Subgroups — C₁₉×#21288 #18027247

Order 4864.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#440	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2293	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1973	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1968	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1762	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	—	2	1	no	—
20	C₁₉×#440	C₄	1	8	yes	complemented
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#391	C₂²	1	1	yes	characteristic
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	1	yes	characteristic
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₁₉×#389	C₂²	1	1	yes	characteristic
44	C₁₉×#388	—	2	1	no	—
45	C₁₉×#388	—	2	1	no	—
46	C₁₉×#387	—	2	1	no	—
47	C₁₉×#387	—	2	1	no	—
48	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₁₉×#376	—	2	1	no	—
53	C₄³×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	—
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
74	C₁₉×#117	—	4	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	2	no	—
102	C₁₉×#107	C₂×C₄	1	4	yes	—
103	C₁₉×#106	—	2	2	no	—
104	C₁₉×#103	—	2	2	no	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#103	C₂×C₄	1	4	yes	—
107	C₁₉×#102	—	2	2	no	—
108	C₁₉×#102	—	2	2	no	—
109	C₁₉×#102	C₂×C₄	1	4	yes	—
110	C₁₉×#97	—	2	2	no	—
111	C₁₉×#97	—	2	2	no	—
112	C₁₉×#97	—	2	2	no	—
113	C₁₉×#97	C₂×C₄	1	4	yes	—
114	C₄×C₈×C₁₉	—	2	2	no	—
115	C₄×C₈×C₁₉	—	2	2	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	1	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	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₁₉	—	2	8	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₁₉	#41	1	2	yes	—
166	C₂×C₈×C₁₉	#41	1	2	yes	—
167	C₂×C₈×C₁₉	#41	1	2	yes	—
168	C₂×C₈×C₁₉	#41	1	2	yes	—
169	C₄⋊C₄×C₁₉	—	2	4	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	4	2	no	—
181	C₄⋊C₄×C₁₉	—	4	2	no	—
182	C₄⋊C₄×C₁₉	—	4	2	no	—
183	C₄⋊C₄×C₁₉	—	4	2	no	—
184	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
185	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	—	4	2	no	—
188	C₂²⋊C₄×C₁₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₉	—	4	2	no	—
190	C₂²⋊C₄×C₁₉	—	4	2	no	—
191	C₄²×C₁₉	—	2	4	no	—
192	C₄²×C₁₉	—	2	2	no	—
193	C₄²×C₁₉	—	2	2	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	4	1	no	—
200	C₄²×C₁₉	—	4	2	no	—
201	C₄²×C₁₉	—	4	2	no	—
202	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
203	C₄²×C₁₉	#41	1	2	yes	—
204	#21288	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	—	4	1	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₉	—	2	2	no	—
214	Q₈×C₁₉	—	2	2	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	D₄×C₁₉	—	2	2	no	—
218	D₄×C₁₉	—	2	2	no	—
219	D₄×C₁₉	—	4	1	no	—
220	D₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	4	8	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
260	C₂×C₄×C₁₉	#137	1	2	yes	—
261	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
267	C₈×C₁₉	—	2	2	no	—
268	C₈×C₁₉	—	2	2	no	—
269	C₈×C₁₉	—	2	2	no	—
270	C₈×C₁₉	#117	1	4	yes	complemented
271	C₂×#440	C₂×C₁₉	1	1	yes	characteristic
272	#2295	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#2293	C₂×C₁₉	1	1	yes	characteristic
274	#1973	C₂×C₁₉	1	1	yes	characteristic
275	#1968	C₂×C₁₉	1	1	yes	characteristic
276	#1943	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1942	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1936	C₂×C₁₉	1	1	yes	characteristic
279	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1934	C₂×C₁₉	1	1	yes	characteristic
281	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1776	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1763	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1762	C₂×C₁₉	1	1	yes	characteristic
285	C₄×#97	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	8	1	no	—
290	C₂²×C₁₉	—	8	1	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
294	C₂²×C₁₉	#532	1	1	yes	characteristic
295	C₂²×C₁₉	#532	1	1	yes	characteristic
296	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
298	C₂²×C₁₉	#575	1	1	yes	characteristic
299	C₂²×C₁₉	#575	1	1	yes	characteristic
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	2	2	no	—
302	C₄×C₁₉	—	2	2	no	—
303	C₄×C₁₉	—	2	2	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	2	no	—
307	C₄×C₁₉	—	4	2	no	—
308	C₄×C₁₉	—	4	2	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	—	8	1	no	—
312	C₄×C₁₉	—	8	1	no	—
313	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
314	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
315	C₄×C₁₉	#529	1	1	yes	characteristic
316	C₄×C₁₉	#529	1	1	yes	characteristic
317	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#117	—	2	1	no	—
321	#440	C₄×C₁₉	1	8	yes	complemented
322	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
337	#391	C₂²×C₁₉	1	1	yes	characteristic
338	#391	C₂²×C₁₉	1	1	yes	characteristic
339	#390	C₂²×C₁₉	1	1	yes	characteristic
340	#390	C₂²×C₁₉	1	1	yes	characteristic
341	#389	C₂²×C₁₉	1	1	yes	characteristic
342	#389	C₂²×C₁₉	1	1	yes	characteristic
343	#389	C₂²×C₁₉	1	1	yes	characteristic
344	#389	C₂²×C₁₉	1	1	yes	characteristic
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#387	—	2	1	no	—
348	#387	—	2	1	no	—
349	C₄×C₄⋊C₄	—	2	1	no	—
350	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	—	2	1	no	—
353	#376	—	2	1	no	—
354	C₄³	C₂²×C₁₉	1	1	yes	characteristic
355	#340	C₂²×C₁₉	1	1	yes	characteristic
356	#340	C₂²×C₁₉	1	1	yes	characteristic
357	#340	C₂²×C₁₉	1	1	yes	characteristic
358	#340	C₂²×C₁₉	1	1	yes	characteristic
359	#340	C₂²×C₁₉	1	1	yes	characteristic
360	#340	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×C₁₉	—	8	2	no	—
362	C₂×C₁₉	#2293	1	1	yes	characteristic
363	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
365	C₂×C₁₉	#3180	1	1	yes	characteristic
366	C₂×C₁₉	#3181	1	1	yes	characteristic
367	C₂×C₁₉	#3182	1	1	yes	characteristic
368	C₂×C₁₉	#3183	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂×SD₁₆	—	2	2	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	—
375	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
383	#117	—	4	4	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
405	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
406	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
410	#107	—	2	2	no	—
411	#107	C₂×C₄×C₁₉	1	4	yes	—
412	#106	—	2	2	no	—
413	#103	—	2	2	no	—
414	#103	—	2	2	no	—
415	#103	C₂×C₄×C₁₉	1	4	yes	—
416	#102	—	2	2	no	—
417	#102	—	2	2	no	—
418	#102	C₂×C₄×C₁₉	1	4	yes	—
419	#97	—	2	2	no	—
420	#97	—	2	2	no	—
421	#97	—	2	2	no	—
422	#97	C₂×C₄×C₁₉	1	4	yes	—
423	C₄×C₈	—	2	2	no	—
424	C₄×C₈	—	2	2	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	C₁₉	#21288	1	1	yes	characteristic, direct product factor, Sylow
436	C₂⁴	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
466	SD₁₆	—	2	8	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
474	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
475	C₂×C₈	#41×C₁₉	1	2	yes	—
476	C₂×C₈	#41×C₁₉	1	2	yes	—
477	C₂×C₈	#41×C₁₉	1	2	yes	—
478	C₂×C₈	#41×C₁₉	1	2	yes	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
495	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	—	4	1	no	—
510	C₄²	—	4	2	no	—
511	C₄²	—	4	2	no	—
512	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
513	C₄²	#41×C₁₉	1	2	yes	—
514	C₂³	—	2	2	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
567	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
568	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
569	C₂×C₄	C₁₉×#137	1	2	yes	—
570	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
575	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
576	C₈	—	2	2	no	—
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	C₁₉×#117	1	4	yes	complemented
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	1	no	—
587	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
588	C₂²	C₁₉×#532	1	1	yes	characteristic
589	C₂²	C₁₉×#532	1	1	yes	characteristic
590	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
591	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
592	C₂²	C₁₉×#575	1	1	yes	characteristic
593	C₂²	C₁₉×#575	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	1	no	—
606	C₄	—	8	1	no	—
607	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
608	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
609	C₄	C₁₉×#529	1	1	yes	characteristic
610	C₄	C₁₉×#529	1	1	yes	characteristic
611	C₂	—	8	2	no	—
612	C₂	C₁₉×#2293	1	1	yes	characteristic
613	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
614	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
615	C₂	C₁₉×#3180	1	1	yes	characteristic
616	C₂	C₁₉×#3181	1	1	yes	characteristic
617	C₂	C₁₉×#3182	1	1	yes	characteristic
618	C₂	C₁₉×#3183	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#2295	C₂	semidirect
6. C₁₉×#1943	C₂	semidirect
7. C₁₉×#1942	C₂	semidirect
9. C₁₉×#1935	C₂	semidirect
11. C₁₉×#1933	C₂	semidirect
12. C₁₉×#1776	C₂	semidirect
13. C₁₉×#1763	C₂	semidirect
15. C₄×C₁₉×#97	C₂	semidirect
20. C₁₉×#440	C₄	semidirect
204. #21288	C₁₉	direct (N × H)
270. C₈×C₁₉	#117	semidirect
272. #2295	C₂×C₁₉	semidirect
276. #1943	C₂×C₁₉	semidirect
277. #1942	C₂×C₁₉	semidirect
279. #1935	C₂×C₁₉	semidirect
281. #1933	C₂×C₁₉	semidirect
282. #1776	C₂×C₁₉	semidirect
283. #1763	C₂×C₁₉	semidirect
285. C₄×#97	C₂×C₁₉	semidirect
321. #440	C₄×C₁₉	semidirect
435. C₁₉	#21288	direct (N × H)
579. C₈	C₁₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#440	2
C₁₉×#2295	2
C₁₉×#2293	2
C₁₉×#1973	2
C₁₉×#1968	2
C₁₉×#1943	2
C₁₉×#1942	2
C₁₉×#1936	2
C₁₉×#1935	2
C₁₉×#1934	2
C₁₉×#1933	2
C₁₉×#1776	2
C₁₉×#1763	2
C₁₉×#1762	2
C₄×C₁₉×#97	2
#21288	19

Subgroups — C19×#21288 #18027247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21288 #18027247