Subgroups — C₁₉×#14571 #18020530

Order 4864.

1966 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#394	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#388	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#386	C₂	1	2	yes	maximal
4	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1442	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
9	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#394	C₄	1	8	yes	complemented
21	C₁₉×#388	—	2	8	no	—
22	C₁₉×#386	—	2	8	no	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
34	C₂⁵×C₁₉	C₂³	1	2	yes	—
35	C₂²×D₄×C₁₉	—	2	4	no	—
36	C₂²×D₄×C₁₉	—	2	4	no	—
37	C₂²×D₄×C₁₉	—	4	1	no	—
38	C₂²×D₄×C₁₉	—	4	1	no	—
39	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
40	C₂³×C₄×C₁₉	—	2	4	no	—
41	C₂³×C₄×C₁₉	—	2	4	no	—
42	C₂³×C₄×C₁₉	—	2	4	no	—
43	C₂³×C₄×C₁₉	—	4	2	no	—
44	C₂³×C₄×C₁₉	—	4	2	no	—
45	C₂³×C₄×C₁₉	—	4	2	no	—
46	C₂³×C₄×C₁₉	—	4	2	no	—
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
61	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
74	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
75	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
76	C₂×C₄²×C₁₉	—	2	4	no	—
77	C₂×C₄²×C₁₉	—	4	1	no	—
78	C₁₉×#95	—	2	4	no	—
79	C₁₉×#95	—	2	4	no	—
80	C₁₉×#95	—	2	4	no	—
81	C₁₉×#95	—	2	4	no	—
82	C₁₉×#95	—	2	4	no	—
83	C₁₉×#95	—	4	2	no	—
84	C₁₉×#95	—	4	1	no	—
85	C₁₉×#95	—	4	2	no	—
86	C₁₉×#95	—	4	1	no	—
87	C₁₉×#95	—	4	1	no	—
88	C₁₉×#95	C₂×C₄	1	4	yes	complemented
89	C₂⁴×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	—	2	2	no	—
91	C₂⁴×C₁₉	—	2	2	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	2	no	—
101	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
102	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
103	C₂⁴×C₁₉	#41	1	4	yes	—
104	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂×D₄×C₁₉	—	2	16	no	—
106	C₂×D₄×C₁₉	—	4	4	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	4	8	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	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	—	4	8	no	—
154	C₂²×C₄×C₁₉	—	4	8	no	—
155	C₂²×C₄×C₁₉	—	4	8	no	—
156	C₂²×C₄×C₁₉	—	4	8	no	—
157	C₂²×C₄×C₁₉	—	4	8	no	—
158	C₂²×C₄×C₁₉	—	4	8	no	—
159	C₂²×C₄×C₁₉	—	4	8	no	—
160	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
163	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₁₉	#41	1	4	yes	—
167	C₄⋊C₄×C₁₉	—	4	4	no	—
168	C₄⋊C₄×C₁₉	—	4	8	no	—
169	C₂²⋊C₄×C₁₉	—	2	16	no	—
170	C₂²⋊C₄×C₁₉	—	4	8	no	—
171	C₂²⋊C₄×C₁₉	—	4	8	no	—
172	C₂²⋊C₄×C₁₉	—	4	8	no	—
173	C₂²⋊C₄×C₁₉	—	4	8	no	—
174	C₄²×C₁₉	—	4	4	no	—
175	#14571	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	4	no	—
177	C₂³×C₁₉	—	2	4	no	—
178	C₂³×C₁₉	—	2	4	no	—
179	C₂³×C₁₉	—	2	4	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	2	4	no	—
186	C₂³×C₁₉	—	2	4	no	—
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	2	4	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	2	4	no	—
192	C₂³×C₁₉	—	2	4	no	—
193	C₂³×C₁₉	—	2	4	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	4	2	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	—	4	2	no	—
210	C₂³×C₁₉	C₄×D₄	1	8	yes	—
211	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
212	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
213	C₂³×C₁₉	C₂×#41	1	2	yes	—
214	C₂³×C₁₉	C₂×#41	1	2	yes	—
215	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
216	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
219	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
220	D₄×C₁₉	—	4	16	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	4	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	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	4	32	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	2	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×#394	C₂×C₁₉	1	1	yes	characteristic
273	C₂×#388	C₂×C₁₉	1	2	yes	complemented
274	C₂×#386	C₂×C₁₉	1	2	yes	—
275	#1445	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1442	C₂×C₁₉	1	2	yes	complemented
277	#1439	C₂×C₁₉	1	2	yes	complemented
278	#1436	C₂×C₁₉	1	1	yes	characteristic, complemented
279	C₂²⋊#95	C₂×C₁₉	1	2	yes	complemented
280	C₂²⋊#95	C₂×C₁₉	1	2	yes	complemented
281	C₂²×C₁₉	—	2	8	no	—
282	C₂²×C₁₉	—	2	8	no	—
283	C₂²×C₁₉	—	2	8	no	—
284	C₂²×C₁₉	—	4	4	no	—
285	C₂²×C₁₉	—	4	4	no	—
286	C₂²×C₁₉	—	4	4	no	—
287	C₂²×C₁₉	—	4	4	no	—
288	C₂²×C₁₉	—	4	4	no	—
289	C₂²×C₁₉	—	4	4	no	—
290	C₂²×C₁₉	—	4	4	no	—
291	C₂²×C₁₉	—	4	4	no	—
292	C₂²×C₁₉	—	4	4	no	—
293	C₂²×C₁₉	—	4	4	no	—
294	C₂²×C₁₉	—	4	4	no	—
295	C₂²×C₁₉	—	4	4	no	—
296	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
297	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
298	C₂²×C₁₉	#518	1	1	yes	characteristic
299	C₂²×C₁₉	#518	1	1	yes	characteristic
300	C₂²×C₁₉	#520	1	2	yes	—
301	C₂²×C₁₉	#534	1	2	yes	—
302	C₂²×C₁₉	#537	1	2	yes	—
303	C₂²×C₁₉	#538	1	2	yes	—
304	C₂²×C₁₉	#538	1	2	yes	—
305	C₂²×C₁₉	#539	1	2	yes	—
306	C₂²×C₁₉	#540	1	2	yes	—
307	C₂²×C₁₉	D₄²	1	1	yes	characteristic
308	C₂²×C₁₉	#546	1	2	yes	—
309	C₂²×C₁₉	#546	1	2	yes	—
310	C₂²×C₁₉	#547	1	2	yes	—
311	C₂²×C₁₉	#551	1	1	yes	characteristic
312	C₂²×C₁₉	#551	1	2	yes	—
313	C₂²×C₁₉	#552	1	2	yes	—
314	C₂²×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
315	C₂²×C₁₉	#562	1	2	yes	—
316	C₂²×C₁₉	#563	1	1	yes	characteristic
317	C₄×C₁₉	—	4	4	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	4	2	no	—
320	C₄×C₁₉	—	4	2	no	—
321	C₄×C₁₉	—	4	4	no	—
322	C₄×C₁₉	—	4	4	no	—
323	C₄×C₁₉	—	4	4	no	—
324	C₄×C₁₉	—	8	2	no	—
325	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
326	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
327	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
328	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
330	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
331	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
332	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
333	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
334	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
335	#394	C₄×C₁₉	1	8	yes	complemented
336	#388	—	2	8	no	—
337	#386	—	2	8	no	—
338	C₂×#95	C₂²×C₁₉	1	2	yes	—
339	C₂×#95	C₂²×C₁₉	1	2	yes	—
340	C₂×#95	C₂²×C₁₉	1	2	yes	—
341	C₂×#95	C₂²×C₁₉	1	2	yes	—
342	C₂×#95	C₂²×C₁₉	1	2	yes	—
343	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#95	C₂²×C₁₉	1	2	yes	—
345	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#95	C₂²×C₁₉	1	2	yes	—
347	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×C₁₉	—	4	8	no	—
350	C₂×C₁₉	#2325	1	2	yes	—
351	C₂×C₁₉	#2333	1	1	yes	characteristic
352	C₂×C₁₉	#2358	1	1	yes	characteristic
353	C₂×C₁₉	#2359	1	2	yes	—
354	C₂×C₁₉	#2379	1	1	yes	characteristic
355	C₂×C₁₉	#2671	1	2	yes	—
356	C₂×C₁₉	#2684	1	2	yes	—
357	C₂×C₁₉	#2695	1	2	yes	—
358	C₂×C₁₉	#2743	1	2	yes	—
359	C₂⁵	C₂³×C₁₉	1	2	yes	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	4	no	—
362	C₂²×D₄	—	4	1	no	—
363	C₂²×D₄	—	4	1	no	—
364	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
365	C₂³×C₄	—	2	4	no	—
366	C₂³×C₄	—	2	4	no	—
367	C₂³×C₄	—	2	4	no	—
368	C₂³×C₄	—	4	2	no	—
369	C₂³×C₄	—	4	2	no	—
370	C₂³×C₄	—	4	2	no	—
371	C₂³×C₄	—	4	2	no	—
372	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
378	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
379	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
380	C₂×C₄⋊C₄	—	2	4	no	—
381	C₂×C₄⋊C₄	—	4	1	no	—
382	C₂×C₄⋊C₄	—	4	1	no	—
383	C₂×C₄⋊C₄	—	4	2	no	—
384	C₂×C₄⋊C₄	—	4	2	no	—
385	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
386	C₂×C₂²⋊C₄	—	2	4	no	—
387	C₂×C₂²⋊C₄	—	2	4	no	—
388	C₂×C₂²⋊C₄	—	2	4	no	—
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₂²⋊C₄	—	2	4	no	—
391	C₂×C₂²⋊C₄	—	2	4	no	—
392	C₂×C₂²⋊C₄	—	4	2	no	—
393	C₂×C₂²⋊C₄	—	4	2	no	—
394	C₂×C₂²⋊C₄	—	4	2	no	—
395	C₂×C₂²⋊C₄	—	4	2	no	—
396	C₂×C₂²⋊C₄	—	4	2	no	—
397	C₂×C₂²⋊C₄	—	4	2	no	—
398	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
399	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
400	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
401	C₂×C₄²	—	2	4	no	—
402	C₂×C₄²	—	4	1	no	—
403	#95	—	2	4	no	—
404	#95	—	2	4	no	—
405	#95	—	2	4	no	—
406	#95	—	2	4	no	—
407	#95	—	2	4	no	—
408	#95	—	4	2	no	—
409	#95	—	4	1	no	—
410	#95	—	4	2	no	—
411	#95	—	4	1	no	—
412	#95	—	4	1	no	—
413	#95	C₂×C₄×C₁₉	1	4	yes	complemented
414	C₁₉	#14571	1	1	yes	characteristic, direct product factor, Sylow
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	2	2	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	—	2	2	no	—
420	C₂⁴	—	2	2	no	—
421	C₂⁴	—	2	2	no	—
422	C₂⁴	—	2	2	no	—
423	C₂⁴	—	2	2	no	—
424	C₂⁴	—	2	2	no	—
425	C₂⁴	—	2	2	no	—
426	C₂⁴	—	2	2	no	—
427	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
428	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
429	C₂⁴	#41×C₁₉	1	4	yes	—
430	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
431	C₂×D₄	—	2	16	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	8	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	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	1	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	1	no	—
469	C₂²×C₄	—	2	1	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	—	4	8	no	—
480	C₂²×C₄	—	4	8	no	—
481	C₂²×C₄	—	4	8	no	—
482	C₂²×C₄	—	4	8	no	—
483	C₂²×C₄	—	4	8	no	—
484	C₂²×C₄	—	4	8	no	—
485	C₂²×C₄	—	4	8	no	—
486	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
487	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
488	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
489	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
490	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
491	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
492	C₂²×C₄	#41×C₁₉	1	4	yes	—
493	C₄⋊C₄	—	4	4	no	—
494	C₄⋊C₄	—	4	8	no	—
495	C₂²⋊C₄	—	2	16	no	—
496	C₂²⋊C₄	—	4	8	no	—
497	C₂²⋊C₄	—	4	8	no	—
498	C₂²⋊C₄	—	4	8	no	—
499	C₂²⋊C₄	—	4	8	no	—
500	C₄²	—	4	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	2	4	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	4	2	no	—
535	C₂³	C₄×D₄×C₁₉	1	8	yes	—
536	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
537	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
538	C₂³	C₂×#41×C₁₉	1	2	yes	—
539	C₂³	C₂×#41×C₁₉	1	2	yes	—
540	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
541	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
543	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
544	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
545	D₄	—	4	16	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	4	32	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	2	8	no	—
599	C₂²	—	2	8	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	4	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	4	no	—
612	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
613	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
614	C₂²	C₁₉×#518	1	1	yes	characteristic
615	C₂²	C₁₉×#518	1	1	yes	characteristic
616	C₂²	C₁₉×#520	1	2	yes	—
617	C₂²	C₁₉×#534	1	2	yes	—
618	C₂²	C₁₉×#537	1	2	yes	—
619	C₂²	C₁₉×#538	1	2	yes	—
620	C₂²	C₁₉×#538	1	2	yes	—
621	C₂²	C₁₉×#539	1	2	yes	—
622	C₂²	C₁₉×#540	1	2	yes	—
623	C₂²	D₄²×C₁₉	1	1	yes	characteristic
624	C₂²	C₁₉×#546	1	2	yes	—
625	C₂²	C₁₉×#546	1	2	yes	—
626	C₂²	C₁₉×#547	1	2	yes	—
627	C₂²	C₁₉×#551	1	2	yes	—
628	C₂²	C₁₉×#551	1	1	yes	characteristic
629	C₂²	C₁₉×#552	1	2	yes	—
630	C₂²	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
631	C₂²	C₁₉×#562	1	2	yes	—
632	C₂²	C₁₉×#563	1	1	yes	characteristic
633	C₄	—	4	4	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	4	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	2	no	—
640	C₄	—	8	2	no	—
641	C₂	—	4	8	no	—
642	C₂	C₁₉×#2325	1	2	yes	—
643	C₂	C₁₉×#2333	1	1	yes	characteristic
644	C₂	C₁₉×#2358	1	1	yes	characteristic
645	C₂	C₁₉×#2359	1	2	yes	—
646	C₂	C₁₉×#2379	1	1	yes	characteristic
647	C₂	C₁₉×#2671	1	2	yes	—
648	C₂	C₁₉×#2684	1	2	yes	—
649	C₂	C₁₉×#2695	1	2	yes	—
650	C₂	C₁₉×#2743	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
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
2. C₂×C₁₉×#388	C₂	semidirect
4. C₁₉×#1445	C₂	semidirect
5. C₁₉×#1442	C₂	semidirect
6. C₁₉×#1439	C₂	semidirect
7. C₁₉×#1436	C₂	semidirect
8. C₁₉×C₂²⋊#95	C₂	semidirect
9. C₁₉×C₂²⋊#95	C₂	semidirect
20. C₁₉×#394	C₄	semidirect
60. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
73. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
74. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
88. C₁₉×#95	C₂×C₄	semidirect
175. #14571	C₁₉	direct (N × H)
273. C₂×#388	C₂×C₁₉	semidirect
275. #1445	C₂×C₁₉	semidirect
276. #1442	C₂×C₁₉	semidirect
277. #1439	C₂×C₁₉	semidirect
278. #1436	C₂×C₁₉	semidirect
279. C₂²⋊#95	C₂×C₁₉	semidirect
280. C₂²⋊#95	C₂×C₁₉	semidirect
335. #394	C₄×C₁₉	semidirect
385. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
398. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
399. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
413. #95	C₂×C₄×C₁₉	semidirect
414. C₁₉	#14571	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#394	2
C₂×C₁₉×#388	2
C₂×C₁₉×#386	2
C₁₉×#1445	2
C₁₉×#1442	2
C₁₉×#1439	2
C₁₉×#1436	2
C₁₉×C₂²⋊#95	2
#14571	19

Subgroups — C19×#14571 #18020530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14571 #18020530