Subgroups — C₂×C₁₉×#2528 #18040751

Order 4864.

1878 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2528	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₁₉×#401	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#400	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#400	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#398	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#376	C₂	1	1	yes	maximal, characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#401	C₂²	1	8	yes	—
33	C₁₉×#400	C₂²	1	8	yes	—
34	C₁₉×#400	C₂²	1	8	yes	—
35	C₁₉×#398	C₂²	1	8	yes	—
36	C₁₉×#389	C₂²	1	8	yes	—
37	C₁₉×#387	C₂²	1	8	yes	—
38	C₁₉×#387	C₂²	1	8	yes	—
39	C₁₉×#387	C₂²	1	8	yes	—
40	C₁₉×#387	C₂²	1	8	yes	—
41	C₁₉×#387	C₂²	1	8	yes	—
42	C₁₉×#387	C₂²	1	8	yes	—
43	C₁₉×#387	C₂²	1	8	yes	—
44	C₁₉×#382	C₂²	1	8	yes	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
46	C₁₉×#376	C₂²	1	8	yes	—
47	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
58	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
60	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
61	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
62	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
63	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
64	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
65	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
66	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₉	—	2	4	no	—
103	C₂×C₄²×C₁₉	—	2	4	no	—
104	C₂×C₄²×C₁₉	—	2	4	no	—
105	C₂×C₄²×C₁₉	—	2	4	no	—
106	C₂×C₄²×C₁₉	—	2	4	no	—
107	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
109	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
112	C₁₉×#95	C₂³	1	4	yes	—
113	C₁₉×#95	C₂³	1	4	yes	—
114	C₁₉×#95	C₂³	1	4	yes	—
115	C₁₉×#95	C₂³	1	4	yes	—
116	C₁₉×#95	C₂³	1	4	yes	—
117	C₁₉×#95	C₂³	1	4	yes	—
118	C₁₉×#95	C₂³	1	4	yes	—
119	C₁₉×#95	C₂³	1	4	yes	—
120	C₁₉×#95	C₂³	1	4	yes	—
121	C₁₉×#95	C₂³	1	4	yes	—
122	C₁₉×#95	C₂³	1	4	yes	—
123	C₁₉×#95	C₂³	1	4	yes	—
124	C₁₉×#95	C₂³	1	4	yes	—
125	C₁₉×#95	C₂³	1	4	yes	—
126	C₁₉×#95	C₂³	1	4	yes	—
127	C₁₉×#95	C₂³	1	4	yes	—
128	C₁₉×#95	C₂³	1	4	yes	—
129	C₁₉×#95	C₂³	1	4	yes	—
130	C₁₉×#95	C₂³	1	4	yes	—
131	C₁₉×#95	C₂³	1	4	yes	—
132	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
164	C₂²×C₄×C₁₉	—	2	2	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	#41	1	4	yes	—
174	C₂²×C₄×C₁₉	#41	1	4	yes	—
175	C₂²×C₄×C₁₉	#41	1	4	yes	—
176	C₂²×C₄×C₁₉	#41	1	4	yes	—
177	C₂²×C₄×C₁₉	#41	1	4	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
193	C₄⋊C₄×C₁₉	—	2	8	no	—
194	C₄⋊C₄×C₁₉	—	2	8	no	—
195	C₄⋊C₄×C₁₉	—	2	8	no	—
196	C₄⋊C₄×C₁₉	—	2	8	no	—
197	C₄⋊C₄×C₁₉	—	2	8	no	—
198	C₄⋊C₄×C₁₉	—	2	8	no	—
199	C₄⋊C₄×C₁₉	—	2	8	no	—
200	C₄⋊C₄×C₁₉	—	2	8	no	—
201	C₄⋊C₄×C₁₉	—	2	8	no	—
202	C₄⋊C₄×C₁₉	—	2	8	no	—
203	C₄²×C₁₉	—	2	8	no	—
204	C₄²×C₁₉	—	2	8	no	—
205	C₄²×C₁₉	—	2	8	no	—
206	C₄²×C₁₉	—	2	8	no	—
207	C₄²×C₁₉	—	2	8	no	—
208	C₂×#2528	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₉	C₂×#41	1	2	yes	—
210	C₂³×C₁₉	C₂×#41	1	2	yes	—
211	C₂³×C₁₉	C₂×#41	1	2	yes	—
212	C₂³×C₁₉	C₂×#41	1	2	yes	—
213	C₂³×C₁₉	C₂×#41	1	2	yes	—
214	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
215	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
216	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
217	C₂×C₄×C₁₉	—	2	8	no	—
218	C₂×C₄×C₁₉	—	2	8	no	—
219	C₂×C₄×C₁₉	—	2	8	no	—
220	C₂×C₄×C₁₉	—	2	8	no	—
221	C₂×C₄×C₁₉	—	2	8	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	4	4	no	—
263	C₂×C₄×C₁₉	—	4	4	no	—
264	C₂×C₄×C₁₉	—	4	4	no	—
265	C₂×C₄×C₁₉	—	4	4	no	—
266	C₂×C₄×C₁₉	—	4	4	no	—
267	C₂×C₄×C₁₉	—	4	4	no	—
268	C₂×C₄×C₁₉	—	4	4	no	—
269	C₂×C₄×C₁₉	—	4	4	no	—
270	C₂×C₄×C₁₉	—	4	4	no	—
271	C₂×C₄×C₁₉	—	4	4	no	—
272	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
273	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
274	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
275	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
276	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
277	#2528	C₂×C₁₉	1	16	yes	direct product factor
278	C₂×#401	C₂×C₁₉	1	1	yes	characteristic
279	C₂×#400	C₂×C₁₉	1	1	yes	characteristic
280	C₂×#400	C₂×C₁₉	1	1	yes	characteristic
281	C₂×#398	C₂×C₁₉	1	1	yes	characteristic
282	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
283	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
284	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
285	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
286	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
287	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
288	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
289	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
290	C₂×#382	C₂×C₁₉	1	1	yes	characteristic
291	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
292	C₂×#376	C₂×C₁₉	1	1	yes	characteristic
293	C₂²×C₁₉	#529	1	4	yes	—
294	C₂²×C₁₉	#529	1	4	yes	—
295	C₂²×C₁₉	#541	1	4	yes	—
296	C₂²×C₁₉	#552	1	4	yes	—
297	C₂²×C₁₉	#552	1	4	yes	—
298	C₂²×C₁₉	#552	1	4	yes	—
299	C₂²×C₁₉	#556	1	4	yes	—
300	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
301	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
302	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
303	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
304	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
305	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
306	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
307	C₄×C₁₉	—	2	4	no	—
308	C₄×C₁₉	—	2	4	no	—
309	C₄×C₁₉	—	2	4	no	—
310	C₄×C₁₉	—	2	4	no	—
311	C₄×C₁₉	—	2	4	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₄×C₁₉	—	4	2	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	2	no	—
320	C₄×C₁₉	—	4	2	no	—
321	C₄×C₁₉	—	4	2	no	—
322	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
326	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
332	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
333	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
334	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
335	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
337	#401	C₂²×C₁₉	1	8	yes	—
338	#400	C₂²×C₁₉	1	8	yes	—
339	#400	C₂²×C₁₉	1	8	yes	—
340	#398	C₂²×C₁₉	1	8	yes	—
341	#389	C₂²×C₁₉	1	8	yes	—
342	#387	C₂²×C₁₉	1	8	yes	—
343	#387	C₂²×C₁₉	1	8	yes	—
344	#387	C₂²×C₁₉	1	8	yes	—
345	#387	C₂²×C₁₉	1	8	yes	—
346	#387	C₂²×C₁₉	1	8	yes	—
347	#387	C₂²×C₁₉	1	8	yes	—
348	#387	C₂²×C₁₉	1	8	yes	—
349	#382	C₂²×C₁₉	1	8	yes	—
350	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
351	#376	C₂²×C₁₉	1	8	yes	—
352	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₁₉	#2528	1	8	yes	direct product factor
373	C₂×C₁₉	C₂×#529	1	1	yes	characteristic
374	C₂×C₁₉	C₂×#529	1	1	yes	characteristic
375	C₂×C₁₉	C₂×#541	1	1	yes	characteristic
376	C₂×C₁₉	C₂×#552	1	1	yes	characteristic
377	C₂×C₁₉	C₂×#552	1	1	yes	characteristic
378	C₂×C₁₉	C₂×#552	1	1	yes	characteristic
379	C₂×C₁₉	C₂×#556	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	2	4	no	—
396	C₂×C₄⋊C₄	—	2	4	no	—
397	C₂×C₄⋊C₄	—	2	4	no	—
398	C₂×C₄⋊C₄	—	2	4	no	—
399	C₂×C₄⋊C₄	—	2	4	no	—
400	C₂×C₄⋊C₄	—	2	4	no	—
401	C₂×C₄⋊C₄	—	2	4	no	—
402	C₂×C₄⋊C₄	—	2	4	no	—
403	C₂×C₄⋊C₄	—	2	4	no	—
404	C₂×C₄⋊C₄	—	2	4	no	—
405	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
415	C₂×C₄²	—	2	4	no	—
416	C₂×C₄²	—	2	4	no	—
417	C₂×C₄²	—	2	4	no	—
418	C₂×C₄²	—	2	4	no	—
419	C₂×C₄²	—	2	4	no	—
420	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
421	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
423	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
424	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
425	#95	C₂³×C₁₉	1	4	yes	—
426	#95	C₂³×C₁₉	1	4	yes	—
427	#95	C₂³×C₁₉	1	4	yes	—
428	#95	C₂³×C₁₉	1	4	yes	—
429	#95	C₂³×C₁₉	1	4	yes	—
430	#95	C₂³×C₁₉	1	4	yes	—
431	#95	C₂³×C₁₉	1	4	yes	—
432	#95	C₂³×C₁₉	1	4	yes	—
433	#95	C₂³×C₁₉	1	4	yes	—
434	#95	C₂³×C₁₉	1	4	yes	—
435	#95	C₂³×C₁₉	1	4	yes	—
436	#95	C₂³×C₁₉	1	4	yes	—
437	#95	C₂³×C₁₉	1	4	yes	—
438	#95	C₂³×C₁₉	1	4	yes	—
439	#95	C₂³×C₁₉	1	4	yes	—
440	#95	C₂³×C₁₉	1	4	yes	—
441	#95	C₂³×C₁₉	1	4	yes	—
442	#95	C₂³×C₁₉	1	4	yes	—
443	#95	C₂³×C₁₉	1	4	yes	—
444	#95	C₂³×C₁₉	1	4	yes	—
445	C₁₉	C₂×#2528	1	1	yes	characteristic, direct product factor, Sylow
446	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	#41×C₁₉	1	4	yes	—
488	C₂²×C₄	#41×C₁₉	1	4	yes	—
489	C₂²×C₄	#41×C₁₉	1	4	yes	—
490	C₂²×C₄	#41×C₁₉	1	4	yes	—
491	C₂²×C₄	#41×C₁₉	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	2	8	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	2	8	no	—
516	C₄⋊C₄	—	2	8	no	—
517	C₄²	—	2	8	no	—
518	C₄²	—	2	8	no	—
519	C₄²	—	2	8	no	—
520	C₄²	—	2	8	no	—
521	C₄²	—	2	8	no	—
522	C₂³	C₂×#41×C₁₉	1	2	yes	—
523	C₂³	C₂×#41×C₁₉	1	2	yes	—
524	C₂³	C₂×#41×C₁₉	1	2	yes	—
525	C₂³	C₂×#41×C₁₉	1	2	yes	—
526	C₂³	C₂×#41×C₁₉	1	2	yes	—
527	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
528	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
529	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	8	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
586	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
587	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
588	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
589	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
590	C₂²	C₁₉×#529	1	4	yes	—
591	C₂²	C₁₉×#529	1	4	yes	—
592	C₂²	C₁₉×#541	1	4	yes	—
593	C₂²	C₁₉×#552	1	4	yes	—
594	C₂²	C₁₉×#552	1	4	yes	—
595	C₂²	C₁₉×#552	1	4	yes	—
596	C₂²	C₁₉×#556	1	4	yes	—
597	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
598	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
599	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
600	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
601	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
602	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
603	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
604	C₄	—	2	4	no	—
605	C₄	—	2	4	no	—
606	C₄	—	2	4	no	—
607	C₄	—	2	4	no	—
608	C₄	—	2	4	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₂	C₁₉×#2528	1	8	yes	direct product factor
620	C₂	C₂×C₁₉×#529	1	1	yes	characteristic
621	C₂	C₂×C₁₉×#529	1	1	yes	characteristic
622	C₂	C₂×C₁₉×#541	1	1	yes	characteristic
623	C₂	C₂×C₁₉×#552	1	1	yes	characteristic
624	C₂	C₂×C₁₉×#552	1	1	yes	characteristic
625	C₂	C₂×C₁₉×#552	1	1	yes	characteristic
626	C₂	C₂×C₁₉×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2528	C₂	direct (N × H)
208. C₂×#2528	C₁₉	direct (N × H)
277. #2528	C₂×C₁₉	direct (N × H)
372. C₂×C₁₉	#2528	direct (N × H)
445. C₁₉	C₂×#2528	direct (N × H)
619. C₂	C₁₉×#2528	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×#2528	2
C₂×C₁₉×#401	2
C₂×C₁₉×#400	2
C₂×C₁₉×#398	2
C₂×C₁₉×#389	2
C₂×C₁₉×#387	2
C₂×C₁₉×#382	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#376	2
C₂×#2528	19

Subgroups — C2×C19×#2528 #18040751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2528 #18040751