Subgroups — C₂×C₁₉×#2570 #18040856

Order 4864.

1966 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2570	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₁₉×#400	C₂	1	2	yes	maximal
3	C₂×C₁₉×#398	C₂	1	2	yes	maximal
4	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#387	C₂	1	2	yes	maximal
7	C₂×C₁₉×#387	C₂	1	2	yes	maximal
8	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	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	2	yes	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#400	C₂²	1	16	yes	—
28	C₁₉×#398	C₂²	1	16	yes	—
29	C₁₉×#389	C₂²	1	8	yes	—
30	C₁₉×#389	C₂²	1	8	yes	—
31	C₁₉×#387	C₂²	1	16	yes	—
32	C₁₉×#387	C₂²	1	16	yes	—
33	C₁₉×#384	C₂²	1	8	yes	—
34	C₁₉×#382	C₂²	1	8	yes	—
35	C₁₉×#382	C₂²	1	8	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
38	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
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	C₂×C₁₉×#95	C₂²	1	2	yes	—
44	C₂×C₁₉×#95	C₂²	1	2	yes	—
45	C₂×C₁₉×#95	C₂²	1	2	yes	—
46	C₂×C₁₉×#95	C₂²	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
67	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
78	C₂×C₄²×C₁₉	—	2	4	no	—
79	C₂×C₄²×C₁₉	—	2	4	no	—
80	C₂×C₄²×C₁₉	—	4	4	no	—
81	C₂×C₄²×C₁₉	Q₈	1	8	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
86	C₁₉×#95	C₂³	1	4	yes	—
87	C₁₉×#95	C₂³	1	4	yes	—
88	C₁₉×#95	C₂³	1	8	yes	—
89	C₁₉×#95	C₂³	1	8	yes	—
90	C₁₉×#95	C₂³	1	8	yes	—
91	C₁₉×#95	C₂³	1	8	yes	—
92	C₁₉×#95	C₂³	1	8	yes	—
93	C₁₉×#95	C₂³	1	8	yes	—
94	C₁₉×#95	C₂³	1	8	yes	—
95	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
123	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
125	C₂²×C₄×C₁₉	#41	1	4	yes	—
126	C₂²×C₄×C₁₉	#41	1	4	yes	—
127	C₂²×C₄×C₁₉	#41	1	4	yes	—
128	C₂²×C₄×C₁₉	#41	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
140	C₄⋊C₄×C₁₉	—	2	8	no	—
141	C₄⋊C₄×C₁₉	—	2	8	no	—
142	C₄⋊C₄×C₁₉	—	2	16	no	—
143	C₄⋊C₄×C₁₉	—	2	16	no	—
144	C₄⋊C₄×C₁₉	—	2	8	no	—
145	C₄⋊C₄×C₁₉	—	2	8	no	—
146	C₄⋊C₄×C₁₉	—	2	8	no	—
147	C₄⋊C₄×C₁₉	—	2	8	no	—
148	C₄⋊C₄×C₁₉	—	4	8	no	—
149	C₄⋊C₄×C₁₉	—	4	8	no	—
150	C₄²×C₁₉	—	2	8	no	—
151	C₄²×C₁₉	—	2	8	no	—
152	C₄²×C₁₉	—	4	8	no	—
153	C₄²×C₁₉	C₂×Q₈	1	16	yes	—
154	C₂×#2570	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
156	C₂³×C₁₉	C₂×#41	1	2	yes	—
157	C₂³×C₁₉	C₂×#41	1	2	yes	—
158	C₂³×C₁₉	C₂×#41	1	2	yes	—
159	C₂³×C₁₉	C₂×#41	1	2	yes	—
160	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
161	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
162	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
163	C₂×C₄×C₁₉	—	2	8	no	—
164	C₂×C₄×C₁₉	—	2	8	no	—
165	C₂×C₄×C₁₉	—	2	8	no	—
166	C₂×C₄×C₁₉	—	2	8	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	8	no	—
196	C₂×C₄×C₁₉	—	4	8	no	—
197	C₂×C₄×C₁₉	—	4	8	no	—
198	C₂×C₄×C₁₉	—	4	8	no	—
199	C₂×C₄×C₁₉	#125	1	16	yes	—
200	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
201	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
202	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
203	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
204	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
205	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
206	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
207	#2570	C₂×C₁₉	1	16	yes	direct product factor
208	C₂×#400	C₂×C₁₉	1	2	yes	—
209	C₂×#398	C₂×C₁₉	1	2	yes	—
210	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
211	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
212	C₂×#387	C₂×C₁₉	1	2	yes	—
213	C₂×#387	C₂×C₁₉	1	2	yes	—
214	C₂×#384	C₂×C₁₉	1	1	yes	characteristic
215	C₂×#382	C₂×C₁₉	1	1	yes	characteristic
216	C₂×#382	C₂×C₁₉	1	1	yes	characteristic
217	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
218	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×#125	1	4	yes	—
220	C₂²×C₁₉	#533	1	4	yes	—
221	C₂²×C₁₉	#544	1	4	yes	—
222	C₂²×C₁₉	#552	1	4	yes	—
223	C₂²×C₁₉	#553	1	4	yes	—
224	C₂²×C₁₉	#556	1	4	yes	—
225	C₂²×C₁₉	#559	1	4	yes	—
226	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
227	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
228	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
229	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
230	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
231	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
233	C₄×C₁₉	—	2	4	no	—
234	C₄×C₁₉	—	2	4	no	—
235	C₄×C₁₉	—	2	4	no	—
236	C₄×C₁₉	—	2	4	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	—	4	4	no	—
243	C₄×C₁₉	C₂×#125	1	8	yes	—
244	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
246	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
248	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
253	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
254	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
256	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
257	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
258	#400	C₂²×C₁₉	1	16	yes	—
259	#398	C₂²×C₁₉	1	16	yes	—
260	#389	C₂²×C₁₉	1	8	yes	—
261	#389	C₂²×C₁₉	1	8	yes	—
262	#387	C₂²×C₁₉	1	16	yes	—
263	#387	C₂²×C₁₉	1	16	yes	—
264	#384	C₂²×C₁₉	1	8	yes	—
265	#382	C₂²×C₁₉	1	8	yes	—
266	#382	C₂²×C₁₉	1	8	yes	—
267	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
268	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
269	C₂×#95	C₂²×C₁₉	1	2	yes	—
270	C₂×#95	C₂²×C₁₉	1	2	yes	—
271	C₂×#95	C₂²×C₁₉	1	2	yes	—
272	C₂×#95	C₂²×C₁₉	1	2	yes	—
273	C₂×#95	C₂²×C₁₉	1	2	yes	—
274	C₂×#95	C₂²×C₁₉	1	2	yes	—
275	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#95	C₂²×C₁₉	1	2	yes	—
278	C₂×C₁₉	#2570	1	8	yes	direct product factor
279	C₂×C₁₉	C₂²×#125	1	1	yes	characteristic
280	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#544	1	1	yes	characteristic
282	C₂×C₁₉	C₂×#552	1	1	yes	characteristic
283	C₂×C₁₉	C₂×#553	1	1	yes	characteristic
284	C₂×C₁₉	C₂×#556	1	1	yes	characteristic
285	C₂×C₁₉	C₂×#559	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
287	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
291	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	8	no	—
300	C₂×C₄⋊C₄	—	2	8	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	4	4	no	—
306	C₂×C₄⋊C₄	—	4	4	no	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	—	2	4	no	—
319	C₂×C₄²	—	4	4	no	—
320	C₂×C₄²	Q₈×C₁₉	1	8	yes	—
321	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
322	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
323	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
324	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
325	#95	C₂³×C₁₉	1	4	yes	—
326	#95	C₂³×C₁₉	1	4	yes	—
327	#95	C₂³×C₁₉	1	8	yes	—
328	#95	C₂³×C₁₉	1	8	yes	—
329	#95	C₂³×C₁₉	1	8	yes	—
330	#95	C₂³×C₁₉	1	8	yes	—
331	#95	C₂³×C₁₉	1	8	yes	—
332	#95	C₂³×C₁₉	1	8	yes	—
333	#95	C₂³×C₁₉	1	8	yes	—
334	C₁₉	C₂×#2570	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
363	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
364	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
365	C₂²×C₄	#41×C₁₉	1	4	yes	—
366	C₂²×C₄	#41×C₁₉	1	4	yes	—
367	C₂²×C₄	#41×C₁₉	1	4	yes	—
368	C₂²×C₄	#41×C₁₉	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	16	no	—
383	C₄⋊C₄	—	2	16	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	4	8	no	—
389	C₄⋊C₄	—	4	8	no	—
390	C₄²	—	2	8	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	4	8	no	—
393	C₄²	C₂×Q₈×C₁₉	1	16	yes	—
394	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
395	C₂³	C₂×#41×C₁₉	1	2	yes	—
396	C₂³	C₂×#41×C₁₉	1	2	yes	—
397	C₂³	C₂×#41×C₁₉	1	2	yes	—
398	C₂³	C₂×#41×C₁₉	1	2	yes	—
399	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
400	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
401	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	8	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	C₁₉×#125	1	16	yes	—
439	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
440	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
441	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
442	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
443	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
444	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
445	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
446	C₂²	C₂×C₁₉×#125	1	4	yes	—
447	C₂²	C₁₉×#533	1	4	yes	—
448	C₂²	C₁₉×#544	1	4	yes	—
449	C₂²	C₁₉×#552	1	4	yes	—
450	C₂²	C₁₉×#553	1	4	yes	—
451	C₂²	C₁₉×#556	1	4	yes	—
452	C₂²	C₁₉×#559	1	4	yes	—
453	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
454	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
455	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
456	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
457	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
458	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	4	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	4	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	C₂×C₁₉×#125	1	8	yes	—
471	C₂	C₁₉×#2570	1	8	yes	direct product factor
472	C₂	C₂²×C₁₉×#125	1	1	yes	characteristic
473	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
474	C₂	C₂×C₁₉×#544	1	1	yes	characteristic
475	C₂	C₂×C₁₉×#552	1	1	yes	characteristic
476	C₂	C₂×C₁₉×#553	1	1	yes	characteristic
477	C₂	C₂×C₁₉×#556	1	1	yes	characteristic
478	C₂	C₂×C₁₉×#559	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×#2570	C₂	direct (N × H)
154. C₂×#2570	C₁₉	direct (N × H)
207. #2570	C₂×C₁₉	direct (N × H)
278. C₂×C₁₉	#2570	direct (N × H)
334. C₁₉	C₂×#2570	direct (N × H)
471. C₂	C₁₉×#2570	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×#2570	2
C₂×C₁₉×#400	2
C₂×C₁₉×#398	2
C₂×C₁₉×#389	2
C₂×C₁₉×#387	2
C₂×C₁₉×#384	2
C₂×C₁₉×#382	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×#2570	19

Subgroups — C2×C19×#2570 #18040856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2570 #18040856