	#547	C₂²×C₁₉	1	2	yes	—
536	#546	—	2	2	no	—
537	#542	—	2	2	no	—
538	#539	—	2	2	no	—
539	#539	—	2	2	no	—
540	#533	C₂²×C₁₉	1	2	yes	—
541	#529	C₂²×C₁₉	1	2	yes	—
542	#525	C₂²×C₁₉	1	2	yes	—
543	#525	C₂²×C₁₉	1	2	yes	—
544	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
545	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
546	#520	—	2	2	no	—
547	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
548	#501	C₂²×C₁₉	1	2	yes	complemented
549	#497	C₂²×C₁₉	1	2	yes	complemented
550	#491	C₂²×C₁₉	1	2	yes	complemented
551	#489	C₂²×C₁₉	1	2	yes	complemented
552	#485	C₂²×C₁₉	1	2	yes	complemented
553	#485	C₂²×C₁₉	1	2	yes	complemented
554	#485	C₂²×C₁₉	1	2	yes	complemented
555	#484	C₂²×C₁₉	1	2	yes	complemented
556	#484	C₂²×C₁₉	1	2	yes	complemented
557	#483	C₂²×C₁₉	1	2	yes	complemented
558	#482	C₂²×C₁₉	1	2	yes	complemented
559	#480	C₂²×C₁₉	1	2	yes	complemented
560	#479	C₂²×C₁₉	1	2	yes	complemented
561	#478	C₂²×C₁₉	1	2	yes	complemented
562	#477	C₂²×C₁₉	1	2	yes	complemented
563	#477	C₂²×C₁₉	1	2	yes	complemented
564	#470	C₂²×C₁₉	1	2	yes	complemented
565	#470	C₂²×C₁₉	1	2	yes	complemented
566	#468	C₂²×C₁₉	1	2	yes	complemented
567	#468	C₂²×C₁₉	1	2	yes	complemented
568	#467	C₂²×C₁₉	1	2	yes	—
569	#467	C₂²×C₁₉	1	2	yes	—
570	#467	C₂²×C₁₉	1	1	yes	characteristic
571	#467	C₂²×C₁₉	1	1	yes	characteristic
572	#467	C₂²×C₁₉	1	2	yes	—
573	#467	C₂²×C₁₉	1	1	yes	characteristic
574	#467	C₂²×C₁₉	1	2	yes	complemented
575	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
576	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
577	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
578	#466	C₂²×C₁₉	1	1	yes	characteristic
579	#466	C₂²×C₁₉	1	1	yes	characteristic, complemented
580	#465	C₂²×C₁₉	1	2	yes	—
581	#465	C₂²×C₁₉	1	2	yes	—
582	#465	C₂²×C₁₉	1	2	yes	—
583	#465	C₂²×C₁₉	1	2	yes	complemented
584	#464	C₂²×C₁₉	1	2	yes	complemented
585	#463	C₂²×C₁₉	1	2	yes	complemented
586	#462	C₂²×C₁₉	1	2	yes	complemented
587	#462	C₂²×C₁₉	1	2	yes	complemented
588	#452	C₂²×C₁₉	1	2	yes	complemented
589	#452	C₂²×C₁₉	1	2	yes	complemented
590	#452	C₂²×C₁₉	1	2	yes	complemented
591	#451	C₂²×C₁₉	1	2	yes	complemented
592	#451	C₂²×C₁₉	1	2	yes	complemented
593	#451	C₂²×C₁₉	1	2	yes	complemented
594	#449	C₂²×C₁₉	1	2	yes	complemented
595	#448	C₂²×C₁₉	1	2	yes	complemented
596	#441	C₂²×C₁₉	1	2	yes	complemented
597	#441	C₂²×C₁₉	1	2	yes	complemented
598	#440	C₂²×C₁₉	1	2	yes	complemented
599	#440	C₂²×C₁₉	1	2	yes	complemented
600	#435	C₂²×C₁₉	1	2	yes	—
601	#435	C₂²×C₁₉	1	2	yes	—
602	#435	C₂²×C₁₉	1	2	yes	—
603	#435	C₂²×C₁₉	1	2	yes	—
604	#428	C₂²×C₁₉	1	2	yes	complemented
605	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
606	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
607	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
608	#419	C₂²×C₁₉	1	2	yes	complemented
609	#417	C₂²×C₁₉	1	2	yes	complemented
610	#416	C₂²×C₁₉	1	2	yes	complemented
611	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
612	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
614	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
615	C₂×C₁₉	—	2	2	no	—
616	C₂×C₁₉	—	2	2	no	—
617	C₂×C₁₉	—	4	1	no	—
618	C₂×C₁₉	—	4	2	no	—
619	C₂×C₁₉	—	8	2	no	—
620	C₂×C₁₉	#3496	1	1	yes	characteristic
621	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
622	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
623	C₂×#41	—	2	2	no	—
624	C₂×#41	C₂³×C₁₉	1	2	yes	—
625	C₂×#41	C₂³×C₁₉	1	2	yes	—
626	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
627	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
628	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
631	#137	—	4	4	no	—
632	#135	—	4	2	no	—
633	C₂×Q₁₆	—	4	2	no	—
634	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
635	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
636	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
637	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
638	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
639	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
643	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
644	C₂×M₁₆	—	4	2	no	—
645	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
646	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
647	C₂²×C₈	—	4	2	no	—
648	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
649	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
650	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
651	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
652	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
653	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
654	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
655	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
656	C₄⋊Q₈	—	2	2	no	—
657	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
658	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	C₂³×C₁₉	1	2	yes	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	C₂³×C₁₉	1	2	yes	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
697	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
698	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	C₂³×C₁₉	1	2	yes	—
704	#121	C₂³×C₁₉	1	2	yes	—
705	#121	C₂³×C₁₉	1	2	yes	—
706	#120	—	2	2	no	—
707	#120	—	2	2	no	—
708	C₄×Q₈	—	2	2	no	—
709	C₄×Q₈	—	2	2	no	—
710	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
711	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
712	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	2	no	—
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	D₄×C₁₉	1	2	yes	—
722	C₄×D₄	D₄×C₁₉	1	2	yes	—
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	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	—	2	2	no	—
729	#117	—	2	2	no	—
730	#117	C₂³×C₁₉	1	2	yes	—
731	#117	C₂³×C₁₉	1	2	yes	—
732	C₂×C₄⋊C₄	—	2	2	no	—
733	C₂×C₄⋊C₄	—	2	2	no	—
734	C₂×C₄⋊C₄	—	2	2	no	—
735	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
738	C₂×C₂²⋊C₄	—	2	2	no	—
739	C₂×C₂²⋊C₄	—	2	2	no	—
740	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
743	#107	C₂³×C₁₉	1	2	yes	—
744	#107	C₂³×C₁₉	1	1	yes	characteristic
745	#107	C₂³×C₁₉	1	1	yes	characteristic
746	#107	C₂³×C₁₉	1	1	yes	characteristic
747	#107	C₂³×C₁₉	1	1	yes	characteristic
748	#107	C₂³×C₁₉	1	2	yes	—
749	#107	C₂³×C₁₉	1	2	yes	—
750	#106	C₂³×C₁₉	1	2	yes	—
751	#106	C₂³×C₁₉	1	2	yes	—
752	#106	C₂³×C₁₉	1	2	yes	—
753	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
754	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
755	#103	C₂³×C₁₉	1	2	yes	—
756	#103	C₂³×C₁₉	1	2	yes	—
757	#103	C₂³×C₁₉	1	2	yes	—
758	#103	C₂³×C₁₉	1	2	yes	—
759	#103	C₂³×C₁₉	1	2	yes	—
760	#103	C₂³×C₁₉	1	2	yes	—
761	#103	C₂³×C₁₉	1	2	yes	—
762	#103	C₂³×C₁₉	1	2	yes	—
763	#103	C₂³×C₁₉	1	2	yes	—
764	#103	C₂³×C₁₉	1	2	yes	—
765	#103	C₂³×C₁₉	1	2	yes	—
766	#103	C₂³×C₁₉	1	2	yes	—
767	#102	C₂³×C₁₉	1	2	yes	—
768	#102	C₂³×C₁₉	1	2	yes	—
769	#102	C₂³×C₁₉	1	2	yes	—
770	#102	C₂³×C₁₉	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
775	#97	C₂³×C₁₉	1	2	yes	—
776	#97	C₂³×C₁₉	1	2	yes	—
777	C₁₉	#62258	1	1	yes	characteristic, direct product factor, Sylow
778	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
779	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
780	#41	—	4	2	no	—
781	#41	—	4	2	no	—
782	#41	—	4	2	no	—
783	#41	—	4	2	no	—
784	#41	—	4	8	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	4	2	no	—
789	C₂×Q₈	—	4	2	no	—
790	C₂×Q₈	—	4	2	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
794	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
802	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
803	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
816	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
817	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
818	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
821	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
826	Q₁₆	—	2	4	no	—
827	Q₁₆	—	4	1	no	—
828	Q₁₆	—	4	1	no	—
829	Q₁₆	—	4	2	no	—
830	Q₁₆	—	4	1	no	—
831	Q₁₆	—	4	2	no	—
832	SD₁₆	—	2	4	no	—
833	SD₁₆	—	4	2	no	—
834	SD₁₆	—	4	2	no	—
835	D₈	—	4	1	no	—
836	M₁₆	—	2	4	no	—
837	M₁₆	—	4	2	no	—
838	C₂×C₈	—	2	2	no	—
839	C₂×C₈	—	2	2	no	—
840	C₂×C₈	—	2	2	no	—
841	C₂×C₈	—	4	1	no	—
842	C₂×C₈	—	4	1	no	—
843	C₂×C₈	—	4	1	no	—
844	C₂×C₈	—	4	1	no	—
845	C₂×C₈	—	4	1	no	—
846	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
847	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
848	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
849	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
850	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
851	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
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	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
872	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
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	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	C₂×D₄×C₁₉	1	2	yes	—
904	C₄²	C₂⁴×C₁₉	1	2	yes	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	1	no	—
910	C₂³	—	4	1	no	—
911	C₂³	—	4	1	no	—
912	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
913	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
914	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
915	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	2	2	no	—
920	Q₈	—	2	2	no	—
921	Q₈	—	2	2	no	—
922	Q₈	—	4	4	no	—
923	Q₈	—	8	2	no	—
924	Q₈	—	8	2	no	—
925	D₄	—	2	4	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	4	no	—
930	D₄	—	4	4	no	—
931	D₄	—	4	4	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	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	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	1	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	1	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	—	4	4	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
964	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
966	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
967	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
969	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
970	C₈	—	2	1	no	—
971	C₈	—	2	1	no	—
972	C₈	—	2	1	no	—
973	C₈	—	2	2	no	—
974	C₈	—	2	2	no	—
975	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	4	4	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	8	2	no	—
991	C₂²	C₁₉×#575	1	2	yes	—
992	C₂²	C₁₉×#578	1	2	yes	—
993	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	2	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1008	C₄	C₁₉×#585	1	1	yes	characteristic
1009	C₂	—	2	2	no	—
1010	C₂	—	2	2	no	—
1011	C₂	—	4	1	no	—
1012	C₂	—	4	2	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₁₉×#3496	1	1	yes	characteristic
1015	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
1016	C₂	C₂×C₁₉×#578	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×#3520	C₂	semidirect
2. C₁₉×#3349	C₂	semidirect
3. C₁₉×#3343	C₂	semidirect
4. C₁₉×#3315	C₂	semidirect
5. C₁₉×#3313	C₂	semidirect
6. C₁₉×#3312	C₂	semidirect
7. C₁₉×#3308	C₂	semidirect
8. C₁₉×#3270	C₂	semidirect
9. C₁₉×#3269	C₂	semidirect
10. C₁₉×#3250	C₂	semidirect
11. C₁₉×#3249	C₂	semidirect
12. C₁₉×#3191	C₂	semidirect
13. C₁₉×#3190	C₂	semidirect
14. C₁₉×#3189	C₂	semidirect
15. C₁₉×#3181	C₂	semidirect
16. C₁₉×#3056	C₂	semidirect
17. C₁₉×#3050	C₂	semidirect
18. C₂×C₁₉×#467	C₂	semidirect
19. C₂×C₁₉×#435	C₂	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
21. C₂×C₁₉×#135	C₂²	semidirect
22. C₂²×Q₁₆×C₁₉	C₂²	semidirect
48. C₁₉×#501	C₂²	semidirect
49. C₁₉×#497	C₂²	semidirect
50. C₁₉×#491	C₂²	semidirect
51. C₁₉×#489	C₂²	semidirect
52. C₁₉×#485	C₂²	semidirect
53. C₁₉×#485	C₂²	semidirect
54. C₁₉×#485	C₂²	semidirect
55. C₁₉×#484	C₂²	semidirect
56. C₁₉×#484	C₂²	semidirect
57. C₁₉×#483	C₂²	semidirect
58. C₁₉×#482	C₂²	semidirect
59. C₁₉×#480	C₂²	semidirect
60. C₁₉×#479	C₂²	semidirect
61. C₁₉×#478	C₂²	semidirect
62. C₁₉×#477	C₂²	semidirect
63. C₁₉×#477	C₂²	semidirect
64. C₁₉×#470	C₂²	semidirect
65. C₁₉×#470	C₂²	semidirect
66. C₁₉×#468	C₂²	semidirect
67. C₁₉×#468	C₂²	semidirect
74. C₁₉×#467	C₂²	semidirect
75. C₁₉×#467	C₂²	semidirect
76. C₁₉×#467	C₂²	semidirect
77. C₁₉×#467	C₂²	semidirect
79. C₁₉×#466	C₂²	semidirect
83. C₁₉×#465	C₂²	semidirect
84. C₁₉×#464	C₂²	semidirect
85. C₁₉×#463	C₂²	semidirect
86. C₁₉×#462	C₂²	semidirect
87. C₁₉×#462	C₂²	semidirect
88. C₁₉×#452	C₂²	semidirect
89. C₁₉×#452	C₂²	semidirect
90. C₁₉×#452	C₂²	semidirect
91. C₁₉×#451	C₂²	semidirect
92. C₁₉×#451	C₂²	semidirect
93. C₁₉×#451	C₂²	semidirect
94. C₁₉×#449	C₂²	semidirect
95. C₁₉×#448	C₂²	semidirect
96. C₁₉×#441	C₂²	semidirect
97. C₁₉×#441	C₂²	semidirect
98. C₁₉×#440	C₂²	semidirect
99. C₁₉×#440	C₂²	semidirect
104. C₁₉×#428	C₂²	semidirect
105. C₁₉×#427	C₂²	semidirect
106. C₂×C₁₉×#107	C₂²	semidirect
108. C₁₉×#419	C₂²	semidirect
109. C₁₉×#417	C₂²	semidirect
110. C₁₉×#416	C₂²	semidirect
111. C₂×C₁₉×#103	C₂²	semidirect
396. #62258	C₁₉	direct (N × H)
468. #3520	C₂×C₁₉	semidirect
469. #3349	C₂×C₁₉	semidirect
470. #3343	C₂×C₁₉	semidirect
471. #3315	C₂×C₁₉	semidirect
472. #3313	C₂×C₁₉	semidirect
473. #3312	C₂×C₁₉	semidirect
474. #3308	C₂×C₁₉	semidirect
475. #3270	C₂×C₁₉	semidirect
476. #3269	C₂×C₁₉	semidirect
477. #3250	C₂×C₁₉	semidirect
478. #3249	C₂×C₁₉	semidirect
479. #3191	C₂×C₁₉	semidirect
480. #3190	C₂×C₁₉	semidirect
481. #3189	C₂×C₁₉	semidirect
482. #3181	C₂×C₁₉	semidirect
483. #3056	C₂×C₁₉	semidirect
484. #3050	C₂×C₁₉	semidirect
485. C₂×#467	C₂×C₁₉	semidirect
486. C₂×#435	C₂×C₁₉	semidirect
520. C₂×#137	C₂²×C₁₉	semidirect
521. C₂×#135	C₂²×C₁₉	semidirect
522. C₂²×Q₁₆	C₂²×C₁₉	semidirect
548. #501	C₂²×C₁₉	semidirect
549. #497	C₂²×C₁₉	semidirect
550. #491	C₂²×C₁₉	semidirect
551. #489	C₂²×C₁₉	semidirect
552. #485	C₂²×C₁₉	semidirect
553. #485	C₂²×C₁₉	semidirect
554. #485	C₂²×C₁₉	semidirect
555. #484	C₂²×C₁₉	semidirect
556. #484	C₂²×C₁₉	semidirect
557. #483	C₂²×C₁₉	semidirect
558. #482	C₂²×C₁₉	semidirect
559. #480	C₂²×C₁₉	semidirect
560. #479	C₂²×C₁₉	semidirect
561. #478	C₂²×C₁₉	semidirect
562. #477	C₂²×C₁₉	semidirect
563. #477	C₂²×C₁₉	semidirect
564. #470	C₂²×C₁₉	semidirect
565. #470	C₂²×C₁₉	semidirect
566. #468	C₂²×C₁₉	semidirect
567. #468	C₂²×C₁₉	semidirect
574. #467	C₂²×C₁₉	semidirect
575. #467	C₂²×C₁₉	semidirect
576. #467	C₂²×C₁₉	semidirect
577. #467	C₂²×C₁₉	semidirect
579. #466	C₂²×C₁₉	semidirect
583. #465	C₂²×C₁₉	semidirect
584. #464	C₂²×C₁₉	semidirect
585. #463	C₂²×C₁₉	semidirect
586. #462	C₂²×C₁₉	semidirect
587. #462	C₂²×C₁₉	semidirect
588. #452	C₂²×C₁₉	semidirect
589. #452	C₂²×C₁₉	semidirect
590. #452	C₂²×C₁₉	semidirect
591. #451	C₂²×C₁₉	semidirect
592. #451	C₂²×C₁₉	semidirect
593. #451	C₂²×C₁₉	semidirect
594. #449	C₂²×C₁₉	semidirect
595. #448	C₂²×C₁₉	semidirect
596. #441	C₂²×C₁₉	semidirect
597. #441	C₂²×C₁₉	semidirect
598. #440	C₂²×C₁₉	semidirect
599. #440	C₂²×C₁₉	semidirect
604. #428	C₂²×C₁₉	semidirect
605. #427	C₂²×C₁₉	semidirect
606. C₂×#107	C₂²×C₁₉	semidirect
608. #419	C₂²×C₁₉	semidirect
609. #417	C₂²×C₁₉	semidirect
610. #416	C₂²×C₁₉	semidirect
611. C₂×#103	C₂²×C₁₉	semidirect
777. C₁₉	#62258	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×#3520	2
C₁₉×#3349	2
C₁₉×#3343	2
C₁₉×#3315	2
C₁₉×#3313	2
C₁₉×#3312	2
C₁₉×#3308	2
C₁₉×#3270	2
C₁₉×#3269	2
C₁₉×#3250	2
C₁₉×#3249	2
C₁₉×#3191	2
C₁₉×#3190	2
C₁₉×#3189	2
C₁₉×#3181	2
C₁₉×#3056	2
C₁₉×#3050	2
C₂×C₁₉×#467	2
C₂×C₁₉×#435	2
#62258	19

Subgroups — C19×#62258 #18068217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62258 #18068217