Subgroups — C₁₉×#62291 #18068250

Order 4864.

1780 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3541	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3356	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3351	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3316	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×#3307	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3277	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3276	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3204	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3202	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3197	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3195	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3173	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3063	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3056	C₂	1	2	yes	maximal, complemented
19	C₁₉×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₉×#137	C₂²	1	2	yes	—
21	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#563	—	2	2	no	—
25	C₁₉×#562	—	2	2	no	—
26	C₁₉×#556	C₂²	1	2	yes	—
27	C₁₉×#554	—	2	2	no	—
28	C₁₉×#554	C₂²	1	2	yes	—
29	C₁₉×#553	—	2	2	no	—
30	C₁₉×#553	C₂²	1	2	yes	—
31	C₁₉×#552	C₂²	1	2	yes	—
32	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#548	C₂²	1	2	yes	—
34	C₁₉×#548	C₂²	1	2	yes	—
35	C₁₉×#547	C₂²	1	2	yes	—
36	C₁₉×#542	—	2	2	no	—
37	C₁₉×#542	C₂²	1	2	yes	—
38	C₁₉×#541	C₂²	1	2	yes	—
39	C₁₉×#539	—	2	2	no	—
40	C₁₉×#538	—	2	2	no	—
41	C₁₉×#538	—	2	2	no	—
42	C₁₉×#537	C₂²	1	2	yes	—
43	C₁₉×#536	C₂²	1	2	yes	—
44	C₁₉×#525	C₂²	1	2	yes	—
45	C₁₉×#525	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
47	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#495	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#491	C₂²	1	2	yes	complemented
52	C₁₉×#489	C₂²	1	2	yes	complemented
53	C₁₉×#485	C₂²	1	2	yes	—
54	C₁₉×#485	C₂²	1	2	yes	complemented
55	C₁₉×#485	C₂²	1	2	yes	complemented
56	C₁₉×#483	C₂²	1	2	yes	—
57	C₁₉×#483	C₂²	1	2	yes	—
58	C₁₉×#483	C₂²	1	2	yes	complemented
59	C₁₉×#482	C₂²	1	2	yes	—
60	C₁₉×#481	C₂²	1	2	yes	complemented
61	C₁₉×#479	C₂²	1	2	yes	complemented
62	C₁₉×#478	C₂²	1	2	yes	complemented
63	C₁₉×#477	C₂²	1	2	yes	complemented
64	C₁₉×#475	C₂²	1	2	yes	complemented
65	C₁₉×#470	C₂²	1	1	yes	characteristic
66	C₁₉×#470	C₂²	1	1	yes	characteristic
67	C₁₉×#470	C₂²	1	1	yes	characteristic
68	C₁₉×#470	C₂²	1	2	yes	—
69	C₁₉×#470	C₂²	1	2	yes	—
70	C₁₉×#470	C₂²	1	2	yes	—
71	C₁₉×#470	C₂²	1	2	yes	complemented
72	C₁₉×#469	C₂²	1	1	yes	characteristic
73	C₁₉×#468	C₂²	1	2	yes	—
74	C₁₉×#468	C₂²	1	2	yes	—
75	C₁₉×#468	C₂²	1	2	yes	—
76	C₁₉×#468	C₂²	1	2	yes	complemented
77	C₁₉×#467	C₂²	1	2	yes	—
78	C₁₉×#467	C₂²	1	2	yes	—
79	C₁₉×#467	C₂²	1	2	yes	complemented
80	C₁₉×#465	C₂²	1	2	yes	—
81	C₁₉×#465	C₂²	1	2	yes	—
82	C₁₉×#465	C₂²	1	2	yes	complemented
83	C₁₉×#464	C₂²	1	2	yes	complemented
84	C₁₉×#464	C₂²	1	2	yes	complemented
85	C₁₉×#462	C₂²	1	2	yes	complemented
86	C₁₉×#461	C₂²	1	2	yes	complemented
87	C₁₉×#452	C₂²	1	2	yes	—
88	C₁₉×#452	C₂²	1	2	yes	complemented
89	C₁₉×#451	C₂²	1	2	yes	—
90	C₁₉×#451	C₂²	1	2	yes	—
91	C₁₉×#451	C₂²	1	2	yes	complemented
92	C₁₉×#451	C₂²	1	2	yes	complemented
93	C₁₉×#449	C₂²	1	2	yes	—
94	C₁₉×#449	C₂²	1	2	yes	complemented
95	C₁₉×#442	C₂²	1	1	yes	characteristic, complemented
96	C₁₉×#441	C₂²	1	1	yes	characteristic, complemented
97	C₁₉×#441	C₂²	1	1	yes	characteristic, complemented
98	C₁₉×#441	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
101	C₁₉×#436	C₂²	1	2	yes	—
102	C₁₉×#436	C₂²	1	2	yes	—
103	C₁₉×#435	C₂²	1	2	yes	—
104	C₁₉×#435	C₂²	1	2	yes	—
105	C₁₉×#428	C₂²	1	2	yes	—
106	C₁₉×#428	C₂²	1	2	yes	complemented
107	C₁₉×#424	C₂²	1	1	yes	characteristic
108	C₁₉×#419	C₂²	1	2	yes	—
109	C₁₉×#417	C₂²	1	2	yes	—
110	C₁₉×#416	C₂²	1	2	yes	complemented
111	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
112	C₁₉×#408	C₂²	1	1	yes	characteristic
113	C₁₉×#407	C₂²	1	1	yes	characteristic
114	C₁₉×#405	C₂²	1	1	yes	characteristic
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×Q₈×C₁₉	C₂³	1	2	yes	—
119	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#137	—	4	4	no	—
122	C₁₉×#137	—	4	4	no	—
123	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
128	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
132	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
133	C₁₉×#131	—	4	2	no	—
134	C₂×M₁₆×C₁₉	—	4	2	no	—
135	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
136	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
137	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
140	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
143	C₁₉×C₄⋊Q₈	—	2	2	no	—
144	C₁₉×C₄⋊Q₈	—	2	2	no	—
145	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
147	C₁₉×#126	—	2	2	no	—
148	C₁₉×#126	—	2	2	no	—
149	C₁₉×#126	—	2	2	no	—
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×#125	—	2	2	no	—
155	C₁₉×#125	—	2	2	no	—
156	C₁₉×#125	—	2	2	no	—
157	C₁₉×#125	—	2	2	no	—
158	C₁₉×#125	C₂³	1	2	yes	—
159	C₁₉×#124	—	2	2	no	—
160	C₁₉×#124	—	2	2	no	—
161	C₁₉×#124	—	2	2	no	—
162	C₁₉×#124	—	2	2	no	—
163	C₁₉×#124	—	2	2	no	—
164	C₁₉×#124	C₂³	1	2	yes	—
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×#123	D₄	1	2	yes	—
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	—	2	2	no	—
184	C₁₉×C₂²⋊Q₈	D₄	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×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₉×#121	—	2	2	no	—
195	C₁₉×#121	—	2	2	no	—
196	C₁₉×#121	—	2	2	no	—
197	C₁₉×#121	—	2	2	no	—
198	C₁₉×#121	—	2	2	no	—
199	C₁₉×#121	—	2	2	no	—
200	C₁₉×#121	—	2	2	no	—
201	C₁₉×#121	D₄	1	2	yes	—
202	C₁₉×#121	C₂³	1	2	yes	—
203	C₁₉×#121	C₂³	1	2	yes	—
204	C₁₉×#121	C₂³	1	2	yes	—
205	C₁₉×#120	—	2	2	no	—
206	C₁₉×#120	D₄	1	2	yes	—
207	C₄×Q₈×C₁₉	—	2	2	no	—
208	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
209	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
210	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
211	C₄×D₄×C₁₉	—	2	2	no	—
212	C₄×D₄×C₁₉	—	2	2	no	—
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	C₂³	1	2	yes	—
219	C₄×D₄×C₁₉	C₂³	1	2	yes	—
220	C₄×D₄×C₁₉	C₂³	1	2	yes	—
221	C₁₉×#117	—	2	2	no	—
222	C₁₉×#117	C₂³	1	2	yes	—
223	C₁₉×#117	C₂³	1	2	yes	—
224	C₁₉×#117	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
226	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
227	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₁₉×#107	C₂³	1	2	yes	—
231	C₁₉×#107	C₂³	1	2	yes	—
232	C₁₉×#107	C₂³	1	2	yes	—
233	C₁₉×#106	C₂³	1	2	yes	—
234	C₁₉×#106	C₂³	1	2	yes	—
235	C₁₉×#106	C₂³	1	2	yes	—
236	C₁₉×#106	C₂³	1	1	yes	characteristic
237	C₁₉×#106	C₂³	1	1	yes	characteristic
238	C₁₉×#106	C₂³	1	1	yes	characteristic
239	C₁₉×#106	C₂³	1	1	yes	characteristic
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×#103	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×#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	C₂×D₄	1	1	yes	characteristic
267	#41×C₁₉	—	4	1	no	—
268	#41×C₁₉	—	4	1	no	—
269	#41×C₁₉	—	4	2	no	—
270	#41×C₁₉	—	4	2	no	—
271	#41×C₁₉	—	4	2	no	—
272	#41×C₁₉	—	4	2	no	—
273	C₂×Q₈×C₁₉	—	2	2	no	—
274	C₂×Q₈×C₁₉	—	2	2	no	—
275	C₂×Q₈×C₁₉	—	2	2	no	—
276	C₂×Q₈×C₁₉	—	4	2	no	—
277	C₂×Q₈×C₁₉	—	4	2	no	—
278	C₂×Q₈×C₁₉	—	4	2	no	—
279	C₂×Q₈×C₁₉	—	4	2	no	—
280	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
281	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
282	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
283	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
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	C₂×D₄	1	2	yes	—
290	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
291	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
293	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
302	C₂²×C₄×C₁₉	—	4	1	no	—
303	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
308	Q₁₆×C₁₉	—	2	4	no	—
309	Q₁₆×C₁₉	—	4	1	no	—
310	Q₁₆×C₁₉	—	4	1	no	—
311	Q₁₆×C₁₉	—	4	1	no	—
312	Q₁₆×C₁₉	—	4	2	no	—
313	Q₁₆×C₁₉	—	4	2	no	—
314	SD₁₆×C₁₉	—	2	4	no	—
315	SD₁₆×C₁₉	—	4	2	no	—
316	SD₁₆×C₁₉	—	4	2	no	—
317	D₈×C₁₉	—	4	1	no	—
318	M₁₆×C₁₉	—	2	4	no	—
319	M₁₆×C₁₉	—	2	4	no	—
320	M₁₆×C₁₉	—	4	2	no	—
321	M₁₆×C₁₉	—	4	1	no	—
322	M₁₆×C₁₉	—	4	1	no	—
323	C₂×C₈×C₁₉	—	2	2	no	—
324	C₂×C₈×C₁₉	—	4	1	no	—
325	C₂×C₈×C₁₉	—	4	2	no	—
326	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
327	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
328	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
329	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
330	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
331	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₁₉	—	2	2	no	—
333	C₄⋊C₄×C₁₉	—	2	2	no	—
334	C₄⋊C₄×C₁₉	—	2	2	no	—
335	C₄⋊C₄×C₁₉	—	2	2	no	—
336	C₄⋊C₄×C₁₉	—	2	2	no	—
337	C₄⋊C₄×C₁₉	—	2	2	no	—
338	C₄⋊C₄×C₁₉	—	2	2	no	—
339	C₄⋊C₄×C₁₉	—	2	2	no	—
340	C₄⋊C₄×C₁₉	—	2	2	no	—
341	C₄⋊C₄×C₁₉	—	2	2	no	—
342	C₄⋊C₄×C₁₉	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
352	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
358	C₂²⋊C₄×C₁₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
376	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
380	C₄²×C₁₉	—	2	2	no	—
381	C₄²×C₁₉	—	2	2	no	—
382	C₄²×C₁₉	—	2	2	no	—
383	C₄²×C₁₉	—	2	2	no	—
384	C₄²×C₁₉	—	2	2	no	—
385	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
386	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
387	#62291	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂³×C₁₉	—	2	2	no	—
389	C₂³×C₁₉	—	4	1	no	—
390	C₂³×C₁₉	—	4	2	no	—
391	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
392	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
393	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
394	Q₈×C₁₉	—	2	2	no	—
395	Q₈×C₁₉	—	2	2	no	—
396	Q₈×C₁₉	—	2	2	no	—
397	Q₈×C₁₉	—	2	2	no	—
398	Q₈×C₁₉	—	2	2	no	—
399	Q₈×C₁₉	—	2	2	no	—
400	Q₈×C₁₉	—	4	1	no	—
401	Q₈×C₁₉	—	8	2	no	—
402	Q₈×C₁₉	—	8	2	no	—
403	Q₈×C₁₉	—	8	2	no	—
404	D₄×C₁₉	—	2	2	no	—
405	D₄×C₁₉	—	2	2	no	—
406	D₄×C₁₉	—	4	2	no	—
407	D₄×C₁₉	—	4	2	no	—
408	D₄×C₁₉	—	4	1	no	—
409	D₄×C₁₉	—	4	2	no	—
410	D₄×C₁₉	—	4	4	no	—
411	D₄×C₁₉	—	8	2	no	—
412	D₄×C₁₉	—	8	2	no	—
413	D₄×C₁₉	—	8	2	no	—
414	D₄×C₁₉	—	8	2	no	—
415	C₂×C₄×C₁₉	—	2	1	no	—
416	C₂×C₄×C₁₉	—	2	2	no	—
417	C₂×C₄×C₁₉	—	2	2	no	—
418	C₂×C₄×C₁₉	—	2	1	no	—
419	C₂×C₄×C₁₉	—	2	2	no	—
420	C₂×C₄×C₁₉	—	2	2	no	—
421	C₂×C₄×C₁₉	—	2	2	no	—
422	C₂×C₄×C₁₉	—	2	2	no	—
423	C₂×C₄×C₁₉	—	2	2	no	—
424	C₂×C₄×C₁₉	—	2	2	no	—
425	C₂×C₄×C₁₉	—	2	2	no	—
426	C₂×C₄×C₁₉	—	2	2	no	—
427	C₂×C₄×C₁₉	—	2	2	no	—
428	C₂×C₄×C₁₉	—	4	1	no	—
429	C₂×C₄×C₁₉	—	4	2	no	—
430	C₂×C₄×C₁₉	—	8	2	no	—
431	C₂×C₄×C₁₉	—	8	2	no	—
432	C₂×C₄×C₁₉	—	8	2	no	—
433	C₂×C₄×C₁₉	—	8	2	no	—
434	C₂×C₄×C₁₉	—	8	2	no	—
435	C₂×C₄×C₁₉	—	8	2	no	—
436	C₂×C₄×C₁₉	—	8	2	no	—
437	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
443	C₈×C₁₉	—	2	1	no	—
444	C₈×C₁₉	—	2	2	no	—
445	C₈×C₁₉	—	2	2	no	—
446	C₈×C₁₉	—	2	1	no	—
447	C₈×C₁₉	—	2	1	no	—
448	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
449	#3541	C₂×C₁₉	1	2	yes	complemented
450	#3356	C₂×C₁₉	1	2	yes	complemented
451	#3351	C₂×C₁₉	1	2	yes	complemented
452	#3316	C₂×C₁₉	1	2	yes	complemented
453	#3313	C₂×C₁₉	1	2	yes	complemented
454	#3312	C₂×C₁₉	1	2	yes	complemented
455	#3307	C₂×C₁₉	1	2	yes	complemented
456	#3277	C₂×C₁₉	1	2	yes	complemented
457	#3276	C₂×C₁₉	1	2	yes	complemented
458	#3258	C₂×C₁₉	1	2	yes	complemented
459	#3204	C₂×C₁₉	1	1	yes	characteristic, complemented
460	#3202	C₂×C₁₉	1	1	yes	characteristic, complemented
461	#3197	C₂×C₁₉	1	1	yes	characteristic, complemented
462	#3195	C₂×C₁₉	1	1	yes	characteristic, complemented
463	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
464	#3173	C₂×C₁₉	1	1	yes	characteristic, complemented
465	#3063	C₂×C₁₉	1	2	yes	complemented
466	#3056	C₂×C₁₉	1	2	yes	complemented
467	#2930	C₂×C₁₉	1	1	yes	characteristic, complemented
468	C₂²×C₁₉	—	2	2	no	—
469	C₂²×C₁₉	—	2	2	no	—
470	C₂²×C₁₉	—	2	2	no	—
471	C₂²×C₁₉	—	2	2	no	—
472	C₂²×C₁₉	—	2	2	no	—
473	C₂²×C₁₉	—	2	2	no	—
474	C₂²×C₁₉	—	2	1	no	—
475	C₂²×C₁₉	—	2	2	no	—
476	C₂²×C₁₉	—	4	2	no	—
477	C₂²×C₁₉	—	4	2	no	—
478	C₂²×C₁₉	—	4	2	no	—
479	C₂²×C₁₉	—	8	2	no	—
480	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
481	C₄×C₁₉	—	2	2	no	—
482	C₄×C₁₉	—	2	2	no	—
483	C₄×C₁₉	—	2	2	no	—
484	C₄×C₁₉	—	2	1	no	—
485	C₄×C₁₉	—	2	2	no	—
486	C₄×C₁₉	—	4	2	no	—
487	C₄×C₁₉	—	4	2	no	—
488	C₄×C₁₉	—	4	2	no	—
489	C₄×C₁₉	—	4	2	no	—
490	C₄×C₁₉	—	4	2	no	—
491	C₄×C₁₉	—	4	2	no	—
492	C₄×C₁₉	—	4	2	no	—
493	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₄×C₁₉	#585	1	1	yes	characteristic
495	C₂×#137	C₂²×C₁₉	1	2	yes	—
496	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
497	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
498	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
499	#563	—	2	2	no	—
500	#562	—	2	2	no	—
501	#556	C₂²×C₁₉	1	2	yes	—
502	#554	—	2	2	no	—
503	#554	C₂²×C₁₉	1	2	yes	—
504	#553	—	2	2	no	—
505	#553	C₂²×C₁₉	1	2	yes	—
506	#552	C₂²×C₁₉	1	2	yes	—
507	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
508	#548	C₂²×C₁₉	1	2	yes	—
509	#548	C₂²×C₁₉	1	2	yes	—
510	#547	C₂²×C₁₉	1	2	yes	—
511	#542	—	2	2	no	—
512	#542	C₂²×C₁₉	1	2	yes	—
513	#541	C₂²×C₁₉	1	2	yes	—
514	#539	—	2	2	no	—
515	#538	—	2	2	no	—
516	#538	—	2	2	no	—
517	#537	C₂²×C₁₉	1	2	yes	—
518	#536	C₂²×C₁₉	1	2	yes	—
519	#525	C₂²×C₁₉	1	2	yes	—
520	#525	C₂²×C₁₉	1	1	yes	characteristic
521	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
522	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
523	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
524	#495	C₂²×C₁₉	1	1	yes	characteristic, complemented
525	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
526	#491	C₂²×C₁₉	1	2	yes	complemented
527	#489	C₂²×C₁₉	1	2	yes	complemented
528	#485	C₂²×C₁₉	1	2	yes	—
529	#485	C₂²×C₁₉	1	2	yes	complemented
530	#485	C₂²×C₁₉	1	2	yes	complemented
531	#483	C₂²×C₁₉	1	2	yes	—
532	#483	C₂²×C₁₉	1	2	yes	—
533	#483	C₂²×C₁₉	1	2	yes	complemented
534	#482	C₂²×C₁₉	1	2	yes	—
535	#481	C₂²×C₁₉	1	2	yes	complemented
536	#479	C₂²×C₁₉	1	2	yes	complemented
537	#478	C₂²×C₁₉	1	2	yes	complemented
538	#477	C₂²×C₁₉	1	2	yes	complemented
539	#475	C₂²×C₁₉	1	2	yes	complemented
540	#470	C₂²×C₁₉	1	2	yes	—
541	#470	C₂²×C₁₉	1	1	yes	characteristic
542	#470	C₂²×C₁₉	1	1	yes	characteristic
543	#470	C₂²×C₁₉	1	1	yes	characteristic
544	#470	C₂²×C₁₉	1	2	yes	—
545	#470	C₂²×C₁₉	1	2	yes	—
546	#470	C₂²×C₁₉	1	2	yes	complemented
547	#469	C₂²×C₁₉	1	1	yes	characteristic
548	#468	C₂²×C₁₉	1	2	yes	—
549	#468	C₂²×C₁₉	1	2	yes	—
550	#468	C₂²×C₁₉	1	2	yes	—
551	#468	C₂²×C₁₉	1	2	yes	complemented
552	#467	C₂²×C₁₉	1	2	yes	—
553	#467	C₂²×C₁₉	1	2	yes	—
554	#467	C₂²×C₁₉	1	2	yes	complemented
555	#465	C₂²×C₁₉	1	2	yes	—
556	#465	C₂²×C₁₉	1	2	yes	—
557	#465	C₂²×C₁₉	1	2	yes	complemented
558	#464	C₂²×C₁₉	1	2	yes	complemented
559	#464	C₂²×C₁₉	1	2	yes	complemented
560	#462	C₂²×C₁₉	1	2	yes	complemented
561	#461	C₂²×C₁₉	1	2	yes	complemented
562	#452	C₂²×C₁₉	1	2	yes	—
563	#452	C₂²×C₁₉	1	2	yes	complemented
564	#451	C₂²×C₁₉	1	2	yes	—
565	#451	C₂²×C₁₉	1	2	yes	—
566	#451	C₂²×C₁₉	1	2	yes	complemented
567	#451	C₂²×C₁₉	1	2	yes	complemented
568	#449	C₂²×C₁₉	1	2	yes	—
569	#449	C₂²×C₁₉	1	2	yes	complemented
570	#442	C₂²×C₁₉	1	1	yes	characteristic, complemented
571	#441	C₂²×C₁₉	1	1	yes	characteristic, complemented
572	#441	C₂²×C₁₉	1	1	yes	characteristic, complemented
573	#441	C₂²×C₁₉	1	1	yes	characteristic, complemented
574	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
575	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
576	#436	C₂²×C₁₉	1	2	yes	—
577	#436	C₂²×C₁₉	1	2	yes	—
578	#435	C₂²×C₁₉	1	2	yes	—
579	#435	C₂²×C₁₉	1	2	yes	—
580	#428	C₂²×C₁₉	1	2	yes	—
581	#428	C₂²×C₁₉	1	2	yes	complemented
582	#424	C₂²×C₁₉	1	1	yes	characteristic
583	#419	C₂²×C₁₉	1	2	yes	—
584	#417	C₂²×C₁₉	1	2	yes	—
585	#416	C₂²×C₁₉	1	2	yes	complemented
586	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
587	#408	C₂²×C₁₉	1	1	yes	characteristic
588	#407	C₂²×C₁₉	1	1	yes	characteristic
589	#405	C₂²×C₁₉	1	1	yes	characteristic
590	C₂×C₁₉	—	4	2	no	—
591	C₂×C₁₉	—	4	2	no	—
592	C₂×C₁₉	—	4	1	no	—
593	C₂×C₁₉	—	8	2	no	—
594	C₂×C₁₉	#3496	1	1	yes	characteristic
595	C₂×C₁₉	#3586	1	2	yes	—
596	C₂×#41	C₂³×C₁₉	1	2	yes	—
597	C₂×#41	C₂³×C₁₉	1	2	yes	—
598	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
599	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
600	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
601	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
602	#137	—	4	4	no	—
603	#137	—	4	4	no	—
604	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
605	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
606	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
607	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
608	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
609	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
610	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
613	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
614	#131	—	4	2	no	—
615	C₂×M₁₆	—	4	2	no	—
616	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
617	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
618	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
619	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
620	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
622	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
623	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
624	C₄⋊Q₈	—	2	2	no	—
625	C₄⋊Q₈	—	2	2	no	—
626	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	C₂³×C₁₉	1	2	yes	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	2	no	—
643	#124	—	2	2	no	—
644	#124	—	2	2	no	—
645	#124	C₂³×C₁₉	1	2	yes	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	D₄×C₁₉	1	2	yes	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
666	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
667	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
668	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
669	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
670	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
671	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
672	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
673	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
674	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
675	#121	—	2	2	no	—
676	#121	—	2	2	no	—
677	#121	—	2	2	no	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	—	2	2	no	—
681	#121	—	2	2	no	—
682	#121	D₄×C₁₉	1	2	yes	—
683	#121	C₂³×C₁₉	1	2	yes	—
684	#121	C₂³×C₁₉	1	2	yes	—
685	#121	C₂³×C₁₉	1	2	yes	—
686	#120	—	2	2	no	—
687	#120	D₄×C₁₉	1	2	yes	—
688	C₄×Q₈	—	2	2	no	—
689	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
690	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
691	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	2	no	—
699	C₄×D₄	C₂³×C₁₉	1	2	yes	—
700	C₄×D₄	C₂³×C₁₉	1	2	yes	—
701	C₄×D₄	C₂³×C₁₉	1	2	yes	—
702	#117	—	2	2	no	—
703	#117	C₂³×C₁₉	1	2	yes	—
704	#117	C₂³×C₁₉	1	2	yes	—
705	#117	C₂³×C₁₉	1	1	yes	characteristic
706	C₂×C₄⋊C₄	—	2	2	no	—
707	C₂×C₄⋊C₄	—	2	2	no	—
708	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	#107	C₂³×C₁₉	1	2	yes	—
712	#107	C₂³×C₁₉	1	2	yes	—
713	#107	C₂³×C₁₉	1	2	yes	—
714	#106	C₂³×C₁₉	1	2	yes	—
715	#106	C₂³×C₁₉	1	2	yes	—
716	#106	C₂³×C₁₉	1	2	yes	—
717	#106	C₂³×C₁₉	1	1	yes	characteristic
718	#106	C₂³×C₁₉	1	1	yes	characteristic
719	#106	C₂³×C₁₉	1	1	yes	characteristic
720	#106	C₂³×C₁₉	1	1	yes	characteristic
721	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
722	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
723	#103	C₂³×C₁₉	1	2	yes	—
724	#103	C₂³×C₁₉	1	2	yes	—
725	#103	C₂³×C₁₉	1	2	yes	—
726	#103	C₂³×C₁₉	1	2	yes	—
727	#103	C₂³×C₁₉	1	2	yes	—
728	#103	C₂³×C₁₉	1	2	yes	—
729	#103	C₂³×C₁₉	1	2	yes	—
730	#103	C₂³×C₁₉	1	2	yes	—
731	#103	C₂³×C₁₉	1	2	yes	—
732	#103	C₂³×C₁₉	1	2	yes	—
733	#103	C₂³×C₁₉	1	2	yes	—
734	#103	C₂³×C₁₉	1	2	yes	—
735	#102	C₂³×C₁₉	1	2	yes	—
736	#102	C₂³×C₁₉	1	2	yes	—
737	#102	C₂³×C₁₉	1	2	yes	—
738	#102	C₂³×C₁₉	1	2	yes	—
739	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
741	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
742	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
743	#97	C₂³×C₁₉	1	1	yes	characteristic
744	#97	C₂³×C₁₉	1	1	yes	characteristic
745	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
746	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
747	C₁₉	#62291	1	1	yes	characteristic, direct product factor, Sylow
748	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
749	#41	—	4	1	no	—
750	#41	—	4	1	no	—
751	#41	—	4	2	no	—
752	#41	—	4	2	no	—
753	#41	—	4	2	no	—
754	#41	—	4	2	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	2	no	—
760	C₂×Q₈	—	4	2	no	—
761	C₂×Q₈	—	4	2	no	—
762	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
763	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
764	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
765	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
772	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
773	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
774	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
775	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	4	1	no	—
784	C₂²×C₄	—	4	1	no	—
785	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
786	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
790	Q₁₆	—	2	4	no	—
791	Q₁₆	—	4	1	no	—
792	Q₁₆	—	4	1	no	—
793	Q₁₆	—	4	1	no	—
794	Q₁₆	—	4	2	no	—
795	Q₁₆	—	4	2	no	—
796	SD₁₆	—	2	4	no	—
797	SD₁₆	—	4	2	no	—
798	SD₁₆	—	4	2	no	—
799	D₈	—	4	1	no	—
800	M₁₆	—	2	4	no	—
801	M₁₆	—	2	4	no	—
802	M₁₆	—	4	2	no	—
803	M₁₆	—	4	1	no	—
804	M₁₆	—	4	1	no	—
805	C₂×C₈	—	2	2	no	—
806	C₂×C₈	—	4	1	no	—
807	C₂×C₈	—	4	2	no	—
808	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
809	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
810	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
811	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
812	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
813	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
858	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
859	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
860	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
868	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
869	C₂³	—	2	2	no	—
870	C₂³	—	4	1	no	—
871	C₂³	—	4	2	no	—
872	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
873	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
874	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
875	Q₈	—	2	2	no	—
876	Q₈	—	2	2	no	—
877	Q₈	—	2	2	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	4	1	no	—
882	Q₈	—	8	2	no	—
883	Q₈	—	8	2	no	—
884	Q₈	—	8	2	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	4	1	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	2	no	—
890	D₄	—	4	2	no	—
891	D₄	—	4	4	no	—
892	D₄	—	8	2	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	D₄	—	8	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	2	no	—
911	C₂×C₄	—	8	2	no	—
912	C₂×C₄	—	8	2	no	—
913	C₂×C₄	—	8	2	no	—
914	C₂×C₄	—	8	2	no	—
915	C₂×C₄	—	8	2	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
919	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
920	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
921	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
922	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
923	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
924	C₈	—	2	1	no	—
925	C₈	—	2	2	no	—
926	C₈	—	2	2	no	—
927	C₈	—	2	1	no	—
928	C₈	—	2	1	no	—
929	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	8	2	no	—
942	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
943	C₄	—	2	2	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
956	C₄	C₁₉×#585	1	1	yes	characteristic
957	C₂	—	4	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	2	no	—
960	C₂	—	8	2	no	—
961	C₂	C₁₉×#3496	1	1	yes	characteristic
962	C₂	C₁₉×#3586	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×#3541	C₂	semidirect
2. C₁₉×#3356	C₂	semidirect
3. C₁₉×#3351	C₂	semidirect
4. C₁₉×#3316	C₂	semidirect
5. C₁₉×#3313	C₂	semidirect
6. C₁₉×#3312	C₂	semidirect
7. C₁₉×#3307	C₂	semidirect
8. C₁₉×#3277	C₂	semidirect
9. C₁₉×#3276	C₂	semidirect
10. C₁₉×#3258	C₂	semidirect
11. C₁₉×#3204	C₂	semidirect
12. C₁₉×#3202	C₂	semidirect
13. C₁₉×#3197	C₂	semidirect
14. C₁₉×#3195	C₂	semidirect
15. C₁₉×#3177	C₂	semidirect
16. C₁₉×#3173	C₂	semidirect
17. C₁₉×#3063	C₂	semidirect
18. C₁₉×#3056	C₂	semidirect
19. C₁₉×#2930	C₂	semidirect
21. C₂×C₁₉×#137	C₂²	semidirect
47. C₁₉×#499	C₂²	semidirect
48. C₁₉×#498	C₂²	semidirect
49. C₁₉×#495	C₂²	semidirect
50. C₁₉×#494	C₂²	semidirect
51. C₁₉×#491	C₂²	semidirect
52. C₁₉×#489	C₂²	semidirect
54. C₁₉×#485	C₂²	semidirect
55. C₁₉×#485	C₂²	semidirect
58. C₁₉×#483	C₂²	semidirect
60. C₁₉×#481	C₂²	semidirect
61. C₁₉×#479	C₂²	semidirect
62. C₁₉×#478	C₂²	semidirect
63. C₁₉×#477	C₂²	semidirect
64. C₁₉×#475	C₂²	semidirect
71. C₁₉×#470	C₂²	semidirect
76. C₁₉×#468	C₂²	semidirect
79. C₁₉×#467	C₂²	semidirect
82. C₁₉×#465	C₂²	semidirect
83. C₁₉×#464	C₂²	semidirect
84. C₁₉×#464	C₂²	semidirect
85. C₁₉×#462	C₂²	semidirect
86. C₁₉×#461	C₂²	semidirect
88. C₁₉×#452	C₂²	semidirect
91. C₁₉×#451	C₂²	semidirect
92. C₁₉×#451	C₂²	semidirect
94. C₁₉×#449	C₂²	semidirect
95. C₁₉×#442	C₂²	semidirect
96. C₁₉×#441	C₂²	semidirect
97. C₁₉×#441	C₂²	semidirect
98. C₁₉×#441	C₂²	semidirect
99. C₄×Q₁₆×C₁₉	C₂²	semidirect
100. C₄×SD₁₆×C₁₉	C₂²	semidirect
106. C₁₉×#428	C₂²	semidirect
110. C₁₉×#416	C₂²	semidirect
111. C₂×C₁₉×#103	C₂²	semidirect
387. #62291	C₁₉	direct (N × H)
449. #3541	C₂×C₁₉	semidirect
450. #3356	C₂×C₁₉	semidirect
451. #3351	C₂×C₁₉	semidirect
452. #3316	C₂×C₁₉	semidirect
453. #3313	C₂×C₁₉	semidirect
454. #3312	C₂×C₁₉	semidirect
455. #3307	C₂×C₁₉	semidirect
456. #3277	C₂×C₁₉	semidirect
457. #3276	C₂×C₁₉	semidirect
458. #3258	C₂×C₁₉	semidirect
459. #3204	C₂×C₁₉	semidirect
460. #3202	C₂×C₁₉	semidirect
461. #3197	C₂×C₁₉	semidirect
462. #3195	C₂×C₁₉	semidirect
463. #3177	C₂×C₁₉	semidirect
464. #3173	C₂×C₁₉	semidirect
465. #3063	C₂×C₁₉	semidirect
466. #3056	C₂×C₁₉	semidirect
467. #2930	C₂×C₁₉	semidirect
496. C₂×#137	C₂²×C₁₉	semidirect
522. #499	C₂²×C₁₉	semidirect
523. #498	C₂²×C₁₉	semidirect
524. #495	C₂²×C₁₉	semidirect
525. #494	C₂²×C₁₉	semidirect
526. #491	C₂²×C₁₉	semidirect
527. #489	C₂²×C₁₉	semidirect
529. #485	C₂²×C₁₉	semidirect
530. #485	C₂²×C₁₉	semidirect
533. #483	C₂²×C₁₉	semidirect
535. #481	C₂²×C₁₉	semidirect
536. #479	C₂²×C₁₉	semidirect
537. #478	C₂²×C₁₉	semidirect
538. #477	C₂²×C₁₉	semidirect
539. #475	C₂²×C₁₉	semidirect
546. #470	C₂²×C₁₉	semidirect
551. #468	C₂²×C₁₉	semidirect
554. #467	C₂²×C₁₉	semidirect
557. #465	C₂²×C₁₉	semidirect
558. #464	C₂²×C₁₉	semidirect
559. #464	C₂²×C₁₉	semidirect
560. #462	C₂²×C₁₉	semidirect
561. #461	C₂²×C₁₉	semidirect
563. #452	C₂²×C₁₉	semidirect
566. #451	C₂²×C₁₉	semidirect
567. #451	C₂²×C₁₉	semidirect
569. #449	C₂²×C₁₉	semidirect
570. #442	C₂²×C₁₉	semidirect
571. #441	C₂²×C₁₉	semidirect
572. #441	C₂²×C₁₉	semidirect
573. #441	C₂²×C₁₉	semidirect
574. C₄×Q₁₆	C₂²×C₁₉	semidirect
575. C₄×SD₁₆	C₂²×C₁₉	semidirect
581. #428	C₂²×C₁₉	semidirect
585. #416	C₂²×C₁₉	semidirect
586. C₂×#103	C₂²×C₁₉	semidirect
747. C₁₉	#62291	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×#3541	2
C₁₉×#3356	2
C₁₉×#3351	2
C₁₉×#3316	2
C₁₉×#3313	2
C₁₉×#3312	2
C₁₉×#3307	2
C₁₉×#3277	2
C₁₉×#3276	2
C₁₉×#3258	2
C₁₉×#3204	2
C₁₉×#3202	2
C₁₉×#3197	2
C₁₉×#3195	2
C₁₉×#3177	2
C₁₉×#3173	2
C₁₉×#3063	2
C₁₉×#3056	2
C₁₉×#2930	2
#62291	19

Subgroups — C19×#62291 #18068250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62291 #18068250