Subgroups — C₁₉×#14224 #18020183

Order 4864.

2162 conjugacy classes of subgroups.

The subgroup lattice has 686 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	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
7	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1434	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	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#394	C₄	1	8	yes	complemented
23	C₁₉×#388	—	2	8	no	—
24	C₁₉×#386	—	2	8	no	—
25	C₄×C₂²⋊C₄×C₁₉	—	2	8	no	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	2	yes	—
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
35	C₂⁵×C₁₉	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₉	—	2	4	no	—
37	C₂²×D₄×C₁₉	—	2	4	no	—
38	C₂²×D₄×C₁₉	—	4	1	no	—
39	C₂²×D₄×C₁₉	—	4	1	no	—
40	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₁₉	—	2	4	no	—
42	C₂³×C₄×C₁₉	—	2	4	no	—
43	C₂³×C₄×C₁₉	—	2	4	no	—
44	C₂³×C₄×C₁₉	—	2	4	no	—
45	C₂³×C₄×C₁₉	—	2	4	no	—
46	C₂³×C₄×C₁₉	—	4	2	no	—
47	C₂³×C₄×C₁₉	—	4	2	no	—
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	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	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
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	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
77	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
78	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
79	C₂×C₄²×C₁₉	—	2	4	no	—
80	C₂×C₄²×C₁₉	—	2	4	no	—
81	C₂×C₄²×C₁₉	—	2	4	no	—
82	C₂×C₄²×C₁₉	—	4	1	no	—
83	C₂×C₄²×C₁₉	—	4	1	no	—
84	C₂×C₄²×C₁₉	D₄	1	4	yes	complemented
85	C₁₉×#95	—	2	4	no	—
86	C₁₉×#95	—	2	4	no	—
87	C₁₉×#95	—	2	4	no	—
88	C₁₉×#95	—	2	4	no	—
89	C₁₉×#95	—	2	4	no	—
90	C₁₉×#95	—	2	4	no	—
91	C₁₉×#95	—	2	4	no	—
92	C₁₉×#95	—	4	1	no	—
93	C₁₉×#95	C₂×C₄	1	4	yes	complemented
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	—	2	2	no	—
102	C₂⁴×C₁₉	—	2	2	no	—
103	C₂⁴×C₁₉	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	2	2	no	—
106	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
107	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
108	C₂⁴×C₁₉	#41	1	4	yes	—
109	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂×D₄×C₁₉	—	2	16	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	—	4	8	no	—
114	C₂×D₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	16	no	—
124	C₂²×C₄×C₁₉	—	2	2	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	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	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	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	—	4	8	no	—
158	C₂²×C₄×C₁₉	—	4	8	no	—
159	C₂²×C₄×C₁₉	—	4	8	no	—
160	C₂²×C₄×C₁₉	—	4	8	no	—
161	C₂²×C₄×C₁₉	—	4	8	no	—
162	C₂²×C₄×C₁₉	—	4	8	no	—
163	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₁₉	#41	1	4	yes	—
172	C₂²×C₄×C₁₉	#41	1	2	yes	—
173	C₂²×C₄×C₁₉	#41	1	4	yes	—
174	C₄⋊C₄×C₁₉	—	4	4	no	—
175	C₄⋊C₄×C₁₉	—	4	4	no	—
176	C₄⋊C₄×C₁₉	—	4	4	no	—
177	C₂²⋊C₄×C₁₉	—	2	16	no	—
178	C₂²⋊C₄×C₁₉	—	2	16	no	—
179	C₂²⋊C₄×C₁₉	—	2	16	no	—
180	C₂²⋊C₄×C₁₉	—	4	8	no	—
181	C₂²⋊C₄×C₁₉	—	4	8	no	—
182	C₄²×C₁₉	—	4	4	no	—
183	C₄²×C₁₉	—	4	8	no	—
184	#14224	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	4	no	—
195	C₂³×C₁₉	—	2	4	no	—
196	C₂³×C₁₉	—	2	4	no	—
197	C₂³×C₁₉	—	2	4	no	—
198	C₂³×C₁₉	—	2	4	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	2	4	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	2	4	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	—	4	2	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	2	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	2	no	—
216	C₂³×C₁₉	—	4	2	no	—
217	C₂³×C₁₉	—	4	2	no	—
218	C₂³×C₁₉	—	4	2	no	—
219	C₂³×C₁₉	C₄×D₄	1	8	yes	—
220	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
221	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₉	C₂×#41	1	2	yes	—
224	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
225	C₂³×C₁₉	C₂×#41	1	2	yes	—
226	C₂³×C₁₉	C₂×#41	1	2	yes	—
227	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
231	D₄×C₁₉	—	4	16	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	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	4	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	4	no	—
252	C₂×C₄×C₁₉	—	2	4	no	—
253	C₂×C₄×C₁₉	—	2	4	no	—
254	C₂×C₄×C₁₉	—	2	4	no	—
255	C₂×C₄×C₁₉	—	2	4	no	—
256	C₂×C₄×C₁₉	—	2	4	no	—
257	C₂×C₄×C₁₉	—	4	32	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	2	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	1	no	—
267	C₂×C₄×C₁₉	—	4	1	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×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	2	no	—
276	C₂×C₄×C₁₉	—	4	2	no	—
277	C₂×C₄×C₁₉	—	4	2	no	—
278	C₂×C₄×C₁₉	—	4	2	no	—
279	C₂×C₄×C₁₉	—	4	2	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
284	C₂×C₄×C₁₉	#121	1	8	yes	—
285	C₂×#394	C₂×C₁₉	1	1	yes	characteristic
286	C₂×#388	C₂×C₁₉	1	2	yes	complemented
287	C₂×#386	C₂×C₁₉	1	2	yes	—
288	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	2	yes	complemented
289	#1441	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1439	C₂×C₁₉	1	2	yes	complemented
291	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1434	C₂×C₁₉	1	2	yes	complemented
293	C₂²⋊#95	C₂×C₁₉	1	2	yes	complemented
294	C₂²×C₁₉	—	2	8	no	—
295	C₂²×C₁₉	—	2	8	no	—
296	C₂²×C₁₉	—	2	8	no	—
297	C₂²×C₁₉	—	4	4	no	—
298	C₂²×C₁₉	—	4	4	no	—
299	C₂²×C₁₉	—	4	4	no	—
300	C₂²×C₁₉	—	4	4	no	—
301	C₂²×C₁₉	—	4	4	no	—
302	C₂²×C₁₉	—	4	4	no	—
303	C₂²×C₁₉	—	4	4	no	—
304	C₂²×C₁₉	—	4	4	no	—
305	C₂²×C₁₉	—	4	4	no	—
306	C₂²×C₁₉	—	4	4	no	—
307	C₂²×C₁₉	—	4	4	no	—
308	C₂²×C₁₉	—	4	4	no	—
309	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
311	C₂²×C₁₉	C₄×#41	1	2	yes	—
312	C₂²×C₁₉	#518	1	1	yes	characteristic
313	C₂²×C₁₉	#520	1	1	yes	characteristic
314	C₂²×C₁₉	C₂×#121	1	2	yes	—
315	C₂²×C₁₉	#525	1	2	yes	—
316	C₂²×C₁₉	#529	1	2	yes	—
317	C₂²×C₁₉	#532	1	2	yes	—
318	C₂²×C₁₉	#534	1	1	yes	characteristic
319	C₂²×C₁₉	#537	1	1	yes	characteristic
320	C₂²×C₁₉	#538	1	1	yes	characteristic
321	C₂²×C₁₉	#539	1	1	yes	characteristic
322	C₂²×C₁₉	D₄²	1	1	yes	characteristic
323	C₂²×C₁₉	#546	1	2	yes	—
324	C₂²×C₁₉	#546	1	2	yes	—
325	C₂²×C₁₉	#547	1	2	yes	—
326	C₂²×C₁₉	#551	1	1	yes	characteristic
327	C₂²×C₁₉	#551	1	2	yes	—
328	C₂²×C₁₉	#551	1	2	yes	—
329	C₂²×C₁₉	#552	1	2	yes	—
330	C₂²×C₁₉	#555	1	1	yes	characteristic
331	C₂²×C₁₉	#555	1	1	yes	characteristic
332	C₄×C₁₉	—	2	4	no	—
333	C₄×C₁₉	—	2	8	no	—
334	C₄×C₁₉	—	4	2	no	—
335	C₄×C₁₉	—	4	2	no	—
336	C₄×C₁₉	—	4	4	no	—
337	C₄×C₁₉	—	4	4	no	—
338	C₄×C₁₉	—	4	4	no	—
339	C₄×C₁₉	—	8	2	no	—
340	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
341	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
342	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
344	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
346	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
350	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
351	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
352	#394	C₄×C₁₉	1	8	yes	complemented
353	#388	—	2	8	no	—
354	#386	—	2	8	no	—
355	C₄×C₂²⋊C₄	—	2	8	no	—
356	C₂×#95	C₂²×C₁₉	1	2	yes	—
357	C₂×#95	C₂²×C₁₉	1	2	yes	—
358	C₂×#95	C₂²×C₁₉	1	2	yes	—
359	C₂×#95	C₂²×C₁₉	1	2	yes	—
360	C₂×#95	C₂²×C₁₉	1	2	yes	—
361	C₂×#95	C₂²×C₁₉	1	2	yes	—
362	C₂×#95	C₂²×C₁₉	1	2	yes	—
363	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×C₁₉	—	4	8	no	—
366	C₂×C₁₉	C₄×#121	1	2	yes	—
367	C₂×C₁₉	#2325	1	1	yes	characteristic
368	C₂×C₁₉	#2358	1	1	yes	characteristic
369	C₂×C₁₉	#2359	1	2	yes	—
370	C₂×C₁₉	#2372	1	1	yes	characteristic
371	C₂×C₁₉	#2534	1	2	yes	—
372	C₂×C₁₉	#2537	1	1	yes	characteristic
373	C₂×C₁₉	#2553	1	2	yes	—
374	C₂×C₁₉	#2555	1	1	yes	characteristic
375	C₂×C₁₉	#2572	1	1	yes	characteristic
376	C₂×C₁₉	#2609	1	1	yes	characteristic
377	C₂⁵	C₂³×C₁₉	1	2	yes	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	—	2	4	no	—
380	C₂²×D₄	—	4	1	no	—
381	C₂²×D₄	—	4	1	no	—
382	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
383	C₂³×C₄	—	2	4	no	—
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	—	2	4	no	—
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	—	2	4	no	—
388	C₂³×C₄	—	4	2	no	—
389	C₂³×C₄	—	4	2	no	—
390	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
391	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
395	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
398	C₂×C₄⋊C₄	—	2	4	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	4	1	no	—
401	C₂×C₄⋊C₄	—	4	1	no	—
402	C₂×C₄⋊C₄	—	4	1	no	—
403	C₂×C₄⋊C₄	—	4	1	no	—
404	C₂×C₄⋊C₄	—	4	1	no	—
405	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
406	C₂×C₂²⋊C₄	—	2	4	no	—
407	C₂×C₂²⋊C₄	—	2	4	no	—
408	C₂×C₂²⋊C₄	—	2	4	no	—
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₂²⋊C₄	—	2	4	no	—
411	C₂×C₂²⋊C₄	—	2	4	no	—
412	C₂×C₂²⋊C₄	—	2	4	no	—
413	C₂×C₂²⋊C₄	—	2	4	no	—
414	C₂×C₂²⋊C₄	—	2	4	no	—
415	C₂×C₂²⋊C₄	—	2	4	no	—
416	C₂×C₂²⋊C₄	—	4	2	no	—
417	C₂×C₂²⋊C₄	—	4	2	no	—
418	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
419	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
420	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
421	C₂×C₄²	—	2	4	no	—
422	C₂×C₄²	—	2	4	no	—
423	C₂×C₄²	—	2	4	no	—
424	C₂×C₄²	—	4	1	no	—
425	C₂×C₄²	—	4	1	no	—
426	C₂×C₄²	D₄×C₁₉	1	4	yes	complemented
427	#95	—	2	4	no	—
428	#95	—	2	4	no	—
429	#95	—	2	4	no	—
430	#95	—	2	4	no	—
431	#95	—	2	4	no	—
432	#95	—	2	4	no	—
433	#95	—	2	4	no	—
434	#95	—	4	1	no	—
435	#95	C₂×C₄×C₁₉	1	4	yes	complemented
436	C₁₉	#14224	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	2	no	—
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	2	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	2	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	2	no	—
449	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
450	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
451	C₂⁴	#41×C₁₉	1	4	yes	—
452	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	8	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	16	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	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	4	8	no	—
501	C₂²×C₄	—	4	8	no	—
502	C₂²×C₄	—	4	8	no	—
503	C₂²×C₄	—	4	8	no	—
504	C₂²×C₄	—	4	8	no	—
505	C₂²×C₄	—	4	8	no	—
506	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
507	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
508	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
509	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
510	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
511	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
512	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
513	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
514	C₂²×C₄	#41×C₁₉	1	4	yes	—
515	C₂²×C₄	#41×C₁₉	1	2	yes	—
516	C₂²×C₄	#41×C₁₉	1	4	yes	—
517	C₄⋊C₄	—	4	4	no	—
518	C₄⋊C₄	—	4	4	no	—
519	C₄⋊C₄	—	4	4	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	2	16	no	—
523	C₂²⋊C₄	—	4	8	no	—
524	C₂²⋊C₄	—	4	8	no	—
525	C₄²	—	4	4	no	—
526	C₄²	—	4	8	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	C₄×D₄×C₁₉	1	8	yes	—
562	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
563	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
564	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
565	C₂³	C₂×#41×C₁₉	1	2	yes	—
566	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
567	C₂³	C₂×#41×C₁₉	1	2	yes	—
568	C₂³	C₂×#41×C₁₉	1	2	yes	—
569	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
572	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
573	D₄	—	4	16	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	4	32	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
626	C₂×C₄	C₁₉×#121	1	8	yes	—
627	C₂²	—	2	8	no	—
628	C₂²	—	2	8	no	—
629	C₂²	—	2	8	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	4	no	—
642	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
643	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
644	C₂²	C₄×#41×C₁₉	1	2	yes	—
645	C₂²	C₁₉×#518	1	1	yes	characteristic
646	C₂²	C₁₉×#520	1	1	yes	characteristic
647	C₂²	C₂×C₁₉×#121	1	2	yes	—
648	C₂²	C₁₉×#525	1	2	yes	—
649	C₂²	C₁₉×#529	1	2	yes	—
650	C₂²	C₁₉×#532	1	2	yes	—
651	C₂²	C₁₉×#534	1	1	yes	characteristic
652	C₂²	C₁₉×#537	1	1	yes	characteristic
653	C₂²	C₁₉×#538	1	1	yes	characteristic
654	C₂²	C₁₉×#539	1	1	yes	characteristic
655	C₂²	D₄²×C₁₉	1	1	yes	characteristic
656	C₂²	C₁₉×#546	1	2	yes	—
657	C₂²	C₁₉×#546	1	2	yes	—
658	C₂²	C₁₉×#547	1	2	yes	—
659	C₂²	C₁₉×#551	1	2	yes	—
660	C₂²	C₁₉×#551	1	2	yes	—
661	C₂²	C₁₉×#551	1	1	yes	characteristic
662	C₂²	C₁₉×#552	1	2	yes	—
663	C₂²	C₁₉×#555	1	1	yes	characteristic
664	C₂²	C₁₉×#555	1	1	yes	characteristic
665	C₄	—	2	8	no	—
666	C₄	—	2	4	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	4	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	8	2	no	—
673	C₂	—	4	8	no	—
674	C₂	C₄×C₁₉×#121	1	2	yes	—
675	C₂	C₁₉×#2325	1	1	yes	characteristic
676	C₂	C₁₉×#2358	1	1	yes	characteristic
677	C₂	C₁₉×#2359	1	2	yes	—
678	C₂	C₁₉×#2372	1	1	yes	characteristic
679	C₂	C₁₉×#2534	1	2	yes	—
680	C₂	C₁₉×#2537	1	1	yes	characteristic
681	C₂	C₁₉×#2553	1	2	yes	—
682	C₂	C₁₉×#2555	1	1	yes	characteristic
683	C₂	C₁₉×#2572	1	1	yes	characteristic
684	C₂	C₁₉×#2609	1	1	yes	characteristic

	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. C₂×C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
5. C₁₉×#1441	C₂	semidirect
6. C₁₉×#1439	C₂	semidirect
7. C₁₉×C₄⋊#95	C₂	semidirect
8. C₁₉×#1434	C₂	semidirect
9. C₁₉×C₂²⋊#95	C₂	semidirect
22. C₁₉×#394	C₄	semidirect
63. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
76. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
77. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
84. C₂×C₄²×C₁₉	D₄	semidirect
93. C₁₉×#95	C₂×C₄	semidirect
184. #14224	C₁₉	direct (N × H)
286. C₂×#388	C₂×C₁₉	semidirect
288. C₂×C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
289. #1441	C₂×C₁₉	semidirect
290. #1439	C₂×C₁₉	semidirect
291. C₄⋊#95	C₂×C₁₉	semidirect
292. #1434	C₂×C₁₉	semidirect
293. C₂²⋊#95	C₂×C₁₉	semidirect
352. #394	C₄×C₁₉	semidirect
405. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
418. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
419. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
426. C₂×C₄²	D₄×C₁₉	semidirect
435. #95	C₂×C₄×C₁₉	semidirect
436. C₁₉	#14224	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
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1441	2
C₁₉×#1439	2
C₁₉×C₄⋊#95	2
C₁₉×#1434	2
C₁₉×C₂²⋊#95	2
#14224	19

Subgroups — C19×#14224 #18020183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14224 #18020183