Subgroups — C₁₉×#14143 #18020102

Order 4864.

1702 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#387	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal
4	C₁₉×#1440	C₂	1	2	yes	maximal
5	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1436	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1436	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1434	C₂	1	2	yes	maximal, complemented
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
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	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#387	—	2	8	no	—
21	C₁₉×#385	C₄	1	8	yes	complemented
22	C₄×C₂²⋊C₄×C₁₉	—	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	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	—	2	4	no	—
37	C₂³×C₄×C₁₉	—	4	1	no	—
38	C₂³×C₄×C₁₉	—	4	1	no	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₉	—	2	4	no	—
68	C₂×C₄²×C₁₉	—	2	4	no	—
69	C₂×C₄²×C₁₉	—	2	4	no	—
70	C₂×C₄²×C₁₉	—	2	4	no	—
71	C₂×C₄²×C₁₉	—	4	2	no	—
72	C₂×C₄²×C₁₉	—	4	2	no	—
73	C₁₉×#95	—	2	4	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₁₉×#95	—	2	4	no	—
76	C₁₉×#95	—	2	4	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₁₉×#95	—	2	4	no	—
79	C₁₉×#95	—	2	4	no	—
80	C₁₉×#95	—	4	1	no	—
81	C₁₉×#95	—	4	1	no	—
82	C₁₉×#95	C₂×C₄	1	8	yes	—
83	C₁₉×#95	D₄	1	8	yes	—
84	C₂⁴×C₁₉	—	2	2	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	—	2	1	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
93	C₂⁴×C₁₉	#41	1	2	yes	—
94	C₂⁴×C₁₉	#41	1	2	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	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	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	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	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	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	16	no	—
139	C₂²×C₄×C₁₉	—	4	4	no	—
140	C₂²×C₄×C₁₉	—	4	4	no	—
141	C₂²×C₄×C₁₉	—	4	8	no	—
142	C₂²×C₄×C₁₉	—	4	4	no	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₉	#41	1	4	yes	—
151	C₂²×C₄×C₁₉	#41	1	4	yes	—
152	C₂²×C₄×C₁₉	#41	1	4	yes	—
153	C₄⋊C₄×C₁₉	—	2	16	no	—
154	C₄⋊C₄×C₁₉	—	4	4	no	—
155	C₄⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	—	2	16	no	—
157	C₂²⋊C₄×C₁₉	—	2	16	no	—
158	C₂²⋊C₄×C₁₉	—	2	8	no	—
159	C₂²⋊C₄×C₁₉	—	4	4	no	—
160	C₄²×C₁₉	—	4	8	no	—
161	C₄²×C₁₉	—	4	8	no	—
162	#14143	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	4	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	4	no	—
168	C₂³×C₁₉	—	2	4	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	4	1	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	#117	1	4	yes	—
186	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
187	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
188	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₂³×C₁₉	C₂×#41	1	2	yes	—
191	C₂³×C₁₉	C₂×#41	1	2	yes	—
192	C₂³×C₁₉	C₂×#41	1	2	yes	—
193	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	4	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	4	16	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	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	1	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
250	C₂×#387	C₂×C₁₉	1	2	yes	complemented
251	C₂×#385	C₂×C₁₉	1	1	yes	characteristic
252	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	2	yes	—
253	#1440	C₂×C₁₉	1	2	yes	—
254	#1439	C₂×C₁₉	1	1	yes	characteristic
255	#1439	C₂×C₁₉	1	1	yes	characteristic
256	#1436	C₂×C₁₉	1	2	yes	complemented
257	#1436	C₂×C₁₉	1	2	yes	complemented
258	#1434	C₂×C₁₉	1	2	yes	complemented
259	C₂²×C₁₉	—	2	4	no	—
260	C₂²×C₁₉	—	2	8	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	4	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
271	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
272	C₂²×C₁₉	C₄×#41	1	2	yes	—
273	C₂²×C₁₉	#518	1	1	yes	characteristic
274	C₂²×C₁₉	#519	1	1	yes	characteristic
275	C₂²×C₁₉	#525	1	2	yes	—
276	C₂²×C₁₉	#525	1	2	yes	—
277	C₂²×C₁₉	#529	1	2	yes	—
278	C₂²×C₁₉	#529	1	2	yes	—
279	C₂²×C₁₉	#539	1	1	yes	characteristic
280	C₂²×C₁₉	#539	1	1	yes	characteristic
281	C₂²×C₁₉	#539	1	1	yes	characteristic
282	C₂²×C₁₉	#539	1	1	yes	characteristic
283	C₂²×C₁₉	D₄²	1	1	yes	characteristic
284	C₂²×C₁₉	#546	1	2	yes	—
285	C₂²×C₁₉	#547	1	2	yes	—
286	C₂²×C₁₉	#548	1	2	yes	—
287	C₂²×C₁₉	#551	1	1	yes	characteristic
288	C₂²×C₁₉	#551	1	1	yes	characteristic
289	C₂²×C₁₉	#552	1	2	yes	—
290	C₂²×C₁₉	#553	1	2	yes	—
291	C₂²×C₁₉	#556	1	2	yes	—
292	C₂²×C₁₉	#559	1	1	yes	characteristic
293	C₄×C₁₉	—	2	8	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	—	4	4	no	—
297	C₄×C₁₉	—	4	4	no	—
298	C₄×C₁₉	—	4	4	no	—
299	C₄×C₁₉	—	4	4	no	—
300	C₄×C₁₉	—	4	4	no	—
301	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
305	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
306	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
309	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
310	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
311	#387	—	2	8	no	—
312	#385	C₄×C₁₉	1	8	yes	complemented
313	C₄×C₂²⋊C₄	—	2	8	no	—
314	C₂×#95	C₂²×C₁₉	1	2	yes	—
315	C₂×#95	C₂²×C₁₉	1	2	yes	—
316	C₂×#95	C₂²×C₁₉	1	2	yes	—
317	C₂×#95	C₂²×C₁₉	1	2	yes	—
318	C₂×#95	C₂²×C₁₉	1	2	yes	—
319	C₂×#95	C₂²×C₁₉	1	2	yes	—
320	C₂×#95	C₂²×C₁₉	1	2	yes	—
321	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#95	C₂²×C₁₉	1	2	yes	—
324	C₂×#95	C₂²×C₁₉	1	2	yes	—
325	C₂×C₁₉	—	4	4	no	—
326	C₂×C₁₉	#2290	1	2	yes	—
327	C₂×C₁₉	#2313	1	1	yes	characteristic
328	C₂×C₁₉	#2358	1	1	yes	characteristic
329	C₂×C₁₉	#2362	1	2	yes	—
330	C₂×C₁₉	#2374	1	1	yes	characteristic
331	C₂×C₁₉	#2455	1	1	yes	characteristic
332	C₂×C₁₉	#2460	1	2	yes	—
333	C₂×C₁₉	#2463	1	1	yes	characteristic
334	C₂×C₁₉	#2466	1	2	yes	—
335	C₂×C₁₉	#2517	1	1	yes	characteristic
336	C₂×C₁₉	#2523	1	1	yes	characteristic
337	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
338	C₂³×C₄	—	2	4	no	—
339	C₂³×C₄	—	2	4	no	—
340	C₂³×C₄	—	4	1	no	—
341	C₂³×C₄	—	4	1	no	—
342	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
343	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
349	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	4	1	no	—
356	C₂×C₄⋊C₄	—	4	1	no	—
357	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₂²⋊C₄	—	2	4	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	—	2	4	no	—
364	C₂×C₂²⋊C₄	—	2	4	no	—
365	C₂×C₂²⋊C₄	—	2	4	no	—
366	C₂×C₂²⋊C₄	—	4	1	no	—
367	C₂×C₂²⋊C₄	—	4	1	no	—
368	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
370	C₂×C₄²	—	2	4	no	—
371	C₂×C₄²	—	2	4	no	—
372	C₂×C₄²	—	2	4	no	—
373	C₂×C₄²	—	2	4	no	—
374	C₂×C₄²	—	4	2	no	—
375	C₂×C₄²	—	4	2	no	—
376	#95	—	2	4	no	—
377	#95	—	2	4	no	—
378	#95	—	2	4	no	—
379	#95	—	2	4	no	—
380	#95	—	2	4	no	—
381	#95	—	2	4	no	—
382	#95	—	2	4	no	—
383	#95	—	4	1	no	—
384	#95	—	4	1	no	—
385	#95	C₂×C₄×C₁₉	1	8	yes	—
386	#95	D₄×C₁₉	1	8	yes	—
387	C₁₉	#14143	1	1	yes	characteristic, direct product factor, Sylow
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	1	no	—
393	C₂⁴	—	2	1	no	—
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	2	1	no	—
396	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
397	C₂⁴	#41×C₁₉	1	2	yes	—
398	C₂⁴	#41×C₁₉	1	2	yes	—
399	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	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	16	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	8	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
449	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
450	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
452	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
454	C₂²×C₄	#41×C₁₉	1	4	yes	—
455	C₂²×C₄	#41×C₁₉	1	4	yes	—
456	C₂²×C₄	#41×C₁₉	1	4	yes	—
457	C₄⋊C₄	—	2	16	no	—
458	C₄⋊C₄	—	4	4	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	—	2	16	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₄²	—	4	8	no	—
465	C₄²	—	4	8	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	1	no	—
488	C₂³	C₁₉×#117	1	4	yes	—
489	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
490	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
491	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
492	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
493	C₂³	C₂×#41×C₁₉	1	2	yes	—
494	C₂³	C₂×#41×C₁₉	1	2	yes	—
495	C₂³	C₂×#41×C₁₉	1	2	yes	—
496	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
498	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
499	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	4	16	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
553	C₂²	—	2	8	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	2	no	—
564	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
565	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
566	C₂²	C₄×#41×C₁₉	1	2	yes	—
567	C₂²	C₁₉×#518	1	1	yes	characteristic
568	C₂²	C₁₉×#519	1	1	yes	characteristic
569	C₂²	C₁₉×#525	1	2	yes	—
570	C₂²	C₁₉×#525	1	2	yes	—
571	C₂²	C₁₉×#529	1	2	yes	—
572	C₂²	C₁₉×#529	1	2	yes	—
573	C₂²	C₁₉×#539	1	1	yes	characteristic
574	C₂²	C₁₉×#539	1	1	yes	characteristic
575	C₂²	C₁₉×#539	1	1	yes	characteristic
576	C₂²	C₁₉×#539	1	1	yes	characteristic
577	C₂²	D₄²×C₁₉	1	1	yes	characteristic
578	C₂²	C₁₉×#546	1	2	yes	—
579	C₂²	C₁₉×#547	1	2	yes	—
580	C₂²	C₁₉×#548	1	2	yes	—
581	C₂²	C₁₉×#551	1	1	yes	characteristic
582	C₂²	C₁₉×#551	1	1	yes	characteristic
583	C₂²	C₁₉×#552	1	2	yes	—
584	C₂²	C₁₉×#553	1	2	yes	—
585	C₂²	C₁₉×#556	1	2	yes	—
586	C₂²	C₁₉×#559	1	1	yes	characteristic
587	C₄	—	2	8	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	4	no	—
590	C₄	—	4	4	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₂	—	4	4	no	—
596	C₂	C₁₉×#2290	1	2	yes	—
597	C₂	C₁₉×#2313	1	1	yes	characteristic
598	C₂	C₁₉×#2358	1	1	yes	characteristic
599	C₂	C₁₉×#2362	1	2	yes	—
600	C₂	C₁₉×#2374	1	1	yes	characteristic
601	C₂	C₁₉×#2455	1	1	yes	characteristic
602	C₂	C₁₉×#2460	1	2	yes	—
603	C₂	C₁₉×#2463	1	1	yes	characteristic
604	C₂	C₁₉×#2466	1	2	yes	—
605	C₂	C₁₉×#2517	1	1	yes	characteristic
606	C₂	C₁₉×#2523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
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. C₂×C₁₉×#387	C₂	semidirect
7. C₁₉×#1436	C₂	semidirect
8. C₁₉×#1436	C₂	semidirect
9. C₁₉×#1434	C₂	semidirect
21. C₁₉×#385	C₄	semidirect
162. #14143	C₁₉	direct (N × H)
250. C₂×#387	C₂×C₁₉	semidirect
256. #1436	C₂×C₁₉	semidirect
257. #1436	C₂×C₁₉	semidirect
258. #1434	C₂×C₁₉	semidirect
312. #385	C₄×C₁₉	semidirect
387. C₁₉	#14143	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×#387	2
C₂×C₁₉×#385	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1440	2
C₁₉×#1439	2
C₁₉×#1436	2
C₁₉×#1434	2
#14143	19

Subgroups — C19×#14143 #18020102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14143 #18020102