Subgroups — C₁₉×#18416 #18024375

Order 4864.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3194	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3187	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2661	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1612	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1611	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1609	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1608	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1600	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1599	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1597	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1596	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1508	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1501	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1468	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	—	2	1	no	—
17	C₁₉×#562	—	2	1	no	—
18	C₁₉×#554	—	2	1	no	—
19	C₁₉×#552	—	2	1	no	—
20	C₁₉×#551	—	2	1	no	—
21	C₁₉×#551	—	2	1	no	—
22	C₁₉×#547	—	2	1	no	—
23	C₁₉×#546	—	2	1	no	—
24	C₁₉×#544	C₂²	1	1	yes	characteristic
25	C₁₉×#543	C₂²	1	1	yes	characteristic
26	C₁₉×#542	—	2	1	no	—
27	C₁₉×#539	—	2	1	no	—
28	C₁₉×#539	—	2	1	no	—
29	C₁₉×#539	C₂²	1	1	yes	characteristic
30	C₁₉×#538	C₂²	1	1	yes	characteristic
31	C₁₉×#536	—	2	1	no	—
32	C₁₉×#525	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
36	C₁₉×#483	C₂²	1	1	yes	characteristic
37	C₁₉×#483	C₂²	1	1	yes	characteristic
38	C₁₉×#483	C₂²	1	1	yes	characteristic
39	C₁₉×#482	—	2	1	no	—
40	C₁₉×#481	—	2	1	no	—
41	C₁₉×#480	C₂²	1	1	yes	characteristic
42	C₁₉×#469	—	2	1	no	—
43	C₁₉×#468	—	2	1	no	—
44	C₁₉×#465	—	2	1	no	—
45	C₁₉×#465	—	2	1	no	—
46	C₁₉×#450	C₂²	1	1	yes	characteristic
47	C₁₉×#450	C₂²	1	1	yes	characteristic
48	C₁₉×#450	C₂²	1	1	yes	characteristic
49	C₁₉×#449	—	2	1	no	—
50	C₁₉×#448	—	2	1	no	—
51	C₁₉×#447	C₂²	1	1	yes	characteristic
52	C₁₉×#407	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₁₉×#398	C₂²	1	1	yes	characteristic
55	C₁₉×#397	C₂²	1	1	yes	characteristic
56	C₁₉×#394	—	2	1	no	—
57	C₁₉×#394	C₂²	1	1	yes	characteristic
58	C₁₉×#392	—	2	1	no	—
59	C₁₉×#392	C₂²	1	1	yes	characteristic
60	C₁₉×#390	—	2	1	no	—
61	C₁₉×#388	—	2	1	no	—
62	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
63	C₁₉×#328	C₂²	1	1	yes	characteristic
64	C₁₉×#328	C₂²	1	1	yes	characteristic
65	C₁₉×#328	C₂²	1	1	yes	characteristic
66	C₁₉×#328	C₂²	1	1	yes	characteristic
67	C₁₉×#328	C₂²	1	1	yes	characteristic
68	C₁₉×#328	C₂²	1	1	yes	characteristic
69	C₁₉×#327	C₂²	1	1	yes	characteristic
70	C₁₉×#327	C₂²	1	1	yes	characteristic
71	C₁₉×#324	C₂²	1	1	yes	characteristic
72	C₁₉×#324	C₂²	1	1	yes	characteristic
73	C₁₉×#323	C₂²	1	1	yes	characteristic
74	C₁₉×#323	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
77	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
78	C₂²×D₄×C₁₉	—	2	1	no	—
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×SD₁₆×C₁₉	—	2	1	no	—
84	C₂×SD₁₆×C₁₉	—	2	1	no	—
85	C₂×SD₁₆×C₁₉	—	2	1	no	—
86	C₂×D₈×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂²×C₈×C₁₉	—	2	1	no	—
89	C₁₉×C₄⋊Q₈	—	2	1	no	—
90	C₁₉×C₄⋊Q₈	—	2	1	no	—
91	C₁₉×C₄⋊Q₈	—	2	1	no	—
92	C₁₉×#126	—	2	1	no	—
93	C₁₉×#126	—	2	1	no	—
94	C₁₉×#126	—	2	1	no	—
95	C₁₉×#126	—	2	1	no	—
96	C₁₉×#126	—	2	1	no	—
97	C₁₉×#126	—	2	1	no	—
98	C₁₉×#125	—	2	1	no	—
99	C₁₉×#125	—	2	1	no	—
100	C₁₉×#125	—	2	1	no	—
101	C₁₉×#125	—	2	1	no	—
102	C₁₉×#125	—	2	1	no	—
103	C₁₉×#124	—	2	1	no	—
104	C₁₉×#124	—	2	1	no	—
105	C₁₉×#124	—	2	1	no	—
106	C₁₉×#124	—	2	1	no	—
107	C₁₉×#123	—	2	1	no	—
108	C₁₉×#123	—	2	1	no	—
109	C₁₉×#123	—	2	1	no	—
110	C₁₉×#123	—	2	1	no	—
111	C₁₉×#123	—	2	1	no	—
112	C₁₉×#123	—	2	1	no	—
113	C₁₉×#123	—	2	1	no	—
114	C₁₉×#123	—	2	1	no	—
115	C₁₉×#123	—	2	1	no	—
116	C₁₉×#123	—	2	1	no	—
117	C₁₉×#123	—	2	1	no	—
118	C₁₉×#123	—	2	1	no	—
119	C₁₉×#123	—	2	1	no	—
120	C₁₉×#123	—	2	1	no	—
121	C₁₉×C₂²⋊Q₈	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	—	2	1	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	—	2	1	no	—
132	C₁₉×C₂²⋊Q₈	—	2	1	no	—
133	C₁₉×C₂²⋊Q₈	—	2	1	no	—
134	C₁₉×C₂²⋊Q₈	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
136	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
137	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
138	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
141	C₁₉×#121	—	2	1	no	—
142	C₁₉×#121	—	2	1	no	—
143	C₁₉×#121	—	2	1	no	—
144	C₁₉×#121	—	2	1	no	—
145	C₁₉×#121	—	2	1	no	—
146	C₁₉×#121	—	2	1	no	—
147	C₁₉×#121	—	2	1	no	—
148	C₁₉×#121	—	2	1	no	—
149	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
150	C₁₉×#121	C₂³	1	1	yes	characteristic
151	C₁₉×#120	—	2	1	no	—
152	C₁₉×#120	—	2	1	no	—
153	C₄×Q₈×C₁₉	—	2	1	no	—
154	C₄×D₄×C₁₉	—	2	1	no	—
155	C₄×D₄×C₁₉	—	2	1	no	—
156	C₄×D₄×C₁₉	—	2	1	no	—
157	C₄×D₄×C₁₉	—	2	1	no	—
158	C₄×D₄×C₁₉	—	2	1	no	—
159	C₄×D₄×C₁₉	—	2	1	no	—
160	C₄×D₄×C₁₉	—	2	1	no	—
161	C₁₉×#117	—	2	1	no	—
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	—	2	1	no	—
164	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
165	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
170	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
173	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₉	—	2	1	no	—
184	C₁₉×#107	—	2	1	no	—
185	C₁₉×#106	—	2	1	no	—
186	C₁₉×#106	—	2	1	no	—
187	C₁₉×#106	—	2	1	no	—
188	C₁₉×#103	—	2	1	no	—
189	C₁₉×#103	—	2	1	no	—
190	C₁₉×#103	—	2	1	no	—
191	C₁₉×#102	—	2	1	no	—
192	C₁₉×#102	—	2	1	no	—
193	C₁₉×#102	—	2	1	no	—
194	C₁₉×#102	—	2	1	no	—
195	C₁₉×#102	—	2	1	no	—
196	C₁₉×C₂²⋊C₈	—	2	1	no	—
197	C₁₉×C₂²⋊C₈	—	2	1	no	—
198	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
199	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
200	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
202	C₁₉×#95	—	2	1	no	—
203	C₁₉×#95	—	2	1	no	—
204	C₁₉×#95	C₂³	1	1	yes	characteristic
205	C₁₉×#95	C₂³	1	1	yes	characteristic
206	C₂⁴×C₁₉	—	2	1	no	—
207	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
209	#41×C₁₉	—	8	2	no	—
210	#41×C₁₉	—	8	1	no	—
211	C₂×Q₈×C₁₉	—	2	1	no	—
212	C₂×Q₈×C₁₉	—	2	1	no	—
213	C₂×Q₈×C₁₉	—	2	1	no	—
214	C₂×Q₈×C₁₉	—	8	1	no	—
215	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₁₉	—	2	1	no	—
219	C₂×D₄×C₁₉	—	2	1	no	—
220	C₂×D₄×C₁₉	—	2	1	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	1	no	—
227	C₂×D₄×C₁₉	—	4	2	no	—
228	C₂×D₄×C₁₉	—	4	1	no	—
229	C₂×D₄×C₁₉	—	4	1	no	—
230	C₂×D₄×C₁₉	—	8	1	no	—
231	C₂×D₄×C₁₉	—	8	1	no	—
232	C₂×D₄×C₁₉	—	8	1	no	—
233	C₂×D₄×C₁₉	—	8	1	no	—
234	C₂×D₄×C₁₉	—	8	1	no	—
235	C₂×D₄×C₁₉	—	8	1	no	—
236	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	2	1	no	—
239	C₂²×C₄×C₁₉	—	2	1	no	—
240	C₂²×C₄×C₁₉	—	2	1	no	—
241	C₂²×C₄×C₁₉	—	2	1	no	—
242	C₂²×C₄×C₁₉	—	2	1	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	—	8	1	no	—
248	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
257	SD₁₆×C₁₉	—	8	1	no	—
258	SD₁₆×C₁₉	—	8	1	no	—
259	SD₁₆×C₁₉	—	8	1	no	—
260	D₈×C₁₉	—	8	1	no	—
261	M₁₆×C₁₉	—	8	1	no	—
262	C₂×C₈×C₁₉	—	2	1	no	—
263	C₂×C₈×C₁₉	—	2	1	no	—
264	C₂×C₈×C₁₉	—	2	1	no	—
265	C₂×C₈×C₁₉	—	2	1	no	—
266	C₂×C₈×C₁₉	—	8	1	no	—
267	C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₄⋊C₄×C₁₉	—	2	1	no	—
271	C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₄⋊C₄×C₁₉	—	2	1	no	—
273	C₄⋊C₄×C₁₉	—	2	1	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	1	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	—	2	1	no	—
284	C₄⋊C₄×C₁₉	—	2	1	no	—
285	C₄⋊C₄×C₁₉	—	2	1	no	—
286	C₄⋊C₄×C₁₉	—	2	1	no	—
287	C₄⋊C₄×C₁₉	—	2	1	no	—
288	C₄⋊C₄×C₁₉	—	2	1	no	—
289	C₄⋊C₄×C₁₉	—	2	1	no	—
290	C₄⋊C₄×C₁₉	—	2	1	no	—
291	C₄⋊C₄×C₁₉	—	2	1	no	—
292	C₄⋊C₄×C₁₉	—	8	1	no	—
293	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
297	C₂²⋊C₄×C₁₉	—	2	1	no	—
298	C₂²⋊C₄×C₁₉	—	2	1	no	—
299	C₂²⋊C₄×C₁₉	—	2	1	no	—
300	C₂²⋊C₄×C₁₉	—	2	1	no	—
301	C₂²⋊C₄×C₁₉	—	2	1	no	—
302	C₂²⋊C₄×C₁₉	—	2	1	no	—
303	C₂²⋊C₄×C₁₉	—	2	1	no	—
304	C₂²⋊C₄×C₁₉	—	2	1	no	—
305	C₂²⋊C₄×C₁₉	—	2	1	no	—
306	C₂²⋊C₄×C₁₉	—	2	1	no	—
307	C₂²⋊C₄×C₁₉	—	2	1	no	—
308	C₂²⋊C₄×C₁₉	—	2	1	no	—
309	C₂²⋊C₄×C₁₉	—	2	1	no	—
310	C₂²⋊C₄×C₁₉	—	2	1	no	—
311	C₂²⋊C₄×C₁₉	—	2	1	no	—
312	C₂²⋊C₄×C₁₉	—	2	1	no	—
313	C₂²⋊C₄×C₁₉	—	2	1	no	—
314	C₂²⋊C₄×C₁₉	—	2	1	no	—
315	C₂²⋊C₄×C₁₉	—	2	1	no	—
316	C₂²⋊C₄×C₁₉	—	2	1	no	—
317	C₂²⋊C₄×C₁₉	—	2	1	no	—
318	C₂²⋊C₄×C₁₉	—	2	1	no	—
319	C₂²⋊C₄×C₁₉	—	2	1	no	—
320	C₂²⋊C₄×C₁₉	—	4	2	no	—
321	C₂²⋊C₄×C₁₉	—	4	2	no	—
322	C₂²⋊C₄×C₁₉	—	4	1	no	—
323	C₂²⋊C₄×C₁₉	—	4	1	no	—
324	C₂²⋊C₄×C₁₉	—	8	1	no	—
325	C₂²⋊C₄×C₁₉	—	8	1	no	—
326	C₂²⋊C₄×C₁₉	—	8	1	no	—
327	C₄²×C₁₉	—	2	1	no	—
328	C₄²×C₁₉	—	2	1	no	—
329	C₄²×C₁₉	—	2	1	no	—
330	C₄²×C₁₉	—	2	1	no	—
331	C₄²×C₁₉	—	2	1	no	—
332	C₄²×C₁₉	—	8	1	no	—
333	#18416	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₁₉	—	2	1	no	—
335	C₂³×C₁₉	—	2	1	no	—
336	C₂³×C₁₉	—	2	1	no	—
337	C₂³×C₁₉	—	2	1	no	—
338	C₂³×C₁₉	—	2	1	no	—
339	C₂³×C₁₉	—	2	1	no	—
340	C₂³×C₁₉	—	4	1	no	—
341	C₂³×C₁₉	—	4	1	no	—
342	C₂³×C₁₉	—	4	1	no	—
343	C₂³×C₁₉	—	4	1	no	—
344	C₂³×C₁₉	—	4	1	no	—
345	C₂³×C₁₉	—	4	1	no	—
346	C₂³×C₁₉	—	4	1	no	—
347	C₂³×C₁₉	—	4	1	no	—
348	C₂³×C₁₉	—	4	1	no	—
349	C₂³×C₁₉	—	4	1	no	—
350	C₂³×C₁₉	—	4	1	no	—
351	C₂³×C₁₉	#120	1	1	yes	characteristic
352	C₂³×C₁₉	#120	1	1	yes	characteristic
353	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
354	Q₈×C₁₉	—	4	1	no	—
355	Q₈×C₁₉	—	4	1	no	—
356	Q₈×C₁₉	—	4	1	no	—
357	Q₈×C₁₉	—	8	1	no	—
358	Q₈×C₁₉	—	8	1	no	—
359	Q₈×C₁₉	—	8	1	no	—
360	D₄×C₁₉	—	4	1	no	—
361	D₄×C₁₉	—	4	1	no	—
362	D₄×C₁₉	—	4	1	no	—
363	D₄×C₁₉	—	4	1	no	—
364	D₄×C₁₉	—	4	1	no	—
365	D₄×C₁₉	—	4	2	no	—
366	D₄×C₁₉	—	4	2	no	—
367	D₄×C₁₉	—	4	1	no	—
368	D₄×C₁₉	—	4	1	no	—
369	D₄×C₁₉	—	8	1	no	—
370	D₄×C₁₉	—	8	1	no	—
371	D₄×C₁₉	—	8	1	no	—
372	D₄×C₁₉	—	8	1	no	—
373	D₄×C₁₉	—	8	4	no	—
374	D₄×C₁₉	—	8	2	no	—
375	D₄×C₁₉	—	8	2	no	—
376	C₂×C₄×C₁₉	—	2	2	no	—
377	C₂×C₄×C₁₉	—	2	1	no	—
378	C₂×C₄×C₁₉	—	2	1	no	—
379	C₂×C₄×C₁₉	—	2	1	no	—
380	C₂×C₄×C₁₉	—	2	1	no	—
381	C₂×C₄×C₁₉	—	2	1	no	—
382	C₂×C₄×C₁₉	—	2	1	no	—
383	C₂×C₄×C₁₉	—	2	1	no	—
384	C₂×C₄×C₁₉	—	2	1	no	—
385	C₂×C₄×C₁₉	—	2	1	no	—
386	C₂×C₄×C₁₉	—	2	1	no	—
387	C₂×C₄×C₁₉	—	2	1	no	—
388	C₂×C₄×C₁₉	—	2	1	no	—
389	C₂×C₄×C₁₉	—	4	1	no	—
390	C₂×C₄×C₁₉	—	4	1	no	—
391	C₂×C₄×C₁₉	—	4	1	no	—
392	C₂×C₄×C₁₉	—	4	1	no	—
393	C₂×C₄×C₁₉	—	4	1	no	—
394	C₂×C₄×C₁₉	—	4	1	no	—
395	C₂×C₄×C₁₉	—	4	1	no	—
396	C₂×C₄×C₁₉	—	4	2	no	—
397	C₂×C₄×C₁₉	—	4	1	no	—
398	C₂×C₄×C₁₉	—	4	1	no	—
399	C₂×C₄×C₁₉	—	4	1	no	—
400	C₂×C₄×C₁₉	—	4	1	no	—
401	C₂×C₄×C₁₉	—	4	1	no	—
402	C₂×C₄×C₁₉	—	4	1	no	—
403	C₂×C₄×C₁₉	—	4	1	no	—
404	C₂×C₄×C₁₉	—	4	1	no	—
405	C₂×C₄×C₁₉	—	4	1	no	—
406	C₂×C₄×C₁₉	—	8	1	no	—
407	C₂×C₄×C₁₉	—	8	1	no	—
408	C₂×C₄×C₁₉	—	8	1	no	—
409	C₂×C₄×C₁₉	—	8	1	no	—
410	C₂×C₄×C₁₉	—	8	1	no	—
411	C₂×C₄×C₁₉	—	8	1	no	—
412	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
413	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
414	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
416	C₈×C₁₉	—	4	1	no	—
417	C₈×C₁₉	—	4	1	no	—
418	C₈×C₁₉	—	4	1	no	—
419	C₈×C₁₉	—	4	1	no	—
420	#3535	C₂×C₁₉	1	1	yes	characteristic, complemented
421	#3194	C₂×C₁₉	1	1	yes	characteristic, complemented
422	#3187	C₂×C₁₉	1	1	yes	characteristic, complemented
423	#2661	C₂×C₁₉	1	1	yes	characteristic, complemented
424	#1612	C₂×C₁₉	1	1	yes	characteristic, complemented
425	#1611	C₂×C₁₉	1	1	yes	characteristic, complemented
426	#1609	C₂×C₁₉	1	1	yes	characteristic, complemented
427	#1608	C₂×C₁₉	1	1	yes	characteristic, complemented
428	#1600	C₂×C₁₉	1	1	yes	characteristic, complemented
429	#1599	C₂×C₁₉	1	1	yes	characteristic, complemented
430	#1597	C₂×C₁₉	1	1	yes	characteristic, complemented
431	#1596	C₂×C₁₉	1	1	yes	characteristic, complemented
432	#1508	C₂×C₁₉	1	1	yes	characteristic, complemented
433	#1501	C₂×C₁₉	1	1	yes	characteristic, complemented
434	#1468	C₂×C₁₉	1	1	yes	characteristic, complemented
435	C₂²×C₁₉	—	2	1	no	—
436	C₂²×C₁₉	—	2	1	no	—
437	C₂²×C₁₉	—	2	1	no	—
438	C₂²×C₁₉	—	2	1	no	—
439	C₂²×C₁₉	—	2	1	no	—
440	C₂²×C₁₉	—	2	1	no	—
441	C₂²×C₁₉	—	2	1	no	—
442	C₂²×C₁₉	—	2	1	no	—
443	C₂²×C₁₉	—	4	1	no	—
444	C₂²×C₁₉	—	4	1	no	—
445	C₂²×C₁₉	—	4	1	no	—
446	C₂²×C₁₉	—	4	1	no	—
447	C₂²×C₁₉	—	4	1	no	—
448	C₂²×C₁₉	—	4	1	no	—
449	C₂²×C₁₉	—	8	1	no	—
450	C₂²×C₁₉	—	8	1	no	—
451	C₂²×C₁₉	—	8	1	no	—
452	C₂²×C₁₉	—	8	1	no	—
453	C₂²×C₁₉	—	8	1	no	—
454	C₂²×C₁₉	—	8	1	no	—
455	C₂²×C₁₉	—	8	1	no	—
456	C₂²×C₁₉	—	8	1	no	—
457	C₂²×C₁₉	—	8	1	no	—
458	C₂²×C₁₉	—	8	1	no	—
459	C₂²×C₁₉	—	8	1	no	—
460	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
461	C₂²×C₁₉	#577	1	1	yes	characteristic
462	C₂²×C₁₉	#577	1	1	yes	characteristic
463	C₄×C₁₉	—	2	1	no	—
464	C₄×C₁₉	—	2	1	no	—
465	C₄×C₁₉	—	2	1	no	—
466	C₄×C₁₉	—	2	1	no	—
467	C₄×C₁₉	—	4	2	no	—
468	C₄×C₁₉	—	4	1	no	—
469	C₄×C₁₉	—	4	1	no	—
470	C₄×C₁₉	—	4	1	no	—
471	C₄×C₁₉	—	4	1	no	—
472	C₄×C₁₉	—	4	1	no	—
473	C₄×C₁₉	—	4	1	no	—
474	C₄×C₁₉	—	4	1	no	—
475	C₄×C₁₉	—	4	1	no	—
476	C₄×C₁₉	—	4	1	no	—
477	C₄×C₁₉	—	4	1	no	—
478	C₄×C₁₉	—	8	1	no	—
479	C₄×C₁₉	—	8	1	no	—
480	#563	—	2	1	no	—
481	#562	—	2	1	no	—
482	#554	—	2	1	no	—
483	#552	—	2	1	no	—
484	#551	—	2	1	no	—
485	#551	—	2	1	no	—
486	#547	—	2	1	no	—
487	#546	—	2	1	no	—
488	#544	C₂²×C₁₉	1	1	yes	characteristic
489	#543	C₂²×C₁₉	1	1	yes	characteristic
490	#542	—	2	1	no	—
491	#539	—	2	1	no	—
492	#539	—	2	1	no	—
493	#539	C₂²×C₁₉	1	1	yes	characteristic
494	#538	C₂²×C₁₉	1	1	yes	characteristic
495	#536	—	2	1	no	—
496	#525	C₂²×C₁₉	1	1	yes	characteristic
497	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
498	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
499	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
500	#483	C₂²×C₁₉	1	1	yes	characteristic
501	#483	C₂²×C₁₉	1	1	yes	characteristic
502	#483	C₂²×C₁₉	1	1	yes	characteristic
503	#482	—	2	1	no	—
504	#481	—	2	1	no	—
505	#480	C₂²×C₁₉	1	1	yes	characteristic
506	#469	—	2	1	no	—
507	#468	—	2	1	no	—
508	#465	—	2	1	no	—
509	#465	—	2	1	no	—
510	#450	C₂²×C₁₉	1	1	yes	characteristic
511	#450	C₂²×C₁₉	1	1	yes	characteristic
512	#450	C₂²×C₁₉	1	1	yes	characteristic
513	#449	—	2	1	no	—
514	#448	—	2	1	no	—
515	#447	C₂²×C₁₉	1	1	yes	characteristic
516	#407	C₂²×C₁₉	1	1	yes	characteristic
517	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
518	#398	C₂²×C₁₉	1	1	yes	characteristic
519	#397	C₂²×C₁₉	1	1	yes	characteristic
520	#394	—	2	1	no	—
521	#394	C₂²×C₁₉	1	1	yes	characteristic
522	#392	—	2	1	no	—
523	#392	C₂²×C₁₉	1	1	yes	characteristic
524	#390	—	2	1	no	—
525	#388	—	2	1	no	—
526	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
527	#328	C₂²×C₁₉	1	1	yes	characteristic
528	#328	C₂²×C₁₉	1	1	yes	characteristic
529	#328	C₂²×C₁₉	1	1	yes	characteristic
530	#328	C₂²×C₁₉	1	1	yes	characteristic
531	#328	C₂²×C₁₉	1	1	yes	characteristic
532	#328	C₂²×C₁₉	1	1	yes	characteristic
533	#327	C₂²×C₁₉	1	1	yes	characteristic
534	#327	C₂²×C₁₉	1	1	yes	characteristic
535	#324	C₂²×C₁₉	1	1	yes	characteristic
536	#324	C₂²×C₁₉	1	1	yes	characteristic
537	#323	C₂²×C₁₉	1	1	yes	characteristic
538	#323	C₂²×C₁₉	1	1	yes	characteristic
539	C₂×C₁₉	—	2	1	no	—
540	C₂×C₁₉	—	2	1	no	—
541	C₂×C₁₉	—	4	1	no	—
542	C₂×C₁₉	—	4	1	no	—
543	C₂×C₁₉	—	8	1	no	—
544	C₂×C₁₉	—	8	1	no	—
545	C₂×C₁₉	—	16	1	no	—
546	C₂×C₁₉	#3010	1	1	yes	characteristic
547	C₂×C₁₉	#3018	1	1	yes	characteristic
548	C₂×C₁₉	#3026	1	1	yes	characteristic
549	C₂×#41	—	2	1	no	—
550	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
551	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
557	C₂×SD₁₆	—	2	1	no	—
558	C₂×SD₁₆	—	2	1	no	—
559	C₂×SD₁₆	—	2	1	no	—
560	C₂×D₈	—	2	1	no	—
561	C₂×M₁₆	—	2	1	no	—
562	C₂²×C₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	#126	—	2	1	no	—
567	#126	—	2	1	no	—
568	#126	—	2	1	no	—
569	#126	—	2	1	no	—
570	#126	—	2	1	no	—
571	#126	—	2	1	no	—
572	#125	—	2	1	no	—
573	#125	—	2	1	no	—
574	#125	—	2	1	no	—
575	#125	—	2	1	no	—
576	#125	—	2	1	no	—
577	#124	—	2	1	no	—
578	#124	—	2	1	no	—
579	#124	—	2	1	no	—
580	#124	—	2	1	no	—
581	#123	—	2	1	no	—
582	#123	—	2	1	no	—
583	#123	—	2	1	no	—
584	#123	—	2	1	no	—
585	#123	—	2	1	no	—
586	#123	—	2	1	no	—
587	#123	—	2	1	no	—
588	#123	—	2	1	no	—
589	#123	—	2	1	no	—
590	#123	—	2	1	no	—
591	#123	—	2	1	no	—
592	#123	—	2	1	no	—
593	#123	—	2	1	no	—
594	#123	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	1	no	—
605	C₂²⋊Q₈	—	2	1	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
610	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
611	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
612	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
613	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
615	#121	—	2	1	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	1	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	1	no	—
622	#121	—	2	1	no	—
623	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
624	#121	C₂³×C₁₉	1	1	yes	characteristic
625	#120	—	2	1	no	—
626	#120	—	2	1	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	1	no	—
635	#117	—	2	1	no	—
636	#117	—	2	1	no	—
637	#117	—	2	1	no	—
638	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
644	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
657	C₂×C₄²	—	2	1	no	—
658	#107	—	2	1	no	—
659	#106	—	2	1	no	—
660	#106	—	2	1	no	—
661	#106	—	2	1	no	—
662	#103	—	2	1	no	—
663	#103	—	2	1	no	—
664	#103	—	2	1	no	—
665	#102	—	2	1	no	—
666	#102	—	2	1	no	—
667	#102	—	2	1	no	—
668	#102	—	2	1	no	—
669	#102	—	2	1	no	—
670	C₂²⋊C₈	—	2	1	no	—
671	C₂²⋊C₈	—	2	1	no	—
672	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
673	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
674	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
675	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
676	#95	—	2	1	no	—
677	#95	—	2	1	no	—
678	#95	C₂³×C₁₉	1	1	yes	characteristic
679	#95	C₂³×C₁₉	1	1	yes	characteristic
680	C₁₉	#18416	1	1	yes	characteristic, direct product factor, Sylow
681	C₂⁴	—	2	1	no	—
682	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
683	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
684	#41	—	8	2	no	—
685	#41	—	8	1	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	8	1	no	—
690	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
691	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
692	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	8	1	no	—
706	C₂×D₄	—	8	1	no	—
707	C₂×D₄	—	8	1	no	—
708	C₂×D₄	—	8	1	no	—
709	C₂×D₄	—	8	1	no	—
710	C₂×D₄	—	8	1	no	—
711	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	8	1	no	—
723	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
732	SD₁₆	—	8	1	no	—
733	SD₁₆	—	8	1	no	—
734	SD₁₆	—	8	1	no	—
735	D₈	—	8	1	no	—
736	M₁₆	—	8	1	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	8	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	8	1	no	—
768	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
769	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
771	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	1	no	—
798	C₂²⋊C₄	—	4	1	no	—
799	C₂²⋊C₄	—	8	1	no	—
800	C₂²⋊C₄	—	8	1	no	—
801	C₂²⋊C₄	—	8	1	no	—
802	C₄²	—	2	1	no	—
803	C₄²	—	2	1	no	—
804	C₄²	—	2	1	no	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	1	no	—
807	C₄²	—	8	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	4	1	no	—
815	C₂³	—	4	1	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	4	1	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	C₁₉×#120	1	1	yes	characteristic
826	C₂³	C₁₉×#120	1	1	yes	characteristic
827	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
828	Q₈	—	4	1	no	—
829	Q₈	—	4	1	no	—
830	Q₈	—	4	1	no	—
831	Q₈	—	8	1	no	—
832	Q₈	—	8	1	no	—
833	Q₈	—	8	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	2	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	8	1	no	—
844	D₄	—	8	1	no	—
845	D₄	—	8	1	no	—
846	D₄	—	8	1	no	—
847	D₄	—	8	4	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	8	1	no	—
881	C₂×C₄	—	8	1	no	—
882	C₂×C₄	—	8	1	no	—
883	C₂×C₄	—	8	1	no	—
884	C₂×C₄	—	8	1	no	—
885	C₂×C₄	—	8	1	no	—
886	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
887	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
890	C₈	—	4	1	no	—
891	C₈	—	4	1	no	—
892	C₈	—	4	1	no	—
893	C₈	—	4	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	8	1	no	—
909	C₂²	—	8	1	no	—
910	C₂²	—	8	1	no	—
911	C₂²	—	8	1	no	—
912	C₂²	—	8	1	no	—
913	C₂²	—	8	1	no	—
914	C₂²	—	8	1	no	—
915	C₂²	—	8	1	no	—
916	C₂²	—	8	1	no	—
917	C₂²	—	8	1	no	—
918	C₂²	—	8	1	no	—
919	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
920	C₂²	C₁₉×#577	1	1	yes	characteristic
921	C₂²	C₁₉×#577	1	1	yes	characteristic
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	1	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	1	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	1	no	—
937	C₄	—	8	1	no	—
938	C₄	—	8	1	no	—
939	C₂	—	2	1	no	—
940	C₂	—	2	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	8	1	no	—
944	C₂	—	8	1	no	—
945	C₂	—	16	1	no	—
946	C₂	C₁₉×#3010	1	1	yes	characteristic
947	C₂	C₁₉×#3018	1	1	yes	characteristic
948	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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. C₁₉×#3535	C₂	semidirect
2. C₁₉×#3194	C₂	semidirect
3. C₁₉×#3187	C₂	semidirect
4. C₁₉×#2661	C₂	semidirect
5. C₁₉×#1612	C₂	semidirect
6. C₁₉×#1611	C₂	semidirect
7. C₁₉×#1609	C₂	semidirect
8. C₁₉×#1608	C₂	semidirect
9. C₁₉×#1600	C₂	semidirect
10. C₁₉×#1599	C₂	semidirect
11. C₁₉×#1597	C₂	semidirect
12. C₁₉×#1596	C₂	semidirect
13. C₁₉×#1508	C₂	semidirect
14. C₁₉×#1501	C₂	semidirect
15. C₁₉×#1468	C₂	semidirect
76. C₂×#41×C₁₉	D₄	semidirect
77. C₂²×Q₈×C₁₉	D₄	semidirect
135. C₁₉×C₂²⋊Q₈	D₄	semidirect
136. C₁₉×C₂²⋊Q₈	D₄	semidirect
137. C₁₉×C₂²⋊Q₈	D₄	semidirect
149. C₁₉×#121	D₄	semidirect
164. C₁₉×#117	D₄	semidirect
169. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
333. #18416	C₁₉	direct (N × H)
420. #3535	C₂×C₁₉	semidirect
421. #3194	C₂×C₁₉	semidirect
422. #3187	C₂×C₁₉	semidirect
423. #2661	C₂×C₁₉	semidirect
424. #1612	C₂×C₁₉	semidirect
425. #1611	C₂×C₁₉	semidirect
426. #1609	C₂×C₁₉	semidirect
427. #1608	C₂×C₁₉	semidirect
428. #1600	C₂×C₁₉	semidirect
429. #1599	C₂×C₁₉	semidirect
430. #1597	C₂×C₁₉	semidirect
431. #1596	C₂×C₁₉	semidirect
432. #1508	C₂×C₁₉	semidirect
433. #1501	C₂×C₁₉	semidirect
434. #1468	C₂×C₁₉	semidirect
550. C₂×#41	D₄×C₁₉	semidirect
551. C₂²×Q₈	D₄×C₁₉	semidirect
609. C₂²⋊Q₈	D₄×C₁₉	semidirect
610. C₂²⋊Q₈	D₄×C₁₉	semidirect
611. C₂²⋊Q₈	D₄×C₁₉	semidirect
623. #121	D₄×C₁₉	semidirect
638. #117	D₄×C₁₉	semidirect
643. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
680. C₁₉	#18416	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×#3535	2
C₁₉×#3194	2
C₁₉×#3187	2
C₁₉×#2661	2
C₁₉×#1612	2
C₁₉×#1611	2
C₁₉×#1609	2
C₁₉×#1608	2
C₁₉×#1600	2
C₁₉×#1599	2
C₁₉×#1597	2
C₁₉×#1596	2
C₁₉×#1508	2
C₁₉×#1501	2
C₁₉×#1468	2
#18416	19

Subgroups — C19×#18416 #18024375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18416 #18024375