Subgroups — C₁₉×#23880 #18029839

Order 4864.

1696 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3489	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#456	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3004	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2007	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2005	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1882	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#137	—	2	1	no	—
16	C₂×C₁₉×#137	—	2	1	no	—
17	C₂×C₁₉×#137	—	2	8	no	—
18	C₂×C₁₉×#137	C₂²	1	2	yes	—
19	C₂×C₁₉×#137	C₂²	1	2	yes	—
20	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
21	C₂²×Q₁₆×C₁₉	—	2	1	no	—
22	C₂²×SD₁₆×C₁₉	—	2	1	no	—
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₁₉	—	2	1	no	—
25	C₁₉×#548	—	2	1	no	—
26	C₁₉×#547	—	2	1	no	—
27	C₁₉×#547	—	2	2	no	—
28	C₁₉×#546	—	2	1	no	—
29	C₁₉×#546	—	2	2	no	—
30	C₁₉×#537	—	2	1	no	—
31	C₁₉×#537	C₂²	1	1	yes	characteristic
32	C₁₉×#536	—	2	1	no	—
33	C₁₉×#536	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
35	C₁₉×#525	—	2	1	no	—
36	C₁₉×#525	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₁₉×#520	C₂²	1	1	yes	characteristic
40	C₁₉×#456	—	2	8	no	—
41	C₁₉×#451	—	2	1	no	—
42	C₁₉×#451	—	2	1	no	—
43	C₁₉×#448	—	2	1	no	—
44	C₁₉×#448	—	2	1	no	—
45	C₂×C₁₉×#104	C₂²	1	2	yes	—
46	C₂×C₁₉×#104	C₂²	1	2	yes	—
47	C₂×C₁₉×#104	C₂²	1	2	yes	complemented
48	C₁₉×#419	C₂²	1	2	yes	complemented
49	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
50	C₁₉×#407	C₂²	1	1	yes	characteristic
51	C₁₉×#395	—	2	2	no	—
52	C₁₉×#391	C₂²	1	2	yes	complemented
53	C₁₉×#385	—	2	2	no	—
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#343	C₂²	1	2	yes	complemented
56	C₁₉×#339	C₂²	1	2	yes	complemented
57	C₁₉×2₋¹⁺⁴	—	2	4	no	—
58	C₁₉×2₋¹⁺⁴	—	4	2	no	—
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂×#41×C₁₉	—	2	1	no	—
61	C₂×#41×C₁₉	—	2	1	no	—
62	C₂×#41×C₁₉	—	2	2	no	—
63	C₂×#41×C₁₉	—	2	1	no	—
64	C₂×#41×C₁₉	—	2	4	no	—
65	C₂×#41×C₁₉	—	4	2	no	—
66	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
67	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
68	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₉	—	2	1	no	—
72	C₂²×Q₈×C₁₉	—	2	1	no	—
73	C₂²×Q₈×C₁₉	—	2	1	no	—
74	C₂²×Q₈×C₁₉	—	2	4	no	—
75	C₂²×Q₈×C₁₉	—	2	1	no	—
76	C₂²×Q₈×C₁₉	—	2	1	no	—
77	C₂²×Q₈×C₁₉	—	2	1	no	—
78	C₂²×Q₈×C₁₉	—	2	1	no	—
79	C₂²×Q₈×C₁₉	—	4	2	no	—
80	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
81	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₉	—	2	1	no	—
84	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₁₉	—	2	1	no	—
86	C₂³×C₄×C₁₉	—	2	1	no	—
87	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×#137	—	2	8	no	—
89	C₁₉×#137	—	2	8	no	—
90	C₁₉×#137	—	2	4	no	—
91	C₁₉×#137	—	2	4	no	—
92	C₁₉×#137	—	2	4	no	—
93	C₁₉×#137	—	2	4	no	—
94	C₁₉×#137	—	4	2	no	—
95	C₁₉×#137	D₄	1	8	yes	complemented
96	C₂×Q₁₆×C₁₉	—	2	8	no	—
97	C₂×Q₁₆×C₁₉	—	2	2	no	—
98	C₂×Q₁₆×C₁₉	—	2	2	no	—
99	C₂×Q₁₆×C₁₉	—	2	2	no	—
100	C₂×SD₁₆×C₁₉	—	2	8	no	—
101	C₂×SD₁₆×C₁₉	—	2	2	no	—
102	C₂×SD₁₆×C₁₉	—	2	2	no	—
103	C₂×SD₁₆×C₁₉	—	2	2	no	—
104	C₂×M₁₆×C₁₉	—	2	1	no	—
105	C₂×M₁₆×C₁₉	—	2	4	no	—
106	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₉	—	2	1	no	—
109	C₁₉×C₄⋊Q₈	—	2	2	no	—
110	C₁₉×C₄⋊Q₈	—	2	1	no	—
111	C₁₉×C₄⋊Q₈	—	2	4	no	—
112	C₁₉×C₄⋊Q₈	—	4	2	no	—
113	C₁₉×#124	—	2	2	no	—
114	C₁₉×#124	—	2	1	no	—
115	C₁₉×#123	—	2	2	no	—
116	C₁₉×#123	—	2	2	no	—
117	C₁₉×#123	—	2	2	no	—
118	C₁₉×#123	—	2	1	no	—
119	C₁₉×#123	—	2	2	no	—
120	C₁₉×C₂²⋊Q₈	—	2	2	no	—
121	C₁₉×C₂²⋊Q₈	—	2	2	no	—
122	C₁₉×C₂²⋊Q₈	—	2	2	no	—
123	C₁₉×C₂²⋊Q₈	—	2	1	no	—
124	C₁₉×C₂²⋊Q₈	—	2	1	no	—
125	C₁₉×C₂²⋊Q₈	—	2	1	no	—
126	C₁₉×C₂²⋊Q₈	—	2	1	no	—
127	C₁₉×C₂²⋊Q₈	—	2	1	no	—
128	C₁₉×C₂²⋊Q₈	—	2	1	no	—
129	C₁₉×C₂²⋊Q₈	—	2	1	no	—
130	C₁₉×C₂²⋊Q₈	—	2	1	no	—
131	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
132	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
133	C₁₉×#121	—	2	2	no	—
134	C₁₉×#121	—	2	2	no	—
135	C₁₉×#121	—	2	2	no	—
136	C₁₉×#121	—	2	1	no	—
137	C₁₉×#121	—	2	1	no	—
138	C₁₉×#121	—	2	2	no	—
139	C₁₉×#121	D₄	1	1	yes	characteristic
140	C₁₉×#121	D₄	1	1	yes	characteristic
141	C₁₉×#120	—	2	2	no	—
142	C₁₉×#120	—	2	1	no	—
143	C₄×Q₈×C₁₉	—	2	1	no	—
144	C₄×D₄×C₁₉	—	2	2	no	—
145	C₄×D₄×C₁₉	—	2	2	no	—
146	C₄×D₄×C₁₉	—	2	1	no	—
147	C₄×D₄×C₁₉	—	2	2	no	—
148	C₄×D₄×C₁₉	—	2	1	no	—
149	C₄×D₄×C₁₉	—	2	1	no	—
150	C₁₉×#117	—	2	1	no	—
151	C₁₉×#117	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
160	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
161	C₁₉×#104	—	2	4	no	—
162	C₁₉×#104	—	2	4	no	—
163	C₁₉×#104	—	4	2	no	—
164	C₁₉×#103	—	2	2	no	—
165	C₁₉×#103	—	2	2	no	—
166	C₁₉×#101	—	2	4	no	—
167	C₁₉×C₂²⋊C₈	—	2	1	no	—
168	C₁₉×C₂²⋊C₈	—	2	1	no	—
169	C₁₉×#95	—	2	1	no	—
170	C₁₉×#95	—	2	4	no	—
171	C₂⁴×C₁₉	—	2	1	no	—
172	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
173	#41×C₁₉	—	2	2	no	—
174	#41×C₁₉	—	2	2	no	—
175	#41×C₁₉	—	2	2	no	—
176	#41×C₁₉	—	2	2	no	—
177	#41×C₁₉	—	2	2	no	—
178	#41×C₁₉	—	2	2	no	—
179	#41×C₁₉	—	2	2	no	—
180	#41×C₁₉	—	4	4	no	—
181	#41×C₁₉	—	4	1	no	—
182	#41×C₁₉	—	4	1	no	—
183	#41×C₁₉	—	4	4	no	—
184	#41×C₁₉	—	4	4	no	—
185	#41×C₁₉	—	4	8	no	—
186	#41×C₁₉	—	4	2	no	—
187	#41×C₁₉	—	4	2	no	—
188	#41×C₁₉	C₂×D₄	1	4	yes	—
189	C₂×Q₈×C₁₉	—	2	2	no	—
190	C₂×Q₈×C₁₉	—	2	1	no	—
191	C₂×Q₈×C₁₉	—	2	1	no	—
192	C₂×Q₈×C₁₉	—	2	1	no	—
193	C₂×Q₈×C₁₉	—	2	2	no	—
194	C₂×Q₈×C₁₉	—	2	2	no	—
195	C₂×Q₈×C₁₉	—	2	2	no	—
196	C₂×Q₈×C₁₉	—	2	4	no	—
197	C₂×Q₈×C₁₉	—	2	4	no	—
198	C₂×Q₈×C₁₉	—	2	2	no	—
199	C₂×Q₈×C₁₉	—	2	2	no	—
200	C₂×Q₈×C₁₉	—	2	2	no	—
201	C₂×Q₈×C₁₉	—	2	2	no	—
202	C₂×Q₈×C₁₉	—	2	2	no	—
203	C₂×Q₈×C₁₉	—	4	4	no	—
204	C₂×Q₈×C₁₉	—	4	1	no	—
205	C₂×Q₈×C₁₉	—	4	4	no	—
206	C₂×Q₈×C₁₉	—	4	4	no	—
207	C₂×Q₈×C₁₉	—	4	4	no	—
208	C₂×Q₈×C₁₉	—	4	2	no	—
209	C₂×Q₈×C₁₉	—	4	2	no	—
210	C₂×Q₈×C₁₉	—	4	2	no	—
211	C₂×Q₈×C₁₉	—	4	2	no	—
212	C₂×Q₈×C₁₉	—	4	1	no	—
213	C₂×Q₈×C₁₉	—	4	1	no	—
214	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
217	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₁₉	—	2	1	no	—
219	C₂×D₄×C₁₉	—	2	2	no	—
220	C₂×D₄×C₁₉	—	2	2	no	—
221	C₂×D₄×C₁₉	—	2	1	no	—
222	C₂×D₄×C₁₉	—	2	1	no	—
223	C₂×D₄×C₁₉	—	2	1	no	—
224	C₂×D₄×C₁₉	—	2	1	no	—
225	C₂×D₄×C₁₉	—	2	1	no	—
226	C₂×D₄×C₁₉	—	2	2	no	—
227	C₂×D₄×C₁₉	—	2	1	no	—
228	C₂×D₄×C₁₉	—	2	1	no	—
229	C₂×D₄×C₁₉	—	4	1	no	—
230	C₂×D₄×C₁₉	—	4	4	no	—
231	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₉	—	2	1	no	—
235	C₂²×C₄×C₁₉	—	2	2	no	—
236	C₂²×C₄×C₁₉	—	2	2	no	—
237	C₂²×C₄×C₁₉	—	2	2	no	—
238	C₂²×C₄×C₁₉	—	2	2	no	—
239	C₂²×C₄×C₁₉	—	2	1	no	—
240	C₂²×C₄×C₁₉	—	2	2	no	—
241	C₂²×C₄×C₁₉	—	2	2	no	—
242	C₂²×C₄×C₁₉	—	2	2	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	1	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	1	no	—
247	C₂²×C₄×C₁₉	—	4	4	no	—
248	C₂²×C₄×C₁₉	—	4	4	no	—
249	C₂²×C₄×C₁₉	—	4	1	no	—
250	C₂²×C₄×C₁₉	—	4	1	no	—
251	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₁₉	—	2	8	no	—
260	Q₁₆×C₁₉	—	2	8	no	—
261	Q₁₆×C₁₉	—	4	4	no	—
262	SD₁₆×C₁₉	—	2	8	no	—
263	SD₁₆×C₁₉	—	2	8	no	—
264	SD₁₆×C₁₉	—	4	4	no	—
265	M₁₆×C₁₉	—	2	4	no	—
266	M₁₆×C₁₉	—	2	2	no	—
267	M₁₆×C₁₉	—	2	2	no	—
268	M₁₆×C₁₉	—	2	2	no	—
269	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
270	C₂×C₈×C₁₉	—	2	4	no	—
271	C₂×C₈×C₁₉	—	2	2	no	—
272	C₂×C₈×C₁₉	—	2	2	no	—
273	C₄⋊C₄×C₁₉	—	2	2	no	—
274	C₄⋊C₄×C₁₉	—	2	2	no	—
275	C₄⋊C₄×C₁₉	—	2	2	no	—
276	C₄⋊C₄×C₁₉	—	2	2	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	2	no	—
279	C₄⋊C₄×C₁₉	—	2	2	no	—
280	C₄⋊C₄×C₁₉	—	2	1	no	—
281	C₄⋊C₄×C₁₉	—	2	1	no	—
282	C₄⋊C₄×C₁₉	—	2	1	no	—
283	C₄⋊C₄×C₁₉	—	4	8	no	—
284	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
285	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
286	C₂²⋊C₄×C₁₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₉	—	2	2	no	—
288	C₂²⋊C₄×C₁₉	—	2	2	no	—
289	C₂²⋊C₄×C₁₉	—	2	2	no	—
290	C₂²⋊C₄×C₁₉	—	2	2	no	—
291	C₂²⋊C₄×C₁₉	—	2	2	no	—
292	C₂²⋊C₄×C₁₉	—	2	1	no	—
293	C₂²⋊C₄×C₁₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₉	—	2	1	no	—
296	C₂²⋊C₄×C₁₉	—	2	1	no	—
297	C₂²⋊C₄×C₁₉	—	2	1	no	—
298	C₂²⋊C₄×C₁₉	—	2	1	no	—
299	C₄²×C₁₉	—	2	2	no	—
300	C₄²×C₁₉	—	2	1	no	—
301	C₄²×C₁₉	—	2	2	no	—
302	C₄²×C₁₉	—	2	2	no	—
303	#23880	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₁₉	—	2	1	no	—
305	C₂³×C₁₉	—	2	2	no	—
306	C₂³×C₁₉	—	2	2	no	—
307	C₂³×C₁₉	—	2	1	no	—
308	C₂³×C₁₉	—	2	1	no	—
309	C₂³×C₁₉	—	4	1	no	—
310	C₂³×C₁₉	—	4	2	no	—
311	C₂³×C₁₉	—	4	2	no	—
312	C₂³×C₁₉	—	8	1	no	—
313	C₂³×C₁₉	#120	1	1	yes	characteristic
314	C₂³×C₁₉	#120	1	1	yes	characteristic
315	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₁₉	—	2	1	no	—
317	Q₈×C₁₉	—	2	4	no	—
318	Q₈×C₁₉	—	2	1	no	—
319	Q₈×C₁₉	—	2	1	no	—
320	Q₈×C₁₉	—	2	4	no	—
321	Q₈×C₁₉	—	2	2	no	—
322	Q₈×C₁₉	—	4	2	no	—
323	Q₈×C₁₉	—	4	4	no	—
324	Q₈×C₁₉	—	4	4	no	—
325	Q₈×C₁₉	—	4	4	no	—
326	Q₈×C₁₉	—	4	1	no	—
327	Q₈×C₁₉	—	4	2	no	—
328	Q₈×C₁₉	—	4	1	no	—
329	Q₈×C₁₉	—	4	2	no	—
330	Q₈×C₁₉	—	4	2	no	—
331	Q₈×C₁₉	#120	1	2	yes	—
332	D₄×C₁₉	—	2	4	no	—
333	D₄×C₁₉	—	2	1	no	—
334	D₄×C₁₉	—	2	1	no	—
335	D₄×C₁₉	—	2	1	no	—
336	D₄×C₁₉	—	2	2	no	—
337	D₄×C₁₉	—	4	2	no	—
338	D₄×C₁₉	—	4	2	no	—
339	D₄×C₁₉	—	4	2	no	—
340	D₄×C₁₉	—	4	4	no	—
341	D₄×C₁₉	—	4	2	no	—
342	D₄×C₁₉	—	4	2	no	—
343	D₄×C₁₉	—	4	2	no	—
344	D₄×C₁₉	—	8	1	no	—
345	D₄×C₁₉	—	8	2	no	—
346	D₄×C₁₉	#120	1	2	yes	—
347	C₂×C₄×C₁₉	—	2	1	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	2	1	no	—
350	C₂×C₄×C₁₉	—	2	1	no	—
351	C₂×C₄×C₁₉	—	2	1	no	—
352	C₂×C₄×C₁₉	—	2	1	no	—
353	C₂×C₄×C₁₉	—	2	2	no	—
354	C₂×C₄×C₁₉	—	2	2	no	—
355	C₂×C₄×C₁₉	—	2	4	no	—
356	C₂×C₄×C₁₉	—	2	4	no	—
357	C₂×C₄×C₁₉	—	2	1	no	—
358	C₂×C₄×C₁₉	—	2	2	no	—
359	C₂×C₄×C₁₉	—	2	1	no	—
360	C₂×C₄×C₁₉	—	2	1	no	—
361	C₂×C₄×C₁₉	—	2	2	no	—
362	C₂×C₄×C₁₉	—	2	1	no	—
363	C₂×C₄×C₁₉	—	2	4	no	—
364	C₂×C₄×C₁₉	—	2	4	no	—
365	C₂×C₄×C₁₉	—	4	2	no	—
366	C₂×C₄×C₁₉	—	4	2	no	—
367	C₂×C₄×C₁₉	—	4	2	no	—
368	C₂×C₄×C₁₉	—	4	4	no	—
369	C₂×C₄×C₁₉	—	4	2	no	—
370	C₂×C₄×C₁₉	—	4	4	no	—
371	C₂×C₄×C₁₉	—	4	4	no	—
372	C₂×C₄×C₁₉	—	4	4	no	—
373	C₂×C₄×C₁₉	—	4	2	no	—
374	C₂×C₄×C₁₉	—	4	2	no	—
375	C₂×C₄×C₁₉	—	4	2	no	—
376	C₂×C₄×C₁₉	—	4	1	no	—
377	C₂×C₄×C₁₉	—	4	1	no	—
378	C₂×C₄×C₁₉	—	4	2	no	—
379	C₂×C₄×C₁₉	—	4	2	no	—
380	C₂×C₄×C₁₉	—	8	2	no	—
381	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
382	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
383	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
387	C₈×C₁₉	—	2	4	no	—
388	C₈×C₁₉	—	4	2	no	—
389	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#3489	C₂×C₁₉	1	1	yes	characteristic
391	C₂×#456	C₂×C₁₉	1	2	yes	complemented
392	#3004	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#2434	C₂×C₁₉	1	1	yes	characteristic, complemented
394	#2007	C₂×C₁₉	1	2	yes	complemented
395	#2005	C₂×C₁₉	1	2	yes	complemented
396	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
397	#1882	C₂×C₁₉	1	2	yes	complemented
398	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
399	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
400	C₂²×C₁₉	—	2	1	no	—
401	C₂²×C₁₉	—	2	1	no	—
402	C₂²×C₁₉	—	2	1	no	—
403	C₂²×C₁₉	—	2	1	no	—
404	C₂²×C₁₉	—	2	1	no	—
405	C₂²×C₁₉	—	2	2	no	—
406	C₂²×C₁₉	—	2	1	no	—
407	C₂²×C₁₉	—	2	1	no	—
408	C₂²×C₁₉	—	4	4	no	—
409	C₂²×C₁₉	—	4	1	no	—
410	C₂²×C₁₉	—	4	1	no	—
411	C₂²×C₁₉	—	4	1	no	—
412	C₂²×C₁₉	—	4	1	no	—
413	C₂²×C₁₉	—	4	1	no	—
414	C₂²×C₁₉	—	4	1	no	—
415	C₂²×C₁₉	—	4	1	no	—
416	C₂²×C₁₉	—	4	1	no	—
417	C₂²×C₁₉	—	8	4	no	—
418	C₂²×C₁₉	#456	1	2	yes	complemented
419	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
420	C₂²×C₁₉	D₄²	1	2	yes	—
421	C₄×C₁₉	—	2	1	no	—
422	C₄×C₁₉	—	2	1	no	—
423	C₄×C₁₉	—	2	2	no	—
424	C₄×C₁₉	—	4	4	no	—
425	C₄×C₁₉	—	4	2	no	—
426	C₄×C₁₉	—	4	1	no	—
427	C₄×C₁₉	—	4	1	no	—
428	C₄×C₁₉	—	4	4	no	—
429	C₄×C₁₉	—	4	1	no	—
430	C₄×C₁₉	—	4	2	no	—
431	C₄×C₁₉	—	4	1	no	—
432	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
433	C₄×C₁₉	#534	1	1	yes	characteristic
434	C₄×C₁₉	D₄²	1	2	yes	—
435	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
436	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
437	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
438	C₂×#137	—	2	1	no	—
439	C₂×#137	—	2	1	no	—
440	C₂×#137	—	2	8	no	—
441	C₂×#137	C₂²×C₁₉	1	2	yes	—
442	C₂×#137	C₂²×C₁₉	1	2	yes	—
443	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
444	C₂²×Q₁₆	—	2	1	no	—
445	C₂²×SD₁₆	—	2	1	no	—
446	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
447	D₄×Q₈	—	2	1	no	—
448	#548	—	2	1	no	—
449	#547	—	2	1	no	—
450	#547	—	2	2	no	—
451	#546	—	2	1	no	—
452	#546	—	2	2	no	—
453	#537	—	2	1	no	—
454	#537	C₂²×C₁₉	1	1	yes	characteristic
455	#536	—	2	1	no	—
456	#536	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
458	#525	—	2	1	no	—
459	#525	C₂²×C₁₉	1	1	yes	characteristic
460	C₂×C₂²⋊Q₈	—	2	1	no	—
461	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
462	#520	C₂²×C₁₉	1	1	yes	characteristic
463	#456	—	2	8	no	—
464	#451	—	2	1	no	—
465	#451	—	2	1	no	—
466	#448	—	2	1	no	—
467	#448	—	2	1	no	—
468	C₂×#104	C₂²×C₁₉	1	2	yes	—
469	C₂×#104	C₂²×C₁₉	1	2	yes	—
470	C₂×#104	C₂²×C₁₉	1	2	yes	complemented
471	#419	C₂²×C₁₉	1	2	yes	complemented
472	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
473	#407	C₂²×C₁₉	1	1	yes	characteristic
474	#395	—	2	2	no	—
475	#391	C₂²×C₁₉	1	2	yes	complemented
476	#385	—	2	2	no	—
477	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
478	#343	C₂²×C₁₉	1	2	yes	complemented
479	#339	C₂²×C₁₉	1	2	yes	complemented
480	C₂×C₁₉	—	2	2	no	—
481	C₂×C₁₉	—	2	2	no	—
482	C₂×C₁₉	—	4	1	no	—
483	C₂×C₁₉	—	4	2	no	—
484	C₂×C₁₉	—	8	1	no	—
485	C₂×C₁₉	—	8	1	no	—
486	C₂×C₁₉	#2403	1	1	yes	characteristic
487	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
488	C₂×C₁₉	#3022	1	1	yes	characteristic
489	2₋¹⁺⁴	—	2	4	no	—
490	2₋¹⁺⁴	—	4	2	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	—	2	4	no	—
497	C₂×#41	—	4	2	no	—
498	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
499	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
500	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
501	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
502	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×Q₈	—	2	1	no	—
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	—	2	4	no	—
507	C₂²×Q₈	—	2	1	no	—
508	C₂²×Q₈	—	2	1	no	—
509	C₂²×Q₈	—	2	1	no	—
510	C₂²×Q₈	—	2	1	no	—
511	C₂²×Q₈	—	4	2	no	—
512	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
514	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
520	#137	—	2	8	no	—
521	#137	—	2	8	no	—
522	#137	—	2	4	no	—
523	#137	—	2	4	no	—
524	#137	—	2	4	no	—
525	#137	—	2	4	no	—
526	#137	—	4	2	no	—
527	#137	D₄×C₁₉	1	8	yes	complemented
528	C₂×Q₁₆	—	2	8	no	—
529	C₂×Q₁₆	—	2	2	no	—
530	C₂×Q₁₆	—	2	2	no	—
531	C₂×Q₁₆	—	2	2	no	—
532	C₂×SD₁₆	—	2	8	no	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×M₁₆	—	2	1	no	—
537	C₂×M₁₆	—	2	4	no	—
538	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
539	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
540	C₂²×C₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	4	no	—
544	C₄⋊Q₈	—	4	2	no	—
545	#124	—	2	2	no	—
546	#124	—	2	1	no	—
547	#123	—	2	2	no	—
548	#123	—	2	2	no	—
549	#123	—	2	2	no	—
550	#123	—	2	1	no	—
551	#123	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
564	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
565	#121	—	2	2	no	—
566	#121	—	2	2	no	—
567	#121	—	2	2	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	2	no	—
571	#121	D₄×C₁₉	1	1	yes	characteristic
572	#121	D₄×C₁₉	1	1	yes	characteristic
573	#120	—	2	2	no	—
574	#120	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	#117	—	2	1	no	—
583	#117	C₂³×C₁₉	1	1	yes	characteristic
584	C₂×C₄⋊C₄	—	2	2	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	4	no	—
587	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	—	2	2	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
592	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
593	#104	—	2	4	no	—
594	#104	—	2	4	no	—
595	#104	—	4	2	no	—
596	#103	—	2	2	no	—
597	#103	—	2	2	no	—
598	#101	—	2	4	no	—
599	C₂²⋊C₈	—	2	1	no	—
600	C₂²⋊C₈	—	2	1	no	—
601	#95	—	2	1	no	—
602	#95	—	2	4	no	—
603	C₁₉	#23880	1	1	yes	characteristic, direct product factor, Sylow
604	C₂⁴	—	2	1	no	—
605	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
606	#41	—	2	2	no	—
607	#41	—	2	2	no	—
608	#41	—	2	2	no	—
609	#41	—	2	2	no	—
610	#41	—	2	2	no	—
611	#41	—	2	2	no	—
612	#41	—	2	2	no	—
613	#41	—	4	4	no	—
614	#41	—	4	1	no	—
615	#41	—	4	1	no	—
616	#41	—	4	4	no	—
617	#41	—	4	4	no	—
618	#41	—	4	8	no	—
619	#41	—	4	2	no	—
620	#41	—	4	2	no	—
621	#41	C₂×D₄×C₁₉	1	4	yes	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	4	no	—
630	C₂×Q₈	—	2	4	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	4	4	no	—
637	C₂×Q₈	—	4	1	no	—
638	C₂×Q₈	—	4	4	no	—
639	C₂×Q₈	—	4	4	no	—
640	C₂×Q₈	—	4	4	no	—
641	C₂×Q₈	—	4	2	no	—
642	C₂×Q₈	—	4	2	no	—
643	C₂×Q₈	—	4	2	no	—
644	C₂×Q₈	—	4	2	no	—
645	C₂×Q₈	—	4	1	no	—
646	C₂×Q₈	—	4	1	no	—
647	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
648	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
649	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
650	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	4	1	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
665	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
666	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	4	4	no	—
681	C₂²×C₄	—	4	4	no	—
682	C₂²×C₄	—	4	1	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
692	Q₁₆	—	2	8	no	—
693	Q₁₆	—	2	8	no	—
694	Q₁₆	—	4	4	no	—
695	SD₁₆	—	2	8	no	—
696	SD₁₆	—	2	8	no	—
697	SD₁₆	—	4	4	no	—
698	M₁₆	—	2	4	no	—
699	M₁₆	—	2	2	no	—
700	M₁₆	—	2	2	no	—
701	M₁₆	—	2	2	no	—
702	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
703	C₂×C₈	—	2	4	no	—
704	C₂×C₈	—	2	2	no	—
705	C₂×C₈	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	4	8	no	—
717	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	8	1	no	—
745	C₂³	C₁₉×#120	1	1	yes	characteristic
746	C₂³	C₁₉×#120	1	1	yes	characteristic
747	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
748	Q₈	—	2	1	no	—
749	Q₈	—	2	4	no	—
750	Q₈	—	2	1	no	—
751	Q₈	—	2	1	no	—
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	4	2	no	—
755	Q₈	—	4	4	no	—
756	Q₈	—	4	4	no	—
757	Q₈	—	4	4	no	—
758	Q₈	—	4	1	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	4	1	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	2	no	—
763	Q₈	C₁₉×#120	1	2	yes	—
764	D₄	—	2	4	no	—
765	D₄	—	2	1	no	—
766	D₄	—	2	1	no	—
767	D₄	—	2	1	no	—
768	D₄	—	2	2	no	—
769	D₄	—	4	2	no	—
770	D₄	—	4	2	no	—
771	D₄	—	4	2	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	2	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	8	1	no	—
777	D₄	—	8	2	no	—
778	D₄	C₁₉×#120	1	2	yes	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
814	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
818	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
819	C₈	—	2	4	no	—
820	C₈	—	4	2	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	8	4	no	—
839	C₂²	C₁₉×#456	1	2	yes	complemented
840	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
841	C₂²	D₄²×C₁₉	1	2	yes	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	4	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
854	C₄	C₁₉×#534	1	1	yes	characteristic
855	C₄	D₄²×C₁₉	1	2	yes	—
856	C₂	—	2	2	no	—
857	C₂	—	2	2	no	—
858	C₂	—	4	1	no	—
859	C₂	—	4	2	no	—
860	C₂	—	8	1	no	—
861	C₂	—	8	1	no	—
862	C₂	C₁₉×#2403	1	1	yes	characteristic
863	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
864	C₂	C₁₉×#3022	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
1. C₂²×C₁₉×#137	C₂	semidirect
3. C₂×C₁₉×#456	C₂	semidirect
4. C₁₉×#3004	C₂	semidirect
5. C₁₉×#2434	C₂	semidirect
6. C₁₉×#2007	C₂	semidirect
7. C₁₉×#2005	C₂	semidirect
8. C₁₉×#1901	C₂	semidirect
9. C₁₉×#1882	C₂	semidirect
10. C₁₉×#1871	C₂	semidirect
11. C₁₉×#1789	C₂	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
34. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
47. C₂×C₁₉×#104	C₂²	semidirect
48. C₁₉×#419	C₂²	semidirect
49. C₂×C₁₉×#101	C₂²	semidirect
52. C₁₉×#391	C₂²	semidirect
55. C₁₉×#343	C₂²	semidirect
56. C₁₉×#339	C₂²	semidirect
95. C₁₉×#137	D₄	semidirect
303. #23880	C₁₉	direct (N × H)
389. C₂²×#137	C₂×C₁₉	semidirect
391. C₂×#456	C₂×C₁₉	semidirect
392. #3004	C₂×C₁₉	semidirect
393. #2434	C₂×C₁₉	semidirect
394. #2007	C₂×C₁₉	semidirect
395. #2005	C₂×C₁₉	semidirect
396. #1901	C₂×C₁₉	semidirect
397. #1882	C₂×C₁₉	semidirect
398. #1871	C₂×C₁₉	semidirect
399. #1789	C₂×C₁₉	semidirect
418. C₂²×C₁₉	#456	semidirect
443. C₂×#137	C₂²×C₁₉	semidirect
457. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
470. C₂×#104	C₂²×C₁₉	semidirect
471. #419	C₂²×C₁₉	semidirect
472. C₂×#101	C₂²×C₁₉	semidirect
475. #391	C₂²×C₁₉	semidirect
478. #343	C₂²×C₁₉	semidirect
479. #339	C₂²×C₁₉	semidirect
527. #137	D₄×C₁₉	semidirect
603. C₁₉	#23880	direct (N × H)
839. 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
C₂²×C₁₉×#137	2
C₁₉×#3489	2
C₂×C₁₉×#456	2
C₁₉×#3004	2
C₁₉×#2434	2
C₁₉×#2007	2
C₁₉×#2005	2
C₁₉×#1901	2
C₁₉×#1882	2
C₁₉×#1871	2
C₁₉×#1789	2
#23880	19

Subgroups — C19×#23880 #18029839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23880 #18029839