Subgroups — C₁₉×#14575 #18020534

Order 4864.

1706 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#393	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#391	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#385	C₂	1	2	yes	maximal
4	C₁₉×#1444	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1442	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1437	C₂	1	2	yes	maximal
8	C₁₉×#1434	C₂	1	2	yes	maximal, complemented
9	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
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	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#393	C₄	1	8	yes	complemented
21	C₁₉×#391	—	2	8	no	—
22	C₁₉×#385	—	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	2	yes	—
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×Q₈×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	—	2	4	no	—
37	C₂²×Q₈×C₁₉	—	4	1	no	—
38	C₂²×Q₈×C₁₉	—	4	1	no	—
39	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	4	no	—
42	C₂³×C₄×C₁₉	—	4	1	no	—
43	C₂³×C₄×C₁₉	—	4	1	no	—
44	C₂³×C₄×C₁₉	—	4	2	no	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
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	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
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	—	4	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	complemented
73	C₂×C₄²×C₁₉	—	2	4	no	—
74	C₂×C₄²×C₁₉	—	2	4	no	—
75	C₂×C₄²×C₁₉	—	4	2	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	2	no	—
82	C₁₉×#95	—	4	2	no	—
83	C₁₉×#95	—	4	2	no	—
84	C₁₉×#95	C₂×C₄	1	4	yes	complemented
85	C₁₉×#95	C₂×C₄	1	8	yes	complemented
86	C₁₉×#95	D₄	1	8	yes	—
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
97	C₂⁴×C₁₉	#41	1	2	yes	—
98	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂×Q₈×C₁₉	—	2	16	no	—
100	C₂×Q₈×C₁₉	—	4	4	no	—
101	C₂×Q₈×C₁₉	—	4	4	no	—
102	C₂×Q₈×C₁₉	—	4	8	no	—
103	C₂×Q₈×C₁₉	—	4	4	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	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	4	4	no	—
148	C₂²×C₄×C₁₉	—	4	8	no	—
149	C₂²×C₄×C₁₉	—	4	8	no	—
150	C₂²×C₄×C₁₉	—	4	4	no	—
151	C₂²×C₄×C₁₉	—	4	4	no	—
152	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
160	C₂²×C₄×C₁₉	#41	1	4	yes	—
161	C₄⋊C₄×C₁₉	—	4	8	no	—
162	C₄⋊C₄×C₁₉	—	4	8	no	—
163	C₄⋊C₄×C₁₉	—	4	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	16	no	—
165	C₂²⋊C₄×C₁₉	—	4	4	no	—
166	C₂²⋊C₄×C₁₉	—	4	4	no	—
167	C₂²⋊C₄×C₁₉	—	4	8	no	—
168	C₄²×C₁₉	—	4	8	no	—
169	#14575	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	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	—	4	2	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	1	no	—
192	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
193	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
194	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
195	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
196	C₂³×C₁₉	C₂×#41	1	2	yes	—
197	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
198	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
202	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
204	Q₈×C₁₉	—	4	16	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	4	no	—
209	C₂×C₄×C₁₉	—	2	4	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	2	no	—
214	C₂×C₄×C₁₉	—	2	2	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	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	4	no	—
227	C₂×C₄×C₁₉	—	4	16	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	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	1	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	2	no	—
244	C₂×C₄×C₁₉	—	4	1	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	1	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	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
258	C₂×#393	C₂×C₁₉	1	1	yes	characteristic
259	C₂×#391	C₂×C₁₉	1	2	yes	complemented
260	C₂×#385	C₂×C₁₉	1	2	yes	—
261	#1444	C₂×C₁₉	1	2	yes	complemented
262	#1442	C₂×C₁₉	1	2	yes	complemented
263	#1439	C₂×C₁₉	1	1	yes	characteristic
264	#1437	C₂×C₁₉	1	2	yes	—
265	#1434	C₂×C₁₉	1	2	yes	complemented
266	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic
267	C₂²×C₁₉	—	2	4	no	—
268	C₂²×C₁₉	—	2	8	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	4	no	—
275	C₂²×C₁₉	—	4	4	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
279	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
280	C₂²×C₁₉	#518	1	1	yes	characteristic
281	C₂²×C₁₉	#520	1	1	yes	characteristic
282	C₂²×C₁₉	#520	1	2	yes	—
283	C₂²×C₁₉	#535	1	2	yes	—
284	C₂²×C₁₉	#536	1	2	yes	—
285	C₂²×C₁₉	#538	1	1	yes	characteristic
286	C₂²×C₁₉	#539	1	1	yes	characteristic
287	C₂²×C₁₉	#542	1	2	yes	—
288	C₂²×C₁₉	#542	1	2	yes	—
289	C₂²×C₁₉	#543	1	1	yes	characteristic
290	C₂²×C₁₉	#544	1	1	yes	characteristic
291	C₂²×C₁₉	D₄²	1	1	yes	characteristic
292	C₂²×C₁₉	#546	1	2	yes	—
293	C₂²×C₁₉	#546	1	2	yes	—
294	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
295	C₂²×C₁₉	#551	1	1	yes	characteristic
296	C₂²×C₁₉	#552	1	2	yes	—
297	C₂²×C₁₉	#554	1	2	yes	—
298	C₂²×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
299	C₂²×C₁₉	#562	1	2	yes	—
300	C₂²×C₁₉	#563	1	1	yes	characteristic
301	C₄×C₁₉	—	2	8	no	—
302	C₄×C₁₉	—	4	4	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	—	4	4	no	—
306	C₄×C₁₉	—	4	4	no	—
307	C₄×C₁₉	—	4	4	no	—
308	C₄×C₁₉	—	8	2	no	—
309	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
310	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
312	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
313	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
316	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
318	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
319	#393	C₄×C₁₉	1	8	yes	complemented
320	#391	—	2	8	no	—
321	#385	—	2	8	no	—
322	C₂×#95	C₂²×C₁₉	1	2	yes	—
323	C₂×#95	C₂²×C₁₉	1	2	yes	—
324	C₂×#95	C₂²×C₁₉	1	2	yes	—
325	C₂×#95	C₂²×C₁₉	1	2	yes	—
326	C₂×#95	C₂²×C₁₉	1	2	yes	—
327	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#95	C₂²×C₁₉	1	2	yes	—
329	C₂×#95	C₂²×C₁₉	1	2	yes	—
330	C₂×#95	C₂²×C₁₉	1	2	yes	—
331	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#95	C₂²×C₁₉	1	2	yes	—
333	C₂×C₁₉	—	4	4	no	—
334	C₂×C₁₉	#2326	1	2	yes	—
335	C₂×C₁₉	#2329	1	1	yes	characteristic
336	C₂×C₁₉	#2358	1	1	yes	characteristic
337	C₂×C₁₉	#2360	1	2	yes	—
338	C₂×C₁₉	#2379	1	1	yes	characteristic
339	C₂×C₁₉	#2670	1	1	yes	characteristic
340	C₂×C₁₉	#2677	1	1	yes	characteristic
341	C₂×C₁₉	#2687	1	2	yes	—
342	C₂×C₁₉	#2692	1	2	yes	—
343	C₂×C₁₉	#2763	1	1	yes	characteristic
344	C₂×C₁₉	#2764	1	1	yes	characteristic
345	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
346	C₂²×Q₈	—	2	4	no	—
347	C₂²×Q₈	—	2	4	no	—
348	C₂²×Q₈	—	4	1	no	—
349	C₂²×Q₈	—	4	1	no	—
350	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
351	C₂³×C₄	—	2	2	no	—
352	C₂³×C₄	—	2	4	no	—
353	C₂³×C₄	—	4	2	no	—
354	C₂³×C₄	—	4	1	no	—
355	C₂³×C₄	—	4	1	no	—
356	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
361	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
364	C₂×C₄⋊C₄	—	2	4	no	—
365	C₂×C₄⋊C₄	—	2	4	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	—	4	2	no	—
368	C₂×C₄⋊C₄	—	4	2	no	—
369	C₂×C₄⋊C₄	—	4	2	no	—
370	C₂×C₄⋊C₄	—	4	2	no	—
371	C₂×C₄⋊C₄	—	4	1	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	—	2	4	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	—	4	1	no	—
377	C₂×C₂²⋊C₄	—	4	1	no	—
378	C₂×C₂²⋊C₄	—	4	1	no	—
379	C₂×C₂²⋊C₄	—	4	1	no	—
380	C₂×C₂²⋊C₄	—	4	2	no	—
381	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
382	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
383	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	complemented
384	C₂×C₄²	—	2	4	no	—
385	C₂×C₄²	—	2	4	no	—
386	C₂×C₄²	—	4	2	no	—
387	#95	—	2	4	no	—
388	#95	—	2	4	no	—
389	#95	—	2	4	no	—
390	#95	—	2	4	no	—
391	#95	—	4	2	no	—
392	#95	—	4	2	no	—
393	#95	—	4	1	no	—
394	#95	—	4	2	no	—
395	#95	C₂×C₄×C₁₉	1	4	yes	complemented
396	#95	C₂×C₄×C₁₉	1	8	yes	complemented
397	#95	D₄×C₁₉	1	8	yes	—
398	C₁₉	#14575	1	1	yes	characteristic, direct product factor, Sylow
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	1	no	—
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	2	1	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
408	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
409	C₂⁴	#41×C₁₉	1	2	yes	—
410	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
411	C₂×Q₈	—	2	16	no	—
412	C₂×Q₈	—	4	4	no	—
413	C₂×Q₈	—	4	4	no	—
414	C₂×Q₈	—	4	8	no	—
415	C₂×Q₈	—	4	4	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	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	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	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	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	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	—	4	4	no	—
460	C₂²×C₄	—	4	8	no	—
461	C₂²×C₄	—	4	8	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
465	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
466	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
467	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
468	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
469	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
471	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
472	C₂²×C₄	#41×C₁₉	1	4	yes	—
473	C₄⋊C₄	—	4	8	no	—
474	C₄⋊C₄	—	4	8	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	2	16	no	—
477	C₂²⋊C₄	—	4	4	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	8	no	—
480	C₄²	—	4	8	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
504	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
505	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
506	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
507	C₂³	C₂×#41×C₁₉	1	2	yes	—
508	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
509	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
513	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
514	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
515	Q₈	—	4	16	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	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	4	16	no	—
539	C₂×C₄	—	4	2	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	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
581	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
582	C₂²	C₁₉×#518	1	1	yes	characteristic
583	C₂²	C₁₉×#520	1	1	yes	characteristic
584	C₂²	C₁₉×#520	1	2	yes	—
585	C₂²	C₁₉×#535	1	2	yes	—
586	C₂²	C₁₉×#536	1	2	yes	—
587	C₂²	C₁₉×#538	1	1	yes	characteristic
588	C₂²	C₁₉×#539	1	1	yes	characteristic
589	C₂²	C₁₉×#542	1	2	yes	—
590	C₂²	C₁₉×#542	1	2	yes	—
591	C₂²	C₁₉×#543	1	1	yes	characteristic
592	C₂²	C₁₉×#544	1	1	yes	characteristic
593	C₂²	D₄²×C₁₉	1	1	yes	characteristic
594	C₂²	C₁₉×#546	1	2	yes	—
595	C₂²	C₁₉×#546	1	2	yes	—
596	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
597	C₂²	C₁₉×#551	1	1	yes	characteristic
598	C₂²	C₁₉×#552	1	2	yes	—
599	C₂²	C₁₉×#554	1	2	yes	—
600	C₂²	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
601	C₂²	C₁₉×#562	1	2	yes	—
602	C₂²	C₁₉×#563	1	1	yes	characteristic
603	C₄	—	2	8	no	—
604	C₄	—	4	4	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	4	no	—
607	C₄	—	4	4	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	8	2	no	—
611	C₂	—	4	4	no	—
612	C₂	C₁₉×#2326	1	2	yes	—
613	C₂	C₁₉×#2329	1	1	yes	characteristic
614	C₂	C₁₉×#2358	1	1	yes	characteristic
615	C₂	C₁₉×#2360	1	2	yes	—
616	C₂	C₁₉×#2379	1	1	yes	characteristic
617	C₂	C₁₉×#2670	1	1	yes	characteristic
618	C₂	C₁₉×#2677	1	1	yes	characteristic
619	C₂	C₁₉×#2687	1	2	yes	—
620	C₂	C₁₉×#2692	1	2	yes	—
621	C₂	C₁₉×#2763	1	1	yes	characteristic
622	C₂	C₁₉×#2764	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
2. C₂×C₁₉×#391	C₂	semidirect
4. C₁₉×#1444	C₂	semidirect
5. C₁₉×#1442	C₂	semidirect
8. C₁₉×#1434	C₂	semidirect
20. C₁₉×#393	C₄	semidirect
39. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
72. C₂×C₂²⋊C₄×C₁₉	Q₈	semidirect
84. C₁₉×#95	C₂×C₄	semidirect
85. C₁₉×#95	C₂×C₄	semidirect
169. #14575	C₁₉	direct (N × H)
259. C₂×#391	C₂×C₁₉	semidirect
261. #1444	C₂×C₁₉	semidirect
262. #1442	C₂×C₁₉	semidirect
265. #1434	C₂×C₁₉	semidirect
319. #393	C₄×C₁₉	semidirect
350. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
383. C₂×C₂²⋊C₄	Q₈×C₁₉	semidirect
395. #95	C₂×C₄×C₁₉	semidirect
396. #95	C₂×C₄×C₁₉	semidirect
398. C₁₉	#14575	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×#393	2
C₂×C₁₉×#391	2
C₂×C₁₉×#385	2
C₁₉×#1444	2
C₁₉×#1442	2
C₁₉×#1439	2
C₁₉×#1437	2
C₁₉×#1434	2
C₁₉×C₂²⋊#95	2
#14575	19

Subgroups — C19×#14575 #18020534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14575 #18020534