Subgroups — C₁₉×#16251 #18022210

Order 4864.

2246 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#123	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#394	C₂	1	2	yes	maximal
5	C₂×C₁₉×#393	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1444	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1440	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
11	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#123	—	2	4	no	—
16	C₂×C₁₉×#123	—	2	4	no	—
17	C₂×C₁₉×#123	—	2	4	no	—
18	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
19	C₂×C₁₉×C₂²⋊Q₈	—	2	8	no	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#395	—	2	4	no	—
33	C₁₉×#394	—	2	8	no	—
34	C₁₉×#393	—	2	4	no	—
35	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂×C₁₉×#95	C₂²	1	2	yes	—
39	C₂×C₁₉×#95	C₂²	1	2	yes	—
40	C₂×C₁₉×#95	C₂²	1	2	yes	—
41	C₂×C₁₉×#95	C₂²	1	2	yes	—
42	C₂×C₁₉×#95	C₂²	1	2	yes	—
43	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
44	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	—	2	4	no	—
46	C₂²×Q₈×C₁₉	—	2	2	no	—
47	C₂²×Q₈×C₁₉	—	2	2	no	—
48	C₂²×Q₈×C₁₉	—	2	2	no	—
49	C₂²×Q₈×C₁₉	—	4	2	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	4	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	—	4	2	no	—
55	C₂³×C₄×C₁₉	—	2	4	no	—
56	C₂³×C₄×C₁₉	—	2	2	no	—
57	C₂³×C₄×C₁₉	—	2	2	no	—
58	C₂³×C₄×C₁₉	—	4	2	no	—
59	C₂³×C₄×C₁₉	D₄	1	4	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#123	—	2	32	no	—
70	C₁₉×C₂²⋊Q₈	—	2	32	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
84	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
106	C₁₉×#95	—	2	4	no	—
107	C₁₉×#95	—	2	2	no	—
108	C₁₉×#95	—	2	4	no	—
109	C₁₉×#95	—	2	4	no	—
110	C₁₉×#95	—	2	2	no	—
111	C₁₉×#95	—	2	4	no	—
112	C₁₉×#95	—	4	2	no	—
113	C₁₉×#95	—	4	2	no	—
114	C₂⁴×C₁₉	—	2	1	no	—
115	C₂⁴×C₁₉	—	2	1	no	—
116	C₂⁴×C₁₉	—	2	2	no	—
117	C₂⁴×C₁₉	—	2	1	no	—
118	C₂⁴×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂⁴×C₁₉	—	2	1	no	—
121	C₂⁴×C₁₉	—	2	2	no	—
122	C₂⁴×C₁₉	—	2	1	no	—
123	C₂⁴×C₁₉	—	2	1	no	—
124	C₂⁴×C₁₉	—	2	1	no	—
125	C₂⁴×C₁₉	—	2	2	no	—
126	C₂⁴×C₁₉	—	2	2	no	—
127	C₂⁴×C₁₉	—	2	1	no	—
128	C₂⁴×C₁₉	—	2	2	no	—
129	C₂⁴×C₁₉	—	2	1	no	—
130	C₂⁴×C₁₉	—	2	1	no	—
131	C₂⁴×C₁₉	—	2	1	no	—
132	C₂⁴×C₁₉	—	2	2	no	—
133	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
134	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
135	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
136	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂×Q₈×C₁₉	—	2	8	no	—
138	C₂×Q₈×C₁₉	—	4	8	no	—
139	C₂×Q₈×C₁₉	—	4	8	no	—
140	C₂×Q₈×C₁₉	—	4	4	no	—
141	C₂×Q₈×C₁₉	—	4	4	no	—
142	C₂×D₄×C₁₉	—	2	8	no	—
143	C₂×D₄×C₁₉	—	4	8	no	—
144	C₂×D₄×C₁₉	—	4	8	no	—
145	C₂×D₄×C₁₉	—	4	4	no	—
146	C₂×D₄×C₁₉	—	4	4	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	8	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	8	no	—
187	C₂²×C₄×C₁₉	—	2	2	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	—	2	2	no	—
192	C₂²×C₄×C₁₉	—	2	2	no	—
193	C₂²×C₄×C₁₉	—	2	2	no	—
194	C₂²×C₄×C₁₉	—	4	4	no	—
195	C₂²×C₄×C₁₉	—	4	8	no	—
196	C₂²×C₄×C₁₉	—	4	8	no	—
197	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₁₉	#41	1	4	yes	—
207	C₄⋊C₄×C₁₉	—	2	8	no	—
208	C₄⋊C₄×C₁₉	—	2	16	no	—
209	C₄⋊C₄×C₁₉	—	2	8	no	—
210	C₄⋊C₄×C₁₉	—	2	8	no	—
211	C₄⋊C₄×C₁₉	—	4	8	no	—
212	C₂²⋊C₄×C₁₉	—	2	8	no	—
213	C₂²⋊C₄×C₁₉	—	2	8	no	—
214	C₂²⋊C₄×C₁₉	—	2	16	no	—
215	C₂²⋊C₄×C₁₉	—	2	8	no	—
216	C₂²⋊C₄×C₁₉	—	4	8	no	—
217	C₂²⋊C₄×C₁₉	—	4	8	no	—
218	C₂²⋊C₄×C₁₉	—	4	8	no	—
219	#16251	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	2	2	no	—
222	C₂³×C₁₉	—	2	2	no	—
223	C₂³×C₁₉	—	2	2	no	—
224	C₂³×C₁₉	—	2	4	no	—
225	C₂³×C₁₉	—	2	4	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	2	2	no	—
228	C₂³×C₁₉	—	2	4	no	—
229	C₂³×C₁₉	—	2	4	no	—
230	C₂³×C₁₉	—	2	4	no	—
231	C₂³×C₁₉	—	2	4	no	—
232	C₂³×C₁₉	—	2	2	no	—
233	C₂³×C₁₉	—	2	2	no	—
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	4	no	—
236	C₂³×C₁₉	—	2	4	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	4	2	no	—
243	C₂³×C₁₉	—	4	2	no	—
244	C₂³×C₁₉	—	4	2	no	—
245	C₂³×C₁₉	—	4	2	no	—
246	C₂³×C₁₉	—	4	2	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	4	2	no	—
253	C₂³×C₁₉	—	4	2	no	—
254	C₂³×C₁₉	—	4	1	no	—
255	C₂³×C₁₉	—	4	1	no	—
256	C₂³×C₁₉	—	4	1	no	—
257	C₂³×C₁₉	—	4	2	no	—
258	C₂³×C₁₉	—	4	2	no	—
259	C₂³×C₁₉	—	4	2	no	—
260	C₂³×C₁₉	—	4	2	no	—
261	C₂³×C₁₉	—	4	2	no	—
262	C₂³×C₁₉	—	4	2	no	—
263	C₂³×C₁₉	—	4	2	no	—
264	C₂³×C₁₉	—	4	2	no	—
265	C₂³×C₁₉	#120	1	4	yes	—
266	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
268	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
269	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₂³×C₁₉	C₂×#41	1	2	yes	—
271	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
272	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
274	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
275	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
276	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
277	Q₈×C₁₉	—	4	16	no	—
278	D₄×C₁₉	—	4	16	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	4	no	—
282	C₂×C₄×C₁₉	—	2	4	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	4	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	4	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	4	no	—
294	C₂×C₄×C₁₉	—	2	4	no	—
295	C₂×C₄×C₁₉	—	2	4	no	—
296	C₂×C₄×C₁₉	—	2	4	no	—
297	C₂×C₄×C₁₉	—	2	4	no	—
298	C₂×C₄×C₁₉	—	2	4	no	—
299	C₂×C₄×C₁₉	—	2	4	no	—
300	C₂×C₄×C₁₉	—	2	4	no	—
301	C₂×C₄×C₁₉	—	2	4	no	—
302	C₂×C₄×C₁₉	—	4	16	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	2	no	—
305	C₂×C₄×C₁₉	—	4	2	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	2	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	2	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	no	—
315	C₂×C₄×C₁₉	—	4	2	no	—
316	C₂×C₄×C₁₉	—	4	2	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	—	4	2	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	4	2	no	—
322	C₂×C₄×C₁₉	—	4	2	no	—
323	C₂×C₄×C₁₉	—	4	2	no	—
324	C₂×C₄×C₁₉	—	4	2	no	—
325	C₂×C₄×C₁₉	—	4	2	no	—
326	C₂×C₄×C₁₉	—	4	2	no	—
327	C₂×C₄×C₁₉	—	4	2	no	—
328	C₂×C₄×C₁₉	—	4	2	no	—
329	C₂×C₄×C₁₉	—	4	2	no	—
330	C₂×C₄×C₁₉	—	4	2	no	—
331	C₂×C₄×C₁₉	—	4	2	no	—
332	C₂×C₄×C₁₉	—	4	2	no	—
333	C₂×C₄×C₁₉	—	4	2	no	—
334	C₂×C₄×C₁₉	#120	1	4	yes	—
335	C₂²×#123	C₂×C₁₉	1	1	yes	characteristic
336	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
337	C₂×#395	C₂×C₁₉	1	1	yes	characteristic, complemented
338	C₂×#394	C₂×C₁₉	1	2	yes	—
339	C₂×#393	C₂×C₁₉	1	1	yes	characteristic, complemented
340	#1444	C₂×C₁₉	1	2	yes	complemented
341	#1441	C₂×C₁₉	1	1	yes	characteristic, complemented
342	#1440	C₂×C₁₉	1	2	yes	complemented
343	#1439	C₂×C₁₉	1	2	yes	complemented
344	#1439	C₂×C₁₉	1	1	yes	characteristic, complemented
345	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
346	C₂²×C₁₉	—	2	4	no	—
347	C₂²×C₁₉	—	2	4	no	—
348	C₂²×C₁₉	—	2	4	no	—
349	C₂²×C₁₉	—	4	2	no	—
350	C₂²×C₁₉	—	4	2	no	—
351	C₂²×C₁₉	—	4	4	no	—
352	C₂²×C₁₉	—	4	4	no	—
353	C₂²×C₁₉	—	4	4	no	—
354	C₂²×C₁₉	—	4	4	no	—
355	C₂²×C₁₉	—	4	2	no	—
356	C₂²×C₁₉	—	4	2	no	—
357	C₂²×C₁₉	—	4	2	no	—
358	C₂²×C₁₉	—	4	2	no	—
359	C₂²×C₁₉	—	4	4	no	—
360	C₂²×C₁₉	—	4	4	no	—
361	C₂²×C₁₉	—	4	2	no	—
362	C₂²×C₁₉	—	8	1	no	—
363	C₂²×C₁₉	—	8	1	no	—
364	C₂²×C₁₉	—	8	2	no	—
365	C₂²×C₁₉	—	8	2	no	—
366	C₂²×C₁₉	—	8	1	no	—
367	C₂²×C₁₉	—	8	1	no	—
368	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
369	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
370	C₂²×C₁₉	#532	1	1	yes	characteristic
371	C₂²×C₁₉	#534	1	1	yes	characteristic
372	C₂²×C₁₉	#536	1	1	yes	characteristic
373	C₂²×C₁₉	#536	1	2	yes	—
374	C₂²×C₁₉	#536	1	2	yes	—
375	C₂²×C₁₉	#536	1	1	yes	characteristic
376	C₂²×C₁₉	#536	1	1	yes	characteristic
377	C₂²×C₁₉	#536	1	1	yes	characteristic
378	C₂²×C₁₉	#537	1	1	yes	characteristic
379	C₂²×C₁₉	#537	1	1	yes	characteristic
380	C₂²×C₁₉	#537	1	1	yes	characteristic
381	C₂²×C₁₉	#539	1	2	yes	—
382	C₂²×C₁₉	#542	1	2	yes	—
383	C₂²×C₁₉	D₄²	1	2	yes	—
384	C₂²×C₁₉	D₄²	1	2	yes	—
385	C₂²×C₁₉	#546	1	2	yes	—
386	C₂²×C₁₉	#547	1	2	yes	—
387	C₂²×C₁₉	#547	1	2	yes	—
388	C₂²×C₁₉	#548	1	2	yes	—
389	C₂²×C₁₉	#562	1	2	yes	—
390	C₂²×C₁₉	#563	1	2	yes	—
391	C₄×C₁₉	—	2	4	no	—
392	C₄×C₁₉	—	4	2	no	—
393	C₄×C₁₉	—	4	2	no	—
394	C₄×C₁₉	—	4	2	no	—
395	C₄×C₁₉	—	4	4	no	—
396	C₄×C₁₉	—	4	4	no	—
397	C₄×C₁₉	—	4	4	no	—
398	C₄×C₁₉	—	4	2	no	—
399	C₄×C₁₉	—	8	2	no	—
400	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
401	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
402	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×#123	—	2	4	no	—
404	C₂×#123	—	2	4	no	—
405	C₂×#123	—	2	4	no	—
406	C₂×C₂²⋊Q₈	—	2	4	no	—
407	C₂×C₂²⋊Q₈	—	2	8	no	—
408	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
410	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
411	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
412	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
416	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
417	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
418	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
420	#395	—	2	4	no	—
421	#394	—	2	8	no	—
422	#393	—	2	4	no	—
423	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
424	C₂×#95	C₂²×C₁₉	1	2	yes	—
425	C₂×#95	C₂²×C₁₉	1	2	yes	—
426	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×#95	C₂²×C₁₉	1	2	yes	—
428	C₂×#95	C₂²×C₁₉	1	2	yes	—
429	C₂×#95	C₂²×C₁₉	1	2	yes	—
430	C₂×#95	C₂²×C₁₉	1	2	yes	—
431	C₂×C₁₉	—	4	4	no	—
432	C₂×C₁₉	—	8	2	no	—
433	C₂×C₁₉	#2403	1	1	yes	characteristic
434	C₂×C₁₉	#2430	1	1	yes	characteristic
435	C₂×C₁₉	#2432	1	1	yes	characteristic
436	C₂×C₁₉	#2614	1	1	yes	characteristic
437	C₂×C₁₉	#2616	1	1	yes	characteristic
438	C₂×C₁₉	#2663	1	1	yes	characteristic
439	C₂×C₁₉	#2672	1	2	yes	—
440	C₂×C₁₉	#2674	1	2	yes	—
441	C₂×C₁₉	#2680	1	2	yes	—
442	C₂×C₁₉	#2681	1	2	yes	—
443	C₂×C₁₉	#2814	1	1	yes	characteristic
444	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
445	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
446	C₂²×Q₈	—	2	4	no	—
447	C₂²×Q₈	—	2	2	no	—
448	C₂²×Q₈	—	2	2	no	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×Q₈	—	4	2	no	—
451	C₂²×D₄	—	2	2	no	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	4	no	—
454	C₂²×D₄	—	2	2	no	—
455	C₂²×D₄	—	4	2	no	—
456	C₂³×C₄	—	2	4	no	—
457	C₂³×C₄	—	2	2	no	—
458	C₂³×C₄	—	2	2	no	—
459	C₂³×C₄	—	4	2	no	—
460	C₂³×C₄	D₄×C₁₉	1	4	yes	—
461	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
462	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
463	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
464	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
470	#123	—	2	32	no	—
471	C₂²⋊Q₈	—	2	32	no	—
472	C₂×C₄⋊C₄	—	2	4	no	—
473	C₂×C₄⋊C₄	—	2	2	no	—
474	C₂×C₄⋊C₄	—	2	4	no	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	—	2	4	no	—
477	C₂×C₄⋊C₄	—	2	2	no	—
478	C₂×C₄⋊C₄	—	2	2	no	—
479	C₂×C₄⋊C₄	—	2	2	no	—
480	C₂×C₄⋊C₄	—	2	2	no	—
481	C₂×C₄⋊C₄	—	2	2	no	—
482	C₂×C₄⋊C₄	—	2	4	no	—
483	C₂×C₄⋊C₄	—	2	4	no	—
484	C₂×C₄⋊C₄	—	4	2	no	—
485	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
486	C₂×C₂²⋊C₄	—	2	4	no	—
487	C₂×C₂²⋊C₄	—	2	4	no	—
488	C₂×C₂²⋊C₄	—	2	2	no	—
489	C₂×C₂²⋊C₄	—	2	2	no	—
490	C₂×C₂²⋊C₄	—	2	2	no	—
491	C₂×C₂²⋊C₄	—	2	2	no	—
492	C₂×C₂²⋊C₄	—	2	2	no	—
493	C₂×C₂²⋊C₄	—	2	2	no	—
494	C₂×C₂²⋊C₄	—	2	2	no	—
495	C₂×C₂²⋊C₄	—	2	2	no	—
496	C₂×C₂²⋊C₄	—	2	4	no	—
497	C₂×C₂²⋊C₄	—	2	4	no	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	—	4	2	no	—
503	C₂×C₂²⋊C₄	—	4	2	no	—
504	C₂×C₂²⋊C₄	—	4	2	no	—
505	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
506	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
507	#95	—	2	4	no	—
508	#95	—	2	2	no	—
509	#95	—	2	4	no	—
510	#95	—	2	2	no	—
511	#95	—	2	4	no	—
512	#95	—	2	4	no	—
513	#95	—	4	2	no	—
514	#95	—	4	2	no	—
515	C₁₉	#16251	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	—	2	1	no	—
517	C₂⁴	—	2	1	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	1	no	—
520	C₂⁴	—	2	2	no	—
521	C₂⁴	—	2	1	no	—
522	C₂⁴	—	2	1	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	1	no	—
525	C₂⁴	—	2	1	no	—
526	C₂⁴	—	2	1	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	1	no	—
530	C₂⁴	—	2	2	no	—
531	C₂⁴	—	2	1	no	—
532	C₂⁴	—	2	1	no	—
533	C₂⁴	—	2	1	no	—
534	C₂⁴	—	2	2	no	—
535	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
536	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
537	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
538	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
539	C₂×Q₈	—	2	8	no	—
540	C₂×Q₈	—	4	8	no	—
541	C₂×Q₈	—	4	8	no	—
542	C₂×Q₈	—	4	4	no	—
543	C₂×Q₈	—	4	4	no	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	4	8	no	—
546	C₂×D₄	—	4	8	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	8	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	8	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	8	no	—
598	C₂²×C₄	—	4	8	no	—
599	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
601	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
602	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
603	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
604	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
605	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
606	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
607	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
608	C₂²×C₄	#41×C₁₉	1	4	yes	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	16	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	4	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	2	8	no	—
616	C₂²⋊C₄	—	2	16	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	4	8	no	—
619	C₂²⋊C₄	—	4	8	no	—
620	C₂²⋊C₄	—	4	8	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	4	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	2	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	2	no	—
659	C₂³	—	4	2	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	C₁₉×#120	1	4	yes	—
667	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
668	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
669	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
671	C₂³	C₂×#41×C₁₉	1	2	yes	—
672	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
673	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
675	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
676	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
677	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
678	Q₈	—	4	16	no	—
679	D₄	—	4	16	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	4	16	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	2	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	C₁₉×#120	1	4	yes	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	2	no	—
754	C₂²	—	8	2	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
759	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
760	C₂²	C₁₉×#532	1	1	yes	characteristic
761	C₂²	C₁₉×#534	1	1	yes	characteristic
762	C₂²	C₁₉×#536	1	1	yes	characteristic
763	C₂²	C₁₉×#536	1	2	yes	—
764	C₂²	C₁₉×#536	1	1	yes	characteristic
765	C₂²	C₁₉×#536	1	1	yes	characteristic
766	C₂²	C₁₉×#536	1	2	yes	—
767	C₂²	C₁₉×#536	1	1	yes	characteristic
768	C₂²	C₁₉×#537	1	1	yes	characteristic
769	C₂²	C₁₉×#537	1	1	yes	characteristic
770	C₂²	C₁₉×#537	1	1	yes	characteristic
771	C₂²	C₁₉×#539	1	2	yes	—
772	C₂²	C₁₉×#542	1	2	yes	—
773	C₂²	D₄²×C₁₉	1	2	yes	—
774	C₂²	D₄²×C₁₉	1	2	yes	—
775	C₂²	C₁₉×#546	1	2	yes	—
776	C₂²	C₁₉×#547	1	2	yes	—
777	C₂²	C₁₉×#547	1	2	yes	—
778	C₂²	C₁₉×#548	1	2	yes	—
779	C₂²	C₁₉×#562	1	2	yes	—
780	C₂²	C₁₉×#563	1	2	yes	—
781	C₄	—	2	4	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	4	no	—
785	C₄	—	4	4	no	—
786	C₄	—	4	4	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	8	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	2	no	—
792	C₂	C₁₉×#2403	1	1	yes	characteristic
793	C₂	C₁₉×#2430	1	1	yes	characteristic
794	C₂	C₁₉×#2432	1	1	yes	characteristic
795	C₂	C₁₉×#2614	1	1	yes	characteristic
796	C₂	C₁₉×#2616	1	1	yes	characteristic
797	C₂	C₁₉×#2663	1	1	yes	characteristic
798	C₂	C₁₉×#2672	1	2	yes	—
799	C₂	C₁₉×#2674	1	2	yes	—
800	C₂	C₁₉×#2680	1	2	yes	—
801	C₂	C₁₉×#2681	1	2	yes	—
802	C₂	C₁₉×#2814	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×C₂²⋊Q₈	C₂	semidirect
3. C₂×C₁₉×#395	C₂	semidirect
5. C₂×C₁₉×#393	C₂	semidirect
6. C₁₉×#1444	C₂	semidirect
7. C₁₉×#1441	C₂	semidirect
8. C₁₉×#1440	C₂	semidirect
9. C₁₉×#1439	C₂	semidirect
10. C₁₉×#1439	C₂	semidirect
11. C₁₉×C₂²⋊#95	C₂	semidirect
219. #16251	C₁₉	direct (N × H)
336. C₂²×C₂²⋊Q₈	C₂×C₁₉	semidirect
337. C₂×#395	C₂×C₁₉	semidirect
339. C₂×#393	C₂×C₁₉	semidirect
340. #1444	C₂×C₁₉	semidirect
341. #1441	C₂×C₁₉	semidirect
342. #1440	C₂×C₁₉	semidirect
343. #1439	C₂×C₁₉	semidirect
344. #1439	C₂×C₁₉	semidirect
345. C₂²⋊#95	C₂×C₁₉	semidirect
515. C₁₉	#16251	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#123	2
C₂²×C₁₉×C₂²⋊Q₈	2
C₂×C₁₉×#395	2
C₂×C₁₉×#394	2
C₂×C₁₉×#393	2
C₁₉×#1444	2
C₁₉×#1441	2
C₁₉×#1440	2
C₁₉×#1439	2
C₁₉×C₂²⋊#95	2
#16251	19

Subgroups — C19×#16251 #18022210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16251 #18022210