Subgroups — C₁₉×#26188 #18032147

Order 4864.

924 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#463	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2448	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2087	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₁₉×#463	—	2	4	no	—
25	C₁₉×#440	—	2	4	no	—
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
38	C₁₉×#399	—	2	1	no	—
39	C₁₉×#397	—	2	1	no	—
40	C₁₉×#391	C₂²	1	1	yes	characteristic
41	C₁₉×#390	C₂²	1	1	yes	characteristic
42	C₁₉×#390	C₂²	1	1	yes	characteristic
43	C₁₉×#389	C₂²	1	1	yes	characteristic
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#389	C₂²	1	1	yes	characteristic
46	C₁₉×#388	—	2	1	no	—
47	C₁₉×#388	—	2	1	no	—
48	C₁₉×#385	—	2	1	no	—
49	C₁₉×#385	—	2	1	no	—
50	C₁₉×#384	C₂²	1	1	yes	characteristic
51	C₁₉×#380	—	2	1	no	—
52	C₄×C₄⋊C₄×C₁₉	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×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂×SD₁₆×C₁₉	—	2	2	no	—
68	C₂×SD₁₆×C₁₉	—	2	2	no	—
69	C₂×SD₁₆×C₁₉	D₄	1	4	yes	—
70	C₂×D₈×C₁₉	—	2	2	no	—
71	C₂×D₈×C₁₉	—	2	2	no	—
72	C₂×D₈×C₁₉	—	2	2	no	—
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	4	1	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	4	1	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	4	1	no	—
86	C₄×D₄×C₁₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
94	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	2	no	—
115	C₁₉×#107	—	4	1	no	—
116	C₁₉×C₄⋊C₈	—	2	2	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	4	1	no	—
125	C₁₉×#97	—	2	2	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	D₄	1	1	yes	characteristic
132	C₁₉×#95	D₄	1	1	yes	characteristic
133	C₂⁴×C₁₉	—	2	1	no	—
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₁₉	#41	1	2	yes	—
152	C₂×D₄×C₁₉	#41	1	2	yes	—
153	C₂²×C₄×C₁₉	—	2	4	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	4	2	no	—
166	C₂²×C₄×C₁₉	—	8	1	no	—
167	C₂²×C₄×C₁₉	—	8	1	no	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
175	SD₁₆×C₁₉	—	2	8	no	—
176	D₈×C₁₉	—	4	4	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	—	4	2	no	—
201	C₄⋊C₄×C₁₉	—	4	2	no	—
202	C₄⋊C₄×C₁₉	—	4	2	no	—
203	C₄⋊C₄×C₁₉	—	4	2	no	—
204	C₄⋊C₄×C₁₉	—	8	1	no	—
205	C₄⋊C₄×C₁₉	—	8	1	no	—
206	C₄⋊C₄×C₁₉	#41	1	2	yes	—
207	C₂²⋊C₄×C₁₉	—	2	4	no	—
208	C₂²⋊C₄×C₁₉	—	4	2	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₂²⋊C₄×C₁₉	—	4	2	no	—
213	C₂²⋊C₄×C₁₉	—	4	2	no	—
214	C₂²⋊C₄×C₁₉	—	8	1	no	—
215	C₂²⋊C₄×C₁₉	—	8	1	no	—
216	C₄²×C₁₉	—	2	1	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	—	4	2	no	—
223	#26188	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₁₉	—	2	2	no	—
225	C₂³×C₁₉	—	2	2	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₉	—	2	2	no	—
240	Q₈×C₁₉	—	2	2	no	—
241	Q₈×C₁₉	—	4	1	no	—
242	Q₈×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	2	2	no	—
244	D₄×C₁₉	—	2	2	no	—
245	D₄×C₁₉	—	2	2	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	#123	1	4	yes	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	4	8	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	8	4	no	—
288	C₂×C₄×C₁₉	—	8	4	no	—
289	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
290	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
296	C₈×C₁₉	—	2	2	no	—
297	C₈×C₁₉	—	4	1	no	—
298	C₈×C₁₉	—	4	1	no	—
299	C₈×C₁₉	—	4	1	no	—
300	C₂×#463	C₂×C₁₉	1	1	yes	characteristic
301	C₂×#440	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#2448	C₂×C₁₉	1	1	yes	characteristic, complemented
303	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#2093	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#2087	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#2072	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1936	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1879	C₂×C₁₉	1	1	yes	characteristic
311	#1879	C₂×C₁₉	1	1	yes	characteristic
312	#1877	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1862	C₂×C₁₉	1	1	yes	characteristic, complemented
315	C₂²×C₁₉	—	2	4	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	—	4	2	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	#525	1	1	yes	characteristic
330	C₂²×C₁₉	D₄²	1	1	yes	characteristic
331	C₂²×C₁₉	#548	1	1	yes	characteristic
332	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
333	C₂²×C₁₉	#575	1	1	yes	characteristic
334	C₂²×C₁₉	#576	1	1	yes	characteristic
335	C₂²×C₁₉	#578	1	1	yes	characteristic
336	C₄×C₁₉	—	2	2	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	4	2	no	—
340	C₄×C₁₉	—	4	1	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	1	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	8	1	no	—
345	C₄×C₁₉	—	8	1	no	—
346	C₄×C₁₉	—	8	1	no	—
347	C₄×C₁₉	—	8	1	no	—
348	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
349	C₄×C₁₉	#539	1	1	yes	characteristic
350	C₄×C₁₉	#547	1	1	yes	characteristic
351	C₄×C₁₉	#553	1	1	yes	characteristic
352	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
353	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
359	C₂²×C₄⋊C₄	—	2	1	no	—
360	#463	—	2	4	no	—
361	#440	—	2	4	no	—
362	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
374	#399	—	2	1	no	—
375	#397	—	2	1	no	—
376	#391	C₂²×C₁₉	1	1	yes	characteristic
377	#390	C₂²×C₁₉	1	1	yes	characteristic
378	#390	C₂²×C₁₉	1	1	yes	characteristic
379	#389	C₂²×C₁₉	1	1	yes	characteristic
380	#389	C₂²×C₁₉	1	1	yes	characteristic
381	#389	C₂²×C₁₉	1	1	yes	characteristic
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#385	—	2	1	no	—
385	#385	—	2	1	no	—
386	#384	C₂²×C₁₉	1	1	yes	characteristic
387	#380	—	2	1	no	—
388	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
389	#340	C₂²×C₁₉	1	1	yes	characteristic
390	#340	C₂²×C₁₉	1	1	yes	characteristic
391	#340	C₂²×C₁₉	1	1	yes	characteristic
392	#340	C₂²×C₁₉	1	1	yes	characteristic
393	#336	C₂²×C₁₉	1	1	yes	characteristic
394	#336	C₂²×C₁₉	1	1	yes	characteristic
395	#336	C₂²×C₁₉	1	1	yes	characteristic
396	#336	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×C₁₉	—	4	4	no	—
398	C₂×C₁₉	—	16	1	no	—
399	C₂×C₁₉	#2443	1	1	yes	characteristic
400	C₂×C₁₉	#3114	1	1	yes	characteristic
401	C₂×C₁₉	#3124	1	1	yes	characteristic
402	C₂×C₁₉	#3269	1	1	yes	characteristic
403	C₂×C₁₉	#3274	1	1	yes	characteristic
404	C₂×C₁₉	#3367	1	1	yes	characteristic
405	C₂×C₁₉	#3370	1	1	yes	characteristic
406	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	—	2	1	no	—
412	C₂×SD₁₆	—	2	2	no	—
413	C₂×SD₁₆	—	2	2	no	—
414	C₂×SD₁₆	D₄×C₁₉	1	4	yes	—
415	C₂×D₈	—	2	2	no	—
416	C₂×D₈	—	2	2	no	—
417	C₂×D₈	—	2	2	no	—
418	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	#124	—	2	2	no	—
423	#124	—	4	1	no	—
424	C₄×Q₈	—	2	2	no	—
425	C₄×Q₈	—	4	1	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	4	1	no	—
431	C₄×D₄	—	4	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	4	4	no	—
439	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
459	#107	—	2	2	no	—
460	#107	—	4	1	no	—
461	C₄⋊C₈	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	#102	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	4	1	no	—
470	#97	—	2	2	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	D₄×C₁₉	1	1	yes	characteristic
477	#95	D₄×C₁₉	1	1	yes	characteristic
478	C₁₉	#26188	1	1	yes	characteristic, direct product factor, Sylow
479	C₂⁴	—	2	1	no	—
480	C₂⁴	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
497	C₂×D₄	#41×C₁₉	1	2	yes	—
498	C₂×D₄	#41×C₁₉	1	2	yes	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	8	1	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
521	SD₁₆	—	2	8	no	—
522	D₈	—	4	4	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	4	1	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	8	1	no	—
551	C₄⋊C₄	—	8	1	no	—
552	C₄⋊C₄	#41×C₁₉	1	2	yes	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₂²⋊C₄	—	8	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	4	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	C₁₉×#123	1	4	yes	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	8	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	—	8	4	no	—
634	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
635	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
638	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
639	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
641	C₈	—	2	2	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	C₁₉×#525	1	1	yes	characteristic
660	C₂²	D₄²×C₁₉	1	1	yes	characteristic
661	C₂²	C₁₉×#548	1	1	yes	characteristic
662	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
663	C₂²	C₁₉×#575	1	1	yes	characteristic
664	C₂²	C₁₉×#576	1	1	yes	characteristic
665	C₂²	C₁₉×#578	1	1	yes	characteristic
666	C₄	—	2	2	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
679	C₄	C₁₉×#539	1	1	yes	characteristic
680	C₄	C₁₉×#547	1	1	yes	characteristic
681	C₄	C₁₉×#553	1	1	yes	characteristic
682	C₂	—	4	4	no	—
683	C₂	—	16	1	no	—
684	C₂	C₁₉×#2443	1	1	yes	characteristic
685	C₂	C₁₉×#3114	1	1	yes	characteristic
686	C₂	C₁₉×#3124	1	1	yes	characteristic
687	C₂	C₁₉×#3269	1	1	yes	characteristic
688	C₂	C₁₉×#3274	1	1	yes	characteristic
689	C₂	C₁₉×#3367	1	1	yes	characteristic
690	C₂	C₁₉×#3370	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#440	C₂	semidirect
3. C₁₉×#2448	C₂	semidirect
4. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
5. C₁₉×#2093	C₂	semidirect
6. C₁₉×#2087	C₂	semidirect
7. C₁₉×#2072	C₂	semidirect
8. C₁₉×#2042	C₂	semidirect
9. C₁₉×#1936	C₂	semidirect
10. C₁₉×#1917	C₂	semidirect
13. C₁₉×#1877	C₂	semidirect
14. C₁₉×#1863	C₂	semidirect
15. C₁₉×#1862	C₂	semidirect
223. #26188	C₁₉	direct (N × H)
301. C₂×#440	C₂×C₁₉	semidirect
302. #2448	C₂×C₁₉	semidirect
303. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
304. #2093	C₂×C₁₉	semidirect
305. #2087	C₂×C₁₉	semidirect
306. #2072	C₂×C₁₉	semidirect
307. #2042	C₂×C₁₉	semidirect
308. #1936	C₂×C₁₉	semidirect
309. #1917	C₂×C₁₉	semidirect
312. #1877	C₂×C₁₉	semidirect
313. #1863	C₂×C₁₉	semidirect
314. #1862	C₂×C₁₉	semidirect
478. C₁₉	#26188	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×#463	2
C₂×C₁₉×#440	2
C₁₉×#2448	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2093	2
C₁₉×#2087	2
C₁₉×#2072	2
C₁₉×#2042	2
C₁₉×#1936	2
C₁₉×#1917	2
C₁₉×#1879	2
C₁₉×#1877	2
C₁₉×#1863	2
C₁₉×#1862	2
#26188	19

Subgroups — C19×#26188 #18032147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26188 #18032147