Subgroups — C₁₉×#24466 #18030425

Order 4864.

1418 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3489	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3007	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2039	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2038	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2007	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1896	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1859	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₉	—	2	1	no	—
23	C₁₉×#548	—	2	1	no	—
24	C₁₉×#547	—	2	1	no	—
25	C₁₉×#547	—	2	2	no	—
26	C₁₉×#546	—	2	1	no	—
27	C₁₉×#546	—	2	2	no	—
28	C₁₉×#537	—	2	1	no	—
29	C₁₉×#537	C₂²	1	1	yes	characteristic
30	C₁₉×#536	—	2	1	no	—
31	C₁₉×#536	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#525	—	2	1	no	—
34	C₁₉×#525	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₁₉×#520	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#470	—	2	1	no	—
41	C₁₉×#468	—	2	1	no	—
42	C₁₉×#467	—	2	1	no	—
43	C₁₉×#465	—	2	1	no	—
44	C₁₉×#456	—	2	4	no	—
45	C₁₉×#452	—	2	1	no	—
46	C₁₉×#452	—	2	1	no	—
47	C₁₉×#451	—	2	1	no	—
48	C₁₉×#450	—	2	1	no	—
49	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₉×#104	—	2	4	no	—
51	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#417	C₂²	1	1	yes	characteristic
59	C₁₉×#417	C₂²	1	1	yes	characteristic
60	C₁₉×#417	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#407	C₂²	1	1	yes	characteristic
64	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#389	—	2	2	no	—
67	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#380	—	2	2	no	—
69	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#343	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×2₋¹⁺⁴	—	2	2	no	—
74	C₁₉×2₋¹⁺⁴	—	2	2	no	—
75	C₁₉×2₋¹⁺⁴	—	4	1	no	—
76	C₁₉×2₋¹⁺⁴	—	4	1	no	—
77	C₂×#41×C₁₉	—	2	1	no	—
78	C₂×#41×C₁₉	—	2	1	no	—
79	C₂×#41×C₁₉	—	2	1	no	—
80	C₂×#41×C₁₉	—	2	2	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	—	2	2	no	—
83	C₂×#41×C₁₉	—	2	2	no	—
84	C₂×#41×C₁₉	—	4	1	no	—
85	C₂×#41×C₁₉	—	4	1	no	—
86	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
87	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
88	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₉	—	2	1	no	—
92	C₂²×Q₈×C₁₉	—	2	1	no	—
93	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
94	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₉	—	2	1	no	—
97	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂³×C₄×C₁₉	—	2	1	no	—
99	C₂³×C₄×C₁₉	—	2	1	no	—
100	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#137	—	2	2	no	—
102	C₁₉×#137	—	2	2	no	—
103	C₁₉×#137	—	2	2	no	—
104	C₁₉×#137	—	4	1	no	—
105	C₁₉×#137	—	4	1	no	—
106	C₁₉×#137	—	4	1	no	—
107	C₂×Q₁₆×C₁₉	—	2	1	no	—
108	C₂×Q₁₆×C₁₉	—	2	1	no	—
109	C₂×Q₁₆×C₁₉	—	2	1	no	—
110	C₂×SD₁₆×C₁₉	—	2	1	no	—
111	C₂×SD₁₆×C₁₉	—	2	1	no	—
112	C₂×SD₁₆×C₁₉	—	2	1	no	—
113	C₂×M₁₆×C₁₉	—	2	1	no	—
114	C₂×M₁₆×C₁₉	—	2	2	no	—
115	C₂×M₁₆×C₁₉	—	4	1	no	—
116	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₉	—	2	1	no	—
121	C₁₉×C₄⋊Q₈	—	2	2	no	—
122	C₁₉×C₄⋊Q₈	—	2	1	no	—
123	C₁₉×C₄⋊Q₈	—	2	2	no	—
124	C₁₉×C₄⋊Q₈	—	4	1	no	—
125	C₁₉×#124	—	2	2	no	—
126	C₁₉×#124	—	2	1	no	—
127	C₁₉×#123	—	2	2	no	—
128	C₁₉×#123	—	2	2	no	—
129	C₁₉×#123	—	2	2	no	—
130	C₁₉×#123	—	2	1	no	—
131	C₁₉×#123	—	2	2	no	—
132	C₁₉×C₂²⋊Q₈	—	2	2	no	—
133	C₁₉×C₂²⋊Q₈	—	2	2	no	—
134	C₁₉×C₂²⋊Q₈	—	2	2	no	—
135	C₁₉×C₂²⋊Q₈	—	2	1	no	—
136	C₁₉×C₂²⋊Q₈	—	2	1	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	—	2	1	no	—
139	C₁₉×C₂²⋊Q₈	—	2	1	no	—
140	C₁₉×C₂²⋊Q₈	—	2	1	no	—
141	C₁₉×C₂²⋊Q₈	—	2	1	no	—
142	C₁₉×C₂²⋊Q₈	—	2	1	no	—
143	C₁₉×C₂²⋊Q₈	—	2	1	no	—
144	C₁₉×C₂²⋊Q₈	—	2	1	no	—
145	C₁₉×C₂²⋊Q₈	—	2	1	no	—
146	C₁₉×C₂²⋊Q₈	—	2	1	no	—
147	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
148	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
149	C₁₉×#121	—	2	2	no	—
150	C₁₉×#121	—	2	2	no	—
151	C₁₉×#121	—	2	2	no	—
152	C₁₉×#121	—	2	1	no	—
153	C₁₉×#121	—	2	1	no	—
154	C₁₉×#121	—	2	2	no	—
155	C₁₉×#121	D₄	1	1	yes	characteristic
156	C₁₉×#121	D₄	1	1	yes	characteristic
157	C₁₉×#120	—	2	2	no	—
158	C₁₉×#120	—	2	1	no	—
159	C₄×Q₈×C₁₉	—	2	1	no	—
160	C₄×D₄×C₁₉	—	2	2	no	—
161	C₄×D₄×C₁₉	—	2	2	no	—
162	C₄×D₄×C₁₉	—	2	1	no	—
163	C₄×D₄×C₁₉	—	2	2	no	—
164	C₄×D₄×C₁₉	—	2	1	no	—
165	C₄×D₄×C₁₉	—	2	1	no	—
166	C₁₉×#117	—	2	1	no	—
167	C₁₉×#117	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
179	C₂×C₄²×C₁₉	—	2	2	no	—
180	C₂×C₄²×C₁₉	—	2	1	no	—
181	C₂×C₄²×C₁₉	—	4	1	no	—
182	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
184	C₁₉×#107	—	2	1	no	—
185	C₁₉×#106	—	2	1	no	—
186	C₁₉×#104	—	2	2	no	—
187	C₁₉×#104	—	2	2	no	—
188	C₁₉×#104	—	2	2	no	—
189	C₁₉×#104	—	2	2	no	—
190	C₁₉×#104	—	4	1	no	—
191	C₁₉×#104	D₄	1	4	yes	complemented
192	C₁₉×#103	—	2	1	no	—
193	C₁₉×#103	—	2	1	no	—
194	C₁₉×#103	—	2	1	no	—
195	C₁₉×#103	—	2	1	no	—
196	C₁₉×#103	—	2	1	no	—
197	C₁₉×#102	—	2	1	no	—
198	C₁₉×#102	—	2	1	no	—
199	C₁₉×#102	—	2	1	no	—
200	C₁₉×#101	—	2	2	no	—
201	C₁₉×#101	—	4	1	no	—
202	C₁₉×C₂²⋊C₈	—	2	1	no	—
203	C₁₉×C₂²⋊C₈	—	2	1	no	—
204	C₁₉×#95	—	2	2	no	—
205	C₁₉×#95	—	2	2	no	—
206	C₂⁴×C₁₉	—	2	1	no	—
207	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
208	#41×C₁₉	—	2	1	no	—
209	#41×C₁₉	—	2	1	no	—
210	#41×C₁₉	—	2	2	no	—
211	#41×C₁₉	—	2	2	no	—
212	#41×C₁₉	—	2	1	no	—
213	#41×C₁₉	—	2	1	no	—
214	#41×C₁₉	—	2	1	no	—
215	#41×C₁₉	—	2	1	no	—
216	#41×C₁₉	—	2	1	no	—
217	#41×C₁₉	—	2	1	no	—
218	#41×C₁₉	—	2	1	no	—
219	#41×C₁₉	—	2	1	no	—
220	#41×C₁₉	—	4	2	no	—
221	#41×C₁₉	—	4	2	no	—
222	#41×C₁₉	—	4	1	no	—
223	#41×C₁₉	—	4	1	no	—
224	#41×C₁₉	—	4	2	no	—
225	#41×C₁₉	—	4	2	no	—
226	#41×C₁₉	—	4	2	no	—
227	#41×C₁₉	—	4	2	no	—
228	#41×C₁₉	—	4	4	no	—
229	#41×C₁₉	—	4	4	no	—
230	#41×C₁₉	—	4	2	no	—
231	#41×C₁₉	—	4	2	no	—
232	#41×C₁₉	C₂×D₄	1	2	yes	—
233	#41×C₁₉	#41	1	2	yes	—
234	C₂×Q₈×C₁₉	—	2	2	no	—
235	C₂×Q₈×C₁₉	—	2	1	no	—
236	C₂×Q₈×C₁₉	—	2	1	no	—
237	C₂×Q₈×C₁₉	—	2	1	no	—
238	C₂×Q₈×C₁₉	—	2	1	no	—
239	C₂×Q₈×C₁₉	—	2	1	no	—
240	C₂×Q₈×C₁₉	—	2	1	no	—
241	C₂×Q₈×C₁₉	—	2	1	no	—
242	C₂×Q₈×C₁₉	—	2	2	no	—
243	C₂×Q₈×C₁₉	—	2	1	no	—
244	C₂×Q₈×C₁₉	—	2	1	no	—
245	C₂×Q₈×C₁₉	—	2	1	no	—
246	C₂×Q₈×C₁₉	—	2	1	no	—
247	C₂×Q₈×C₁₉	—	2	1	no	—
248	C₂×Q₈×C₁₉	—	2	1	no	—
249	C₂×Q₈×C₁₉	—	4	1	no	—
250	C₂×Q₈×C₁₉	—	4	2	no	—
251	C₂×Q₈×C₁₉	—	4	2	no	—
252	C₂×Q₈×C₁₉	—	4	2	no	—
253	C₂×Q₈×C₁₉	—	4	2	no	—
254	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₁₉	—	2	1	no	—
258	C₂×D₄×C₁₉	—	2	2	no	—
259	C₂×D₄×C₁₉	—	2	2	no	—
260	C₂×D₄×C₁₉	—	2	1	no	—
261	C₂×D₄×C₁₉	—	2	1	no	—
262	C₂×D₄×C₁₉	—	2	1	no	—
263	C₂×D₄×C₁₉	—	2	1	no	—
264	C₂×D₄×C₁₉	—	2	1	no	—
265	C₂×D₄×C₁₉	—	2	2	no	—
266	C₂×D₄×C₁₉	—	2	1	no	—
267	C₂×D₄×C₁₉	—	2	1	no	—
268	C₂×D₄×C₁₉	—	4	1	no	—
269	C₂×D₄×C₁₉	—	4	2	no	—
270	C₂×D₄×C₁₉	—	4	2	no	—
271	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₉	—	2	1	no	—
275	C₂²×C₄×C₁₉	—	2	1	no	—
276	C₂²×C₄×C₁₉	—	2	1	no	—
277	C₂²×C₄×C₁₉	—	2	1	no	—
278	C₂²×C₄×C₁₉	—	2	1	no	—
279	C₂²×C₄×C₁₉	—	2	1	no	—
280	C₂²×C₄×C₁₉	—	2	2	no	—
281	C₂²×C₄×C₁₉	—	2	2	no	—
282	C₂²×C₄×C₁₉	—	2	4	no	—
283	C₂²×C₄×C₁₉	—	2	1	no	—
284	C₂²×C₄×C₁₉	—	2	1	no	—
285	C₂²×C₄×C₁₉	—	2	2	no	—
286	C₂²×C₄×C₁₉	—	2	1	no	—
287	C₂²×C₄×C₁₉	—	2	1	no	—
288	C₂²×C₄×C₁₉	—	2	1	no	—
289	C₂²×C₄×C₁₉	—	2	1	no	—
290	C₂²×C₄×C₁₉	—	2	1	no	—
291	C₂²×C₄×C₁₉	—	2	1	no	—
292	C₂²×C₄×C₁₉	—	4	2	no	—
293	C₂²×C₄×C₁₉	—	4	2	no	—
294	C₂²×C₄×C₁₉	—	4	2	no	—
295	C₂²×C₄×C₁₉	—	4	2	no	—
296	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
304	Q₁₆×C₁₉	—	4	2	no	—
305	Q₁₆×C₁₉	—	4	2	no	—
306	Q₁₆×C₁₉	—	4	2	no	—
307	SD₁₆×C₁₉	—	4	2	no	—
308	SD₁₆×C₁₉	—	4	2	no	—
309	SD₁₆×C₁₉	—	4	2	no	—
310	M₁₆×C₁₉	—	2	1	no	—
311	M₁₆×C₁₉	—	2	1	no	—
312	M₁₆×C₁₉	—	2	1	no	—
313	M₁₆×C₁₉	—	2	1	no	—
314	M₁₆×C₁₉	—	2	1	no	—
315	M₁₆×C₁₉	—	2	1	no	—
316	M₁₆×C₁₉	—	2	1	no	—
317	M₁₆×C₁₉	—	4	2	no	—
318	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
319	C₂×C₈×C₁₉	—	2	1	no	—
320	C₂×C₈×C₁₉	—	2	1	no	—
321	C₂×C₈×C₁₉	—	2	1	no	—
322	C₂×C₈×C₁₉	—	2	1	no	—
323	C₂×C₈×C₁₉	—	4	2	no	—
324	C₄⋊C₄×C₁₉	—	2	2	no	—
325	C₄⋊C₄×C₁₉	—	2	2	no	—
326	C₄⋊C₄×C₁₉	—	2	2	no	—
327	C₄⋊C₄×C₁₉	—	2	2	no	—
328	C₄⋊C₄×C₁₉	—	2	1	no	—
329	C₄⋊C₄×C₁₉	—	2	2	no	—
330	C₄⋊C₄×C₁₉	—	2	2	no	—
331	C₄⋊C₄×C₁₉	—	2	1	no	—
332	C₄⋊C₄×C₁₉	—	2	1	no	—
333	C₄⋊C₄×C₁₉	—	2	1	no	—
334	C₄⋊C₄×C₁₉	—	2	1	no	—
335	C₄⋊C₄×C₁₉	—	2	1	no	—
336	C₄⋊C₄×C₁₉	—	4	4	no	—
337	C₄⋊C₄×C₁₉	—	4	4	no	—
338	C₄⋊C₄×C₁₉	—	4	1	no	—
339	C₄⋊C₄×C₁₉	—	4	1	no	—
340	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₉	—	2	1	no	—
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	—	2	2	no	—
350	C₂²⋊C₄×C₁₉	—	2	1	no	—
351	C₂²⋊C₄×C₁₉	—	2	1	no	—
352	C₂²⋊C₄×C₁₉	—	2	1	no	—
353	C₂²⋊C₄×C₁₉	—	2	1	no	—
354	C₂²⋊C₄×C₁₉	—	4	1	no	—
355	C₂²⋊C₄×C₁₉	—	4	1	no	—
356	C₄²×C₁₉	—	2	2	no	—
357	C₄²×C₁₉	—	2	1	no	—
358	C₄²×C₁₉	—	2	1	no	—
359	C₄²×C₁₉	—	2	1	no	—
360	C₄²×C₁₉	—	2	1	no	—
361	C₄²×C₁₉	—	4	2	no	—
362	C₄²×C₁₉	C₂×D₄	1	2	yes	—
363	#24466	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂³×C₁₉	—	2	1	no	—
365	C₂³×C₁₉	—	2	1	no	—
366	C₂³×C₁₉	—	2	1	no	—
367	C₂³×C₁₉	—	2	2	no	—
368	C₂³×C₁₉	—	2	1	no	—
369	C₂³×C₁₉	—	2	1	no	—
370	C₂³×C₁₉	—	4	1	no	—
371	C₂³×C₁₉	—	4	2	no	—
372	C₂³×C₁₉	—	4	2	no	—
373	C₂³×C₁₉	—	8	1	no	—
374	C₂³×C₁₉	#120	1	1	yes	characteristic
375	C₂³×C₁₉	#120	1	1	yes	characteristic
376	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
377	Q₈×C₁₉	—	2	1	no	—
378	Q₈×C₁₉	—	2	1	no	—
379	Q₈×C₁₉	—	2	1	no	—
380	Q₈×C₁₉	—	2	1	no	—
381	Q₈×C₁₉	—	2	1	no	—
382	Q₈×C₁₉	—	4	2	no	—
383	Q₈×C₁₉	—	4	4	no	—
384	Q₈×C₁₉	—	4	1	no	—
385	Q₈×C₁₉	—	4	1	no	—
386	Q₈×C₁₉	—	4	1	no	—
387	Q₈×C₁₉	—	4	1	no	—
388	Q₈×C₁₉	—	4	1	no	—
389	Q₈×C₁₉	—	4	1	no	—
390	Q₈×C₁₉	—	4	1	no	—
391	Q₈×C₁₉	—	4	1	no	—
392	Q₈×C₁₉	#121	1	2	yes	—
393	D₄×C₁₉	—	2	2	no	—
394	D₄×C₁₉	—	2	2	no	—
395	D₄×C₁₉	—	2	1	no	—
396	D₄×C₁₉	—	2	1	no	—
397	D₄×C₁₉	—	2	1	no	—
398	D₄×C₁₉	—	2	1	no	—
399	D₄×C₁₉	—	2	1	no	—
400	D₄×C₁₉	—	4	2	no	—
401	D₄×C₁₉	—	4	2	no	—
402	D₄×C₁₉	—	4	2	no	—
403	D₄×C₁₉	—	4	4	no	—
404	D₄×C₁₉	—	4	1	no	—
405	D₄×C₁₉	—	4	1	no	—
406	D₄×C₁₉	—	4	1	no	—
407	D₄×C₁₉	—	4	1	no	—
408	D₄×C₁₉	—	4	2	no	—
409	D₄×C₁₉	—	8	1	no	—
410	D₄×C₁₉	—	8	2	no	—
411	D₄×C₁₉	#121	1	2	yes	—
412	C₂×C₄×C₁₉	—	2	2	no	—
413	C₂×C₄×C₁₉	—	2	2	no	—
414	C₂×C₄×C₁₉	—	2	1	no	—
415	C₂×C₄×C₁₉	—	2	2	no	—
416	C₂×C₄×C₁₉	—	2	1	no	—
417	C₂×C₄×C₁₉	—	2	1	no	—
418	C₂×C₄×C₁₉	—	2	1	no	—
419	C₂×C₄×C₁₉	—	2	1	no	—
420	C₂×C₄×C₁₉	—	2	1	no	—
421	C₂×C₄×C₁₉	—	2	1	no	—
422	C₂×C₄×C₁₉	—	2	1	no	—
423	C₂×C₄×C₁₉	—	2	1	no	—
424	C₂×C₄×C₁₉	—	2	2	no	—
425	C₂×C₄×C₁₉	—	2	1	no	—
426	C₂×C₄×C₁₉	—	2	1	no	—
427	C₂×C₄×C₁₉	—	2	2	no	—
428	C₂×C₄×C₁₉	—	2	2	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	—	4	2	no	—
438	C₂×C₄×C₁₉	—	4	2	no	—
439	C₂×C₄×C₁₉	—	4	2	no	—
440	C₂×C₄×C₁₉	—	4	8	no	—
441	C₂×C₄×C₁₉	—	4	4	no	—
442	C₂×C₄×C₁₉	—	4	1	no	—
443	C₂×C₄×C₁₉	—	4	4	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	1	no	—
449	C₂×C₄×C₁₉	—	4	2	no	—
450	C₂×C₄×C₁₉	—	4	2	no	—
451	C₂×C₄×C₁₉	—	4	1	no	—
452	C₂×C₄×C₁₉	—	4	1	no	—
453	C₂×C₄×C₁₉	—	4	1	no	—
454	C₂×C₄×C₁₉	—	4	1	no	—
455	C₂×C₄×C₁₉	—	8	2	no	—
456	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
457	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
458	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
462	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
463	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
464	C₈×C₁₉	—	2	2	no	—
465	C₈×C₁₉	—	4	1	no	—
466	C₈×C₁₉	—	4	1	no	—
467	C₈×C₁₉	—	4	1	no	—
468	#3489	C₂×C₁₉	1	1	yes	characteristic
469	#3056	C₂×C₁₉	1	1	yes	characteristic, complemented
470	C₂×#456	C₂×C₁₉	1	1	yes	characteristic, complemented
471	#3007	C₂×C₁₉	1	1	yes	characteristic, complemented
472	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic, complemented
473	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
474	#2039	C₂×C₁₉	1	1	yes	characteristic, complemented
475	#2038	C₂×C₁₉	1	1	yes	characteristic, complemented
476	#2007	C₂×C₁₉	1	1	yes	characteristic, complemented
477	#2005	C₂×C₁₉	1	1	yes	characteristic, complemented
478	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
479	#1896	C₂×C₁₉	1	1	yes	characteristic, complemented
480	#1882	C₂×C₁₉	1	1	yes	characteristic, complemented
481	#1859	C₂×C₁₉	1	1	yes	characteristic, complemented
482	#1793	C₂×C₁₉	1	1	yes	characteristic, complemented
483	C₂²×C₁₉	—	2	1	no	—
484	C₂²×C₁₉	—	2	1	no	—
485	C₂²×C₁₉	—	2	1	no	—
486	C₂²×C₁₉	—	2	1	no	—
487	C₂²×C₁₉	—	2	1	no	—
488	C₂²×C₁₉	—	2	2	no	—
489	C₂²×C₁₉	—	2	1	no	—
490	C₂²×C₁₉	—	2	1	no	—
491	C₂²×C₁₉	—	4	2	no	—
492	C₂²×C₁₉	—	4	2	no	—
493	C₂²×C₁₉	—	4	1	no	—
494	C₂²×C₁₉	—	4	1	no	—
495	C₂²×C₁₉	—	4	1	no	—
496	C₂²×C₁₉	—	4	1	no	—
497	C₂²×C₁₉	—	4	1	no	—
498	C₂²×C₁₉	—	4	1	no	—
499	C₂²×C₁₉	—	4	1	no	—
500	C₂²×C₁₉	—	4	1	no	—
501	C₂²×C₁₉	—	8	4	no	—
502	C₂²×C₁₉	#456	1	2	yes	complemented
503	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
504	C₂²×C₁₉	D₄²	1	1	yes	characteristic
505	C₂²×C₁₉	#546	1	1	yes	characteristic
506	C₄×C₁₉	—	2	4	no	—
507	C₄×C₁₉	—	2	1	no	—
508	C₄×C₁₉	—	2	1	no	—
509	C₄×C₁₉	—	2	2	no	—
510	C₄×C₁₉	—	4	2	no	—
511	C₄×C₁₉	—	4	2	no	—
512	C₄×C₁₉	—	4	1	no	—
513	C₄×C₁₉	—	4	1	no	—
514	C₄×C₁₉	—	4	1	no	—
515	C₄×C₁₉	—	4	2	no	—
516	C₄×C₁₉	—	4	1	no	—
517	C₄×C₁₉	—	8	1	no	—
518	C₄×C₁₉	—	8	1	no	—
519	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
520	C₄×C₁₉	#534	1	1	yes	characteristic
521	C₄×C₁₉	D₄²	1	1	yes	characteristic
522	C₄×C₁₉	#546	1	1	yes	characteristic
523	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
524	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
525	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
526	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
527	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic, complemented
528	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
529	D₄×Q₈	—	2	1	no	—
530	#548	—	2	1	no	—
531	#547	—	2	1	no	—
532	#547	—	2	2	no	—
533	#546	—	2	1	no	—
534	#546	—	2	2	no	—
535	#537	—	2	1	no	—
536	#537	C₂²×C₁₉	1	1	yes	characteristic
537	#536	—	2	1	no	—
538	#536	C₂²×C₁₉	1	1	yes	characteristic
539	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
540	#525	—	2	1	no	—
541	#525	C₂²×C₁₉	1	1	yes	characteristic
542	C₂×C₂²⋊Q₈	—	2	1	no	—
543	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
544	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
545	#520	C₂²×C₁₉	1	1	yes	characteristic
546	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
547	#470	—	2	1	no	—
548	#468	—	2	1	no	—
549	#467	—	2	1	no	—
550	#465	—	2	1	no	—
551	#456	—	2	4	no	—
552	#452	—	2	1	no	—
553	#452	—	2	1	no	—
554	#451	—	2	1	no	—
555	#450	—	2	1	no	—
556	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
557	C₂×#104	—	2	4	no	—
558	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
559	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
560	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
561	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
562	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
563	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
564	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
565	#417	C₂²×C₁₉	1	1	yes	characteristic
566	#417	C₂²×C₁₉	1	1	yes	characteristic
567	#417	C₂²×C₁₉	1	1	yes	characteristic, complemented
568	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
569	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
570	#407	C₂²×C₁₉	1	1	yes	characteristic
571	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
572	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
573	#389	—	2	2	no	—
574	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
575	#380	—	2	2	no	—
576	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
577	#343	C₂²×C₁₉	1	1	yes	characteristic, complemented
578	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
579	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
580	C₂×C₁₉	—	2	1	no	—
581	C₂×C₁₉	—	2	2	no	—
582	C₂×C₁₉	—	2	1	no	—
583	C₂×C₁₉	—	4	1	no	—
584	C₂×C₁₉	—	4	2	no	—
585	C₂×C₁₉	—	8	1	no	—
586	C₂×C₁₉	—	8	1	no	—
587	C₂×C₁₉	#2410	1	1	yes	characteristic
588	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
589	C₂×C₁₉	#3018	1	1	yes	characteristic
590	2₋¹⁺⁴	—	2	2	no	—
591	2₋¹⁺⁴	—	2	2	no	—
592	2₋¹⁺⁴	—	4	1	no	—
593	2₋¹⁺⁴	—	4	1	no	—
594	C₂×#41	—	2	1	no	—
595	C₂×#41	—	2	1	no	—
596	C₂×#41	—	2	1	no	—
597	C₂×#41	—	2	2	no	—
598	C₂×#41	—	2	1	no	—
599	C₂×#41	—	2	2	no	—
600	C₂×#41	—	2	2	no	—
601	C₂×#41	—	4	1	no	—
602	C₂×#41	—	4	1	no	—
603	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
604	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
605	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
606	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
607	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
608	C₂²×Q₈	—	2	1	no	—
609	C₂²×Q₈	—	2	1	no	—
610	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
611	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
612	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
613	C₂²×D₄	—	2	1	no	—
614	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
615	C₂³×C₄	—	2	1	no	—
616	C₂³×C₄	—	2	1	no	—
617	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
618	#137	—	2	2	no	—
619	#137	—	2	2	no	—
620	#137	—	2	2	no	—
621	#137	—	4	1	no	—
622	#137	—	4	1	no	—
623	#137	—	4	1	no	—
624	C₂×Q₁₆	—	2	1	no	—
625	C₂×Q₁₆	—	2	1	no	—
626	C₂×Q₁₆	—	2	1	no	—
627	C₂×SD₁₆	—	2	1	no	—
628	C₂×SD₁₆	—	2	1	no	—
629	C₂×SD₁₆	—	2	1	no	—
630	C₂×M₁₆	—	2	1	no	—
631	C₂×M₁₆	—	2	2	no	—
632	C₂×M₁₆	—	4	1	no	—
633	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
634	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
635	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
636	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
637	C₂²×C₈	—	2	1	no	—
638	C₄⋊Q₈	—	2	2	no	—
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	4	1	no	—
642	#124	—	2	2	no	—
643	#124	—	2	1	no	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	1	no	—
648	#123	—	2	2	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	1	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	1	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	1	no	—
658	C₂²⋊Q₈	—	2	1	no	—
659	C₂²⋊Q₈	—	2	1	no	—
660	C₂²⋊Q₈	—	2	1	no	—
661	C₂²⋊Q₈	—	2	1	no	—
662	C₂²⋊Q₈	—	2	1	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
665	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	1	no	—
670	#121	—	2	1	no	—
671	#121	—	2	2	no	—
672	#121	D₄×C₁₉	1	1	yes	characteristic
673	#121	D₄×C₁₉	1	1	yes	characteristic
674	#120	—	2	2	no	—
675	#120	—	2	1	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	#117	—	2	1	no	—
684	#117	C₂³×C₁₉	1	1	yes	characteristic
685	C₂×C₄⋊C₄	—	2	2	no	—
686	C₂×C₄⋊C₄	—	2	1	no	—
687	C₂×C₄⋊C₄	—	2	1	no	—
688	C₂×C₄⋊C₄	—	2	2	no	—
689	C₂×C₄⋊C₄	—	2	2	no	—
690	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	1	no	—
695	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
696	C₂×C₄²	—	2	2	no	—
697	C₂×C₄²	—	2	1	no	—
698	C₂×C₄²	—	4	1	no	—
699	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
701	#107	—	2	1	no	—
702	#106	—	2	1	no	—
703	#104	—	2	2	no	—
704	#104	—	2	2	no	—
705	#104	—	2	2	no	—
706	#104	—	2	2	no	—
707	#104	—	4	1	no	—
708	#104	D₄×C₁₉	1	4	yes	complemented
709	#103	—	2	1	no	—
710	#103	—	2	1	no	—
711	#103	—	2	1	no	—
712	#103	—	2	1	no	—
713	#103	—	2	1	no	—
714	#102	—	2	1	no	—
715	#102	—	2	1	no	—
716	#102	—	2	1	no	—
717	#101	—	2	2	no	—
718	#101	—	4	1	no	—
719	C₂²⋊C₈	—	2	1	no	—
720	C₂²⋊C₈	—	2	1	no	—
721	#95	—	2	2	no	—
722	#95	—	2	2	no	—
723	C₁₉	#24466	1	1	yes	characteristic, direct product factor, Sylow
724	C₂⁴	—	2	1	no	—
725	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
726	#41	—	2	1	no	—
727	#41	—	2	1	no	—
728	#41	—	2	2	no	—
729	#41	—	2	2	no	—
730	#41	—	2	1	no	—
731	#41	—	2	1	no	—
732	#41	—	2	1	no	—
733	#41	—	2	1	no	—
734	#41	—	2	1	no	—
735	#41	—	2	1	no	—
736	#41	—	2	1	no	—
737	#41	—	2	1	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	#41	—	4	1	no	—
741	#41	—	4	1	no	—
742	#41	—	4	2	no	—
743	#41	—	4	2	no	—
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	#41	—	4	4	no	—
747	#41	—	4	4	no	—
748	#41	—	4	2	no	—
749	#41	—	4	2	no	—
750	#41	C₂×D₄×C₁₉	1	2	yes	—
751	#41	#41×C₁₉	1	2	yes	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	1	no	—
757	C₂×Q₈	—	2	1	no	—
758	C₂×Q₈	—	2	1	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	2	1	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	1	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	1	no	—
767	C₂×Q₈	—	4	1	no	—
768	C₂×Q₈	—	4	2	no	—
769	C₂×Q₈	—	4	2	no	—
770	C₂×Q₈	—	4	2	no	—
771	C₂×Q₈	—	4	2	no	—
772	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
773	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
774	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
790	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
791	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
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	C₂⁴×C₁₉	1	1	yes	characteristic
822	Q₁₆	—	4	2	no	—
823	Q₁₆	—	4	2	no	—
824	Q₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	M₁₆	—	2	1	no	—
829	M₁₆	—	2	1	no	—
830	M₁₆	—	2	1	no	—
831	M₁₆	—	2	1	no	—
832	M₁₆	—	2	1	no	—
833	M₁₆	—	2	1	no	—
834	M₁₆	—	2	1	no	—
835	M₁₆	—	4	2	no	—
836	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
837	C₂×C₈	—	2	1	no	—
838	C₂×C₈	—	2	1	no	—
839	C₂×C₈	—	2	1	no	—
840	C₂×C₈	—	2	1	no	—
841	C₂×C₈	—	4	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	4	4	no	—
855	C₄⋊C₄	—	4	4	no	—
856	C₄⋊C₄	—	4	1	no	—
857	C₄⋊C₄	—	4	1	no	—
858	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
859	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	1	no	—
869	C₂²⋊C₄	—	2	1	no	—
870	C₂²⋊C₄	—	2	1	no	—
871	C₂²⋊C₄	—	2	1	no	—
872	C₂²⋊C₄	—	4	1	no	—
873	C₂²⋊C₄	—	4	1	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	1	no	—
876	C₄²	—	2	1	no	—
877	C₄²	—	2	1	no	—
878	C₄²	—	2	1	no	—
879	C₄²	—	4	2	no	—
880	C₄²	C₂×D₄×C₁₉	1	2	yes	—
881	C₂³	—	2	2	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	4	1	no	—
888	C₂³	—	4	2	no	—
889	C₂³	—	4	2	no	—
890	C₂³	—	8	1	no	—
891	C₂³	C₁₉×#120	1	1	yes	characteristic
892	C₂³	C₁₉×#120	1	1	yes	characteristic
893	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
894	Q₈	—	2	1	no	—
895	Q₈	—	2	1	no	—
896	Q₈	—	2	1	no	—
897	Q₈	—	2	1	no	—
898	Q₈	—	2	1	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	4	no	—
901	Q₈	—	4	1	no	—
902	Q₈	—	4	1	no	—
903	Q₈	—	4	1	no	—
904	Q₈	—	4	1	no	—
905	Q₈	—	4	1	no	—
906	Q₈	—	4	1	no	—
907	Q₈	—	4	1	no	—
908	Q₈	—	4	1	no	—
909	Q₈	C₁₉×#121	1	2	yes	—
910	D₄	—	2	2	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	1	no	—
913	D₄	—	2	1	no	—
914	D₄	—	2	1	no	—
915	D₄	—	2	1	no	—
916	D₄	—	2	1	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	2	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	2	no	—
922	D₄	—	4	1	no	—
923	D₄	—	4	1	no	—
924	D₄	—	4	1	no	—
925	D₄	—	4	1	no	—
926	D₄	—	8	1	no	—
927	D₄	—	8	2	no	—
928	D₄	C₁₉×#121	1	2	yes	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	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	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	4	2	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	8	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	4	4	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
974	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
978	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
979	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
980	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
981	C₈	—	2	2	no	—
982	C₈	—	4	1	no	—
983	C₈	—	4	1	no	—
984	C₈	—	4	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	C₁₉×#456	1	2	yes	complemented
1005	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1006	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1007	C₂²	C₁₉×#546	1	1	yes	characteristic
1008	C₄	—	2	4	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	8	1	no	—
1020	C₄	—	8	1	no	—
1021	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
1022	C₄	C₁₉×#534	1	1	yes	characteristic
1023	C₄	D₄²×C₁₉	1	1	yes	characteristic
1024	C₄	C₁₉×#546	1	1	yes	characteristic
1025	C₂	—	2	1	no	—
1026	C₂	—	2	2	no	—
1027	C₂	—	2	1	no	—
1028	C₂	—	4	1	no	—
1029	C₂	—	4	2	no	—
1030	C₂	—	8	1	no	—
1031	C₂	—	8	1	no	—
1032	C₂	C₁₉×#2410	1	1	yes	characteristic
1033	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
1034	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3489	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3056	C₂	semidirect
3. C₂×C₁₉×#456	C₂	semidirect
4. C₁₉×#3007	C₂	semidirect
5. C₂²×C₁₉×#104	C₂	semidirect
6. C₁₉×#2857	C₂	semidirect
7. C₁₉×#2039	C₂	semidirect
8. C₁₉×#2038	C₂	semidirect
9. C₁₉×#2007	C₂	semidirect
10. C₁₉×#2005	C₂	semidirect
11. C₁₉×#1901	C₂	semidirect
12. C₁₉×#1896	C₂	semidirect
13. C₁₉×#1882	C₂	semidirect
14. C₁₉×#1859	C₂	semidirect
15. C₁₉×#1793	C₂	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
32. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
49. C₁₉×#428	C₂²	semidirect
55. C₂×C₁₉×#104	C₂²	semidirect
56. C₂×C₁₉×#104	C₂²	semidirect
57. C₁₉×#419	C₂²	semidirect
60. C₁₉×#417	C₂²	semidirect
61. C₂×C₁₉×#101	C₂²	semidirect
62. C₂×C₁₉×#101	C₂²	semidirect
64. C₁₉×#391	C₂²	semidirect
65. C₁₉×#391	C₂²	semidirect
67. C₁₉×#384	C₂²	semidirect
69. C₁₉×#343	C₂²	semidirect
70. C₁₉×#343	C₂²	semidirect
71. C₁₉×#339	C₂²	semidirect
72. C₁₉×#339	C₂²	semidirect
191. C₁₉×#104	D₄	semidirect
363. #24466	C₁₉	direct (N × H)
469. #3056	C₂×C₁₉	semidirect
470. C₂×#456	C₂×C₁₉	semidirect
471. #3007	C₂×C₁₉	semidirect
472. C₂²×#104	C₂×C₁₉	semidirect
473. #2857	C₂×C₁₉	semidirect
474. #2039	C₂×C₁₉	semidirect
475. #2038	C₂×C₁₉	semidirect
476. #2007	C₂×C₁₉	semidirect
477. #2005	C₂×C₁₉	semidirect
478. #1901	C₂×C₁₉	semidirect
479. #1896	C₂×C₁₉	semidirect
480. #1882	C₂×C₁₉	semidirect
481. #1859	C₂×C₁₉	semidirect
482. #1793	C₂×C₁₉	semidirect
502. C₂²×C₁₉	#456	semidirect
527. C₂×#137	C₂²×C₁₉	semidirect
539. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
556. #428	C₂²×C₁₉	semidirect
562. C₂×#104	C₂²×C₁₉	semidirect
563. C₂×#104	C₂²×C₁₉	semidirect
564. #419	C₂²×C₁₉	semidirect
567. #417	C₂²×C₁₉	semidirect
568. C₂×#101	C₂²×C₁₉	semidirect
569. C₂×#101	C₂²×C₁₉	semidirect
571. #391	C₂²×C₁₉	semidirect
572. #391	C₂²×C₁₉	semidirect
574. #384	C₂²×C₁₉	semidirect
576. #343	C₂²×C₁₉	semidirect
577. #343	C₂²×C₁₉	semidirect
578. #339	C₂²×C₁₉	semidirect
579. #339	C₂²×C₁₉	semidirect
708. #104	D₄×C₁₉	semidirect
723. C₁₉	#24466	direct (N × H)
1004. C₂²	C₁₉×#456	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3489	2
C₁₉×#3056	2
C₂×C₁₉×#456	2
C₁₉×#3007	2
C₂²×C₁₉×#104	2
C₁₉×#2857	2
C₁₉×#2039	2
C₁₉×#2038	2
C₁₉×#2007	2
C₁₉×#2005	2
C₁₉×#1901	2
C₁₉×#1896	2
C₁₉×#1882	2
C₁₉×#1859	2
C₁₉×#1793	2
#24466	19

Subgroups — C19×#24466 #18030425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24466 #18030425