Subgroups — C₁₉×#26214 #18032173

Order 4864.

890 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2414	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1823	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×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₉×#394	—	2	1	no	—
34	C₁₉×#392	—	2	1	no	—
35	C₁₉×#390	—	2	1	no	—
36	C₁₉×#390	C₂²	1	1	yes	characteristic
37	C₁₉×#389	—	2	1	no	—
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#388	—	2	1	no	—
40	C₁₉×#385	—	2	1	no	—
41	C₁₉×#385	—	2	1	no	—
42	C₁₉×#384	C₂²	1	1	yes	characteristic
43	C₁₉×#380	C₂²	1	1	yes	characteristic
44	C₁₉×#380	C₂²	1	1	yes	characteristic
45	C₁₉×#380	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#340	C₂²	1	1	yes	characteristic
48	C₁₉×#340	C₂²	1	1	yes	characteristic
49	C₁₉×#340	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×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	—	4	1	no	—
69	C₂×M₁₆×C₁₉	—	4	1	no	—
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	4	1	no	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	4	4	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	—	4	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	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	—	4	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	—	2	1	no	—
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#107	—	2	2	no	—
114	C₁₉×#106	—	4	1	no	—
115	C₁₉×#102	—	2	2	no	—
116	C₁₉×#102	—	4	1	no	—
117	C₁₉×#102	—	4	1	no	—
118	C₁₉×#102	—	4	1	no	—
119	C₁₉×C₂²⋊C₈	—	2	2	no	—
120	C₁₉×C₂²⋊C₈	—	4	1	no	—
121	C₁₉×C₂²⋊C₈	—	4	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	C₁₉×#95	—	2	1	no	—
127	C₂⁴×C₁₉	—	2	1	no	—
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
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	—	2	1	no	—
139	C₂×D₄×C₁₉	—	4	2	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	8	1	no	—
143	C₂×D₄×C₁₉	—	8	1	no	—
144	C₂×D₄×C₁₉	—	8	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	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	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	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	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	#41	1	2	yes	—
173	C₂²×C₄×C₁₉	#41	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
175	M₁₆×C₁₉	—	4	4	no	—
176	C₂×C₈×C₁₉	—	2	1	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	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	1	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	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	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	C₄⋊C₄×C₁₉	#41	1	2	yes	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	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	—	4	2	no	—
215	C₂²⋊C₄×C₁₉	—	4	2	no	—
216	C₂²⋊C₄×C₁₉	—	8	1	no	—
217	C₂²⋊C₄×C₁₉	—	8	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	4	2	no	—
221	C₄²×C₁₉	—	4	2	no	—
222	#26214	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	#123	1	2	yes	—
243	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
244	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	D₄×C₁₉	—	2	8	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	—	8	4	no	—
251	D₄×C₁₉	—	8	4	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	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	2	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	8	4	no	—
292	C₂×C₄×C₁₉	—	8	4	no	—
293	C₂×C₄×C₁₉	#123	1	2	yes	—
294	C₂×C₄×C₁₉	#137	1	2	yes	—
295	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
301	C₈×C₁₉	—	4	1	no	—
302	C₈×C₁₉	—	4	1	no	—
303	C₈×C₁₉	—	4	1	no	—
304	C₈×C₁₉	—	4	1	no	—
305	#2414	C₂×C₁₉	1	1	yes	characteristic
306	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#2100	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#2077	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1921	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1895	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1870	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1854	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
320	C₂²×C₁₉	—	2	2	no	—
321	C₂²×C₁₉	—	2	2	no	—
322	C₂²×C₁₉	—	2	2	no	—
323	C₂²×C₁₉	—	2	2	no	—
324	C₂²×C₁₉	—	2	2	no	—
325	C₂²×C₁₉	—	2	2	no	—
326	C₂²×C₁₉	—	4	1	no	—
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	1	no	—
333	C₂²×C₁₉	—	4	1	no	—
334	C₂²×C₁₉	—	8	1	no	—
335	C₂²×C₁₉	—	8	1	no	—
336	C₂²×C₁₉	—	8	1	no	—
337	C₂²×C₁₉	—	8	1	no	—
338	C₂²×C₁₉	—	8	1	no	—
339	C₂²×C₁₉	—	8	1	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
342	C₂²×C₁₉	#546	1	1	yes	characteristic
343	C₂²×C₁₉	#546	1	1	yes	characteristic
344	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
346	C₂²×C₁₉	#576	1	1	yes	characteristic
347	C₂²×C₁₉	#577	1	1	yes	characteristic
348	C₄×C₁₉	—	2	2	no	—
349	C₄×C₁₉	—	2	2	no	—
350	C₄×C₁₉	—	4	1	no	—
351	C₄×C₁₉	—	4	1	no	—
352	C₄×C₁₉	—	4	2	no	—
353	C₄×C₁₉	—	4	2	no	—
354	C₄×C₁₉	—	8	1	no	—
355	C₄×C₁₉	—	8	1	no	—
356	C₄×C₁₉	—	8	1	no	—
357	C₄×C₁₉	—	8	1	no	—
358	C₄×C₁₉	—	8	1	no	—
359	C₄×C₁₉	#529	1	1	yes	characteristic
360	C₄×C₁₉	#538	1	1	yes	characteristic
361	C₄×C₁₉	#553	1	1	yes	characteristic
362	C₄×C₁₉	#553	1	1	yes	characteristic
363	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₄×D₄	—	2	1	no	—
367	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
370	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
380	#394	—	2	1	no	—
381	#392	—	2	1	no	—
382	#390	—	2	1	no	—
383	#390	C₂²×C₁₉	1	1	yes	characteristic
384	#389	—	2	1	no	—
385	#389	C₂²×C₁₉	1	1	yes	characteristic
386	#388	—	2	1	no	—
387	#385	—	2	1	no	—
388	#385	—	2	1	no	—
389	#384	C₂²×C₁₉	1	1	yes	characteristic
390	#380	C₂²×C₁₉	1	1	yes	characteristic
391	#380	C₂²×C₁₉	1	1	yes	characteristic
392	#380	C₂²×C₁₉	1	1	yes	characteristic
393	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
394	#340	C₂²×C₁₉	1	1	yes	characteristic
395	#340	C₂²×C₁₉	1	1	yes	characteristic
396	#340	C₂²×C₁₉	1	1	yes	characteristic
397	#340	C₂²×C₁₉	1	1	yes	characteristic
398	#340	C₂²×C₁₉	1	1	yes	characteristic
399	#340	C₂²×C₁₉	1	1	yes	characteristic
400	#340	C₂²×C₁₉	1	1	yes	characteristic
401	#340	C₂²×C₁₉	1	1	yes	characteristic
402	#340	C₂²×C₁₉	1	1	yes	characteristic
403	#340	C₂²×C₁₉	1	1	yes	characteristic
404	#336	C₂²×C₁₉	1	1	yes	characteristic
405	#336	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×C₁₉	—	4	2	no	—
407	C₂×C₁₉	—	4	2	no	—
408	C₂×C₁₉	—	16	1	no	—
409	C₂×C₁₉	#2444	1	1	yes	characteristic
410	C₂×C₁₉	#3092	1	1	yes	characteristic
411	C₂×C₁₉	#3096	1	1	yes	characteristic
412	C₂×C₁₉	#3306	1	1	yes	characteristic
413	C₂×C₁₉	#3318	1	1	yes	characteristic
414	C₂×C₁₉	#3329	1	1	yes	characteristic
415	C₂×C₁₉	#3333	1	1	yes	characteristic
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
420	C₂³×C₄	—	2	1	no	—
421	C₂³×C₄	—	2	1	no	—
422	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
424	C₂×M₁₆	—	2	2	no	—
425	C₂×M₁₆	—	4	1	no	—
426	C₂×M₁₆	—	4	1	no	—
427	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
431	#121	—	2	2	no	—
432	#121	—	2	2	no	—
433	#121	—	2	2	no	—
434	#121	—	4	1	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	4	4	no	—
438	#117	—	2	2	no	—
439	#117	—	4	1	no	—
440	C₂×C₄⋊C₄	—	2	2	no	—
441	C₂×C₄⋊C₄	—	2	2	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	4	1	no	—
448	C₂×C₄⋊C₄	—	4	1	no	—
449	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
470	#107	—	2	2	no	—
471	#106	—	4	1	no	—
472	#102	—	2	2	no	—
473	#102	—	4	1	no	—
474	#102	—	4	1	no	—
475	#102	—	4	1	no	—
476	C₂²⋊C₈	—	2	2	no	—
477	C₂²⋊C₈	—	4	1	no	—
478	C₂²⋊C₈	—	4	1	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	C₁₉	#26214	1	1	yes	characteristic, direct product factor, Sylow
485	C₂⁴	—	2	1	no	—
486	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	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	—	2	1	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂×D₄	—	4	2	no	—
499	C₂×D₄	—	4	2	no	—
500	C₂×D₄	—	8	1	no	—
501	C₂×D₄	—	8	1	no	—
502	C₂×D₄	—	8	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	8	1	no	—
525	C₂²×C₄	—	8	1	no	—
526	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	#41×C₁₉	1	2	yes	—
531	C₂²×C₄	#41×C₁₉	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
533	M₁₆	—	4	4	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	—	4	2	no	—
561	C₄⋊C₄	—	4	2	no	—
562	C₄⋊C₄	—	8	1	no	—
563	C₄⋊C₄	—	8	1	no	—
564	C₄⋊C₄	#41×C₁₉	1	2	yes	—
565	C₄⋊C₄	#41×C₁₉	1	2	yes	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	8	1	no	—
575	C₂²⋊C₄	—	8	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	4	2	no	—
579	C₄²	—	4	2	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	C₁₉×#123	1	2	yes	—
600	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
601	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
602	D₄	—	2	8	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	8	4	no	—
608	D₄	—	8	4	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	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	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	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	8	4	no	—
649	C₂×C₄	—	8	4	no	—
650	C₂×C₄	C₁₉×#123	1	2	yes	—
651	C₂×C₄	C₁₉×#137	1	2	yes	—
652	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
653	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
654	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
655	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
656	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
684	C₂²	C₁₉×#546	1	1	yes	characteristic
685	C₂²	C₁₉×#546	1	1	yes	characteristic
686	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
687	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
688	C₂²	C₁₉×#576	1	1	yes	characteristic
689	C₂²	C₁₉×#577	1	1	yes	characteristic
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	8	1	no	—
697	C₄	—	8	1	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	C₁₉×#529	1	1	yes	characteristic
702	C₄	C₁₉×#538	1	1	yes	characteristic
703	C₄	C₁₉×#553	1	1	yes	characteristic
704	C₄	C₁₉×#553	1	1	yes	characteristic
705	C₂	—	4	2	no	—
706	C₂	—	4	2	no	—
707	C₂	—	16	1	no	—
708	C₂	C₁₉×#2444	1	1	yes	characteristic
709	C₂	C₁₉×#3092	1	1	yes	characteristic
710	C₂	C₁₉×#3096	1	1	yes	characteristic
711	C₂	C₁₉×#3306	1	1	yes	characteristic
712	C₂	C₁₉×#3318	1	1	yes	characteristic
713	C₂	C₁₉×#3329	1	1	yes	characteristic
714	C₂	C₁₉×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2414	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
3. C₁₉×#2100	C₂	semidirect
4. C₁₉×#2077	C₂	semidirect
5. C₁₉×#2071	C₂	semidirect
6. C₁₉×#2033	C₂	semidirect
7. C₁₉×#1926	C₂	semidirect
8. C₁₉×#1921	C₂	semidirect
9. C₁₉×#1895	C₂	semidirect
10. C₁₉×#1874	C₂	semidirect
11. C₁₉×#1874	C₂	semidirect
12. C₁₉×#1870	C₂	semidirect
13. C₁₉×#1854	C₂	semidirect
14. C₁₉×#1823	C₂	semidirect
15. C₁₉×#1736	C₂	semidirect
222. #26214	C₁₉	direct (N × H)
306. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
307. #2100	C₂×C₁₉	semidirect
308. #2077	C₂×C₁₉	semidirect
309. #2071	C₂×C₁₉	semidirect
310. #2033	C₂×C₁₉	semidirect
311. #1926	C₂×C₁₉	semidirect
312. #1921	C₂×C₁₉	semidirect
313. #1895	C₂×C₁₉	semidirect
314. #1874	C₂×C₁₉	semidirect
315. #1874	C₂×C₁₉	semidirect
316. #1870	C₂×C₁₉	semidirect
317. #1854	C₂×C₁₉	semidirect
318. #1823	C₂×C₁₉	semidirect
319. #1736	C₂×C₁₉	semidirect
484. C₁₉	#26214	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2414	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2100	2
C₁₉×#2077	2
C₁₉×#2071	2
C₁₉×#2033	2
C₁₉×#1926	2
C₁₉×#1921	2
C₁₉×#1895	2
C₁₉×#1874	2
C₁₉×#1870	2
C₁₉×#1854	2
C₁₉×#1823	2
C₁₉×#1736	2
#26214	19

Subgroups — C19×#26214 #18032173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26214 #18032173