Subgroups — C₁₉×#22944 #18028903

Order 4864.

902 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2361	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2347	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₉	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#482	C₄	1	8	yes	complemented
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#106	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×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#390	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#389	C₂²	1	1	yes	characteristic
38	C₁₉×#388	—	2	1	no	—
39	C₁₉×#388	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#385	—	2	1	no	—
43	C₁₉×#383	—	2	1	no	—
44	C₁₉×#380	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	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×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₁₉	—	2	2	no	—
66	C₂×M₁₆×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	—	4	1	no	—
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	C₂×C₄	1	4	yes	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	4	1	no	—
76	C₄×D₄×C₁₉	—	4	4	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	C₂×C₄	1	4	yes	complemented
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#107	C₂×C₄	1	4	yes	complemented
107	C₁₉×#106	—	2	2	no	—
108	C₁₉×#106	—	4	1	no	—
109	C₁₉×#106	C₂×C₄	1	4	yes	complemented
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	4	1	no	—
112	C₁₉×#102	C₂×C₄	1	4	yes	complemented
113	C₁₉×#102	C₂×C₄	1	4	yes	complemented
114	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
115	C₁₉×#97	—	4	1	no	—
116	C₄×C₈×C₁₉	—	2	2	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	D₄	1	1	yes	characteristic
125	C₁₉×#95	D₄	1	1	yes	characteristic
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	4	2	no	—
136	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
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	1	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	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	—	4	2	no	—
150	C₂²×C₄×C₁₉	—	4	2	no	—
151	C₂²×C₄×C₁₉	—	4	2	no	—
152	C₂²×C₄×C₁₉	—	8	1	no	—
153	C₂²×C₄×C₁₉	—	8	1	no	—
154	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	#41	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₁₉	—	4	4	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₁₉	#41	1	2	yes	—
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	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	4	2	no	—
186	C₄⋊C₄×C₁₉	—	4	2	no	—
187	C₄⋊C₄×C₁₉	—	4	2	no	—
188	C₄⋊C₄×C₁₉	—	4	2	no	—
189	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
190	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
192	C₄⋊C₄×C₁₉	#41	1	2	yes	—
193	C₂²⋊C₄×C₁₉	—	2	4	no	—
194	C₂²⋊C₄×C₁₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	2	no	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₂²⋊C₄×C₁₉	—	8	1	no	—
200	C₂²⋊C₄×C₁₉	—	8	1	no	—
201	C₄²×C₁₉	—	2	4	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	4	2	no	—
207	C₄²×C₁₉	—	8	1	no	—
208	C₄²×C₁₉	—	8	1	no	—
209	#22944	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	2	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	—	4	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	C₄×D₄	1	2	yes	—
224	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	D₄×C₁₉	—	2	2	no	—
226	D₄×C₁₉	—	2	2	no	—
227	D₄×C₁₉	—	4	8	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	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	2	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	8	4	no	—
269	C₂×C₄×C₁₉	—	8	4	no	—
270	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
271	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
272	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
278	C₈×C₁₉	—	2	2	no	—
279	C₈×C₁₉	—	2	2	no	—
280	C₈×C₁₉	—	2	2	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₂×#482	C₂×C₁₉	1	1	yes	characteristic
283	#2361	C₂×C₁₉	1	1	yes	characteristic
284	#2347	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1943	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1934	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1920	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1895	C₂×C₁₉	1	1	yes	characteristic
291	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₄×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1762	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1753	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
312	C₂²×C₁₉	#546	1	1	yes	characteristic
313	C₂²×C₁₉	#547	1	1	yes	characteristic
314	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₂²×C₁₉	#575	1	1	yes	characteristic
316	C₂²×C₁₉	#577	1	1	yes	characteristic
317	C₂²×C₁₉	#577	1	1	yes	characteristic
318	C₄×C₁₉	—	2	2	no	—
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	4	2	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	4	2	no	—
324	C₄×C₁₉	—	4	1	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	8	1	no	—
328	C₄×C₁₉	—	8	1	no	—
329	C₄×C₁₉	—	8	1	no	—
330	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
331	C₄×C₁₉	#520	1	1	yes	characteristic
332	C₄×C₁₉	#551	1	1	yes	characteristic
333	C₄×C₁₉	#552	1	1	yes	characteristic
334	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₄×D₄	—	2	1	no	—
337	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
340	#482	C₄×C₁₉	1	8	yes	complemented
341	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
352	#390	C₂²×C₁₉	1	1	yes	characteristic
353	#389	C₂²×C₁₉	1	1	yes	characteristic
354	#389	C₂²×C₁₉	1	1	yes	characteristic
355	#389	C₂²×C₁₉	1	1	yes	characteristic
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#388	—	2	1	no	—
359	#386	—	2	1	no	—
360	#385	—	2	1	no	—
361	#383	—	2	1	no	—
362	#380	C₂²×C₁₉	1	1	yes	characteristic
363	C₄×C₄⋊C₄	—	2	1	no	—
364	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
365	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
366	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
367	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
368	#340	C₂²×C₁₉	1	1	yes	characteristic
369	#340	C₂²×C₁₉	1	1	yes	characteristic
370	#340	C₂²×C₁₉	1	1	yes	characteristic
371	#340	C₂²×C₁₉	1	1	yes	characteristic
372	#340	C₂²×C₁₉	1	1	yes	characteristic
373	#340	C₂²×C₁₉	1	1	yes	characteristic
374	#340	C₂²×C₁₉	1	1	yes	characteristic
375	#340	C₂²×C₁₉	1	1	yes	characteristic
376	#336	C₂²×C₁₉	1	1	yes	characteristic
377	#336	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×C₁₉	—	4	2	no	—
379	C₂×C₁₉	—	8	2	no	—
380	C₂×C₁₉	#2359	1	1	yes	characteristic
381	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂×C₁₉	#2952	1	1	yes	characteristic
383	C₂×C₁₉	#3324	1	1	yes	characteristic
384	C₂×C₁₉	#3326	1	1	yes	characteristic
385	C₂×C₁₉	#3345	1	1	yes	characteristic
386	C₂×C₁₉	#3350	1	1	yes	characteristic
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×M₁₆	—	2	2	no	—
393	C₂×M₁₆	—	2	2	no	—
394	C₂×M₁₆	—	4	1	no	—
395	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
399	#121	—	2	2	no	—
400	#121	C₂×C₄×C₁₉	1	4	yes	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	4	1	no	—
403	C₄×D₄	—	4	4	no	—
404	#117	—	2	2	no	—
405	#117	C₂×C₄×C₁₉	1	4	yes	complemented
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	4	1	no	—
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#107	C₂×C₄×C₁₉	1	4	yes	complemented
434	#106	—	2	2	no	—
435	#106	—	4	1	no	—
436	#106	C₂×C₄×C₁₉	1	4	yes	complemented
437	#102	—	2	2	no	—
438	#102	—	4	1	no	—
439	#102	C₂×C₄×C₁₉	1	4	yes	complemented
440	#102	C₂×C₄×C₁₉	1	4	yes	complemented
441	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	complemented
442	#97	—	4	1	no	—
443	C₄×C₈	—	2	2	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	D₄×C₁₉	1	1	yes	characteristic
452	#95	D₄×C₁₉	1	1	yes	characteristic
453	C₁₉	#22944	1	1	yes	characteristic, direct product factor, Sylow
454	C₂⁴	—	2	1	no	—
455	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	8	1	no	—
481	C₂²×C₄	—	8	1	no	—
482	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	#41×C₁₉	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
490	M₁₆	—	4	4	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
501	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
502	C₂×C₈	#41×C₁₉	1	2	yes	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
518	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
519	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
520	C₄⋊C₄	#41×C₁₉	1	2	yes	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	2	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	8	1	no	—
528	C₂²⋊C₄	—	8	1	no	—
529	C₄²	—	2	4	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	4	2	no	—
535	C₄²	—	8	1	no	—
536	C₄²	—	8	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	C₄×D₄×C₁₉	1	2	yes	—
551	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
552	D₄	—	2	2	no	—
553	D₄	—	2	2	no	—
554	D₄	—	4	8	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	8	4	no	—
596	C₂×C₄	—	8	4	no	—
597	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
598	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
599	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
600	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
601	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
602	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
603	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
605	C₈	—	2	2	no	—
606	C₈	—	2	2	no	—
607	C₈	—	2	2	no	—
608	C₈	—	4	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
624	C₂²	C₁₉×#546	1	1	yes	characteristic
625	C₂²	C₁₉×#547	1	1	yes	characteristic
626	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
627	C₂²	C₁₉×#575	1	1	yes	characteristic
628	C₂²	C₁₉×#577	1	1	yes	characteristic
629	C₂²	C₁₉×#577	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
643	C₄	C₁₉×#520	1	1	yes	characteristic
644	C₄	C₁₉×#551	1	1	yes	characteristic
645	C₄	C₁₉×#552	1	1	yes	characteristic
646	C₂	—	4	2	no	—
647	C₂	—	8	2	no	—
648	C₂	C₁₉×#2359	1	1	yes	characteristic
649	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
650	C₂	C₁₉×#2952	1	1	yes	characteristic
651	C₂	C₁₉×#3324	1	1	yes	characteristic
652	C₂	C₁₉×#3326	1	1	yes	characteristic
653	C₂	C₁₉×#3345	1	1	yes	characteristic
654	C₂	C₁₉×#3350	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	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2347	C₂	semidirect
4. C₁₉×#1943	C₂	semidirect
5. C₁₉×#1934	C₂	semidirect
6. C₁₉×#1926	C₂	semidirect
7. C₁₉×#1920	C₂	semidirect
8. C₁₉×#1918	C₂	semidirect
10. C₁₉×#1864	C₂	semidirect
11. C₁₉×#1853	C₂	semidirect
12. C₄×C₁₉×#106	C₂	semidirect
13. C₁₉×#1762	C₂	semidirect
14. C₁₉×#1753	C₂	semidirect
15. C₁₉×#1736	C₂	semidirect
22. C₁₉×#482	C₄	semidirect
78. C₁₉×#117	C₂×C₄	semidirect
106. C₁₉×#107	C₂×C₄	semidirect
109. C₁₉×#106	C₂×C₄	semidirect
112. C₁₉×#102	C₂×C₄	semidirect
113. C₁₉×#102	C₂×C₄	semidirect
114. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
209. #22944	C₁₉	direct (N × H)
284. #2347	C₂×C₁₉	semidirect
285. #1943	C₂×C₁₉	semidirect
286. #1934	C₂×C₁₉	semidirect
287. #1926	C₂×C₁₉	semidirect
288. #1920	C₂×C₁₉	semidirect
289. #1918	C₂×C₁₉	semidirect
291. #1864	C₂×C₁₉	semidirect
292. #1853	C₂×C₁₉	semidirect
293. C₄×#106	C₂×C₁₉	semidirect
294. #1762	C₂×C₁₉	semidirect
295. #1753	C₂×C₁₉	semidirect
296. #1736	C₂×C₁₉	semidirect
340. #482	C₄×C₁₉	semidirect
405. #117	C₂×C₄×C₁₉	semidirect
433. #107	C₂×C₄×C₁₉	semidirect
436. #106	C₂×C₄×C₁₉	semidirect
439. #102	C₂×C₄×C₁₉	semidirect
440. #102	C₂×C₄×C₁₉	semidirect
441. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
453. C₁₉	#22944	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×#482	2
C₁₉×#2361	2
C₁₉×#2347	2
C₁₉×#1943	2
C₁₉×#1934	2
C₁₉×#1926	2
C₁₉×#1920	2
C₁₉×#1918	2
C₁₉×#1895	2
C₁₉×#1864	2
C₁₉×#1853	2
C₄×C₁₉×#106	2
C₁₉×#1762	2
C₁₉×#1753	2
C₁₉×#1736	2
#22944	19

Subgroups — C19×#22944 #18028903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22944 #18028903